text:
= {10},
  journal = {GEOPHYSICS},
  author = {Thomsen, Leon},
  year = {1986},
  pages = {1954-1966},
  eprint = {http://dx.doi.org/10.1190/1.1442051}
}

@inproceedings{anikiev2014,
  title = {Multiparameter {{Elastic Imaging Improved}} by {{Preconditioning}} with an {{Incomplete Inverse Hessian Approximation}}},
  booktitle = {76th {{EAGE Conference}} and {{Exhibition}} 2014},
  author = {Anikiev, DV and Kashtan, BM and Mulder, WA},
  year = {2014}
}

@article{eaton1994,
  title = {Migration/Inversion for Transversely Isotropic Elastic Media},
  volume = {119},
  issn = {1365-246X},
  doi = {10.1111/j.1365-246X.1994.tb00148.x},
  number = {2},
  journal = {Geophysical Journal International},
  author = {Eaton, David W. S. and Stewart, Robert R.},
  year = {1994},
  keywords = {anisotropy,Born approximation,inverse scattering,inversion},
  pages = {667-683},
  publisher = {{Blackwell Publishing Ltd}}
}

@article{ruger1997,
  title = {P-Wave Reflection Coefficients for Transversely Isotropic Models with Vertical and Horizontal Axis of Symmetry},
  volume = {62},
  number = {3},
  journal = {Geophysics},
  author = {R\"uger, Andreas},
  year = {1997},
  pages = {713-722},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{creager1999large,
  title = {Large-Scale Variations in Inner Core Anisotropy},
  volume = {104},
  number = {B10},
  journal = {Journal of Geophysical Research: Solid Earth},
  author = {Creager, Kenneth C},
  year = {1999},
  pages = {23127-23139},
  publisher = {{Wiley Online Library}}
}

@misc{CarbonateReservoirsSchlumberger,
  title = {Carbonate {{Reservoirs}} | {{Schlumberger}}},
  howpublished = {http://www.slb.com/services/technical\_challenges/carbonates.aspx}
}

@article{dellingerComputingOptimalTransversely2005,
  title = {Computing the Optimal Transversely Isotropic Approximation of a General Elastic Tensor},
  volume = {70},
  issn = {0016-8033},
  doi = {10.1190/1.2073890},
  abstract = {Mathematically, 21 stiffnesses arranged in a 6 \texttimes{} 6 symmetric matrix completely describe the elastic properties of any homogeneous anisotropic medium, regardless of symmetry system and orientation. However, it can be difficult in practice to characterize an anisotropic medium's properties merely from casual inspection of its (often experimentally measured) stiffness matrix. For characterization purposes, it is better to decompose a measured stiffness matrix into a stiffness matrix for a canonically oriented transversely isotropic (TI) medium (whose properties can be readily understood) plus a generally anisotropic perturbation (representing the medium's deviation from perfect symmetry), followed by a rotation (giving the relationship between the medium's natural coordinate system and the measurement coordinate system). To accomplish this decomposition, we must find the rotated symmetric medium that best approximates a given stiffness matrix. An analytical formula exists for calculating the distance between the elastic properties of two anisotropic media. Starting from this formula, I show how to analytically calculate the TI medium with a zz{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}mi{$>$}z{$<$}/mi{$><$}/mrow{$><$}/math{$>$} symmetry axis that is nearest to a given set of 21 stiffness constants. There is no known analytical result if the symmetry axis is not fixed beforehand. I therefore present a simple search algorithm that scans all possible orientations of the nearest TI medium's symmetry axis. The grid is iteratively refined to optimize the solution. The algorithm is simple and robust and works well in practice, but it is not guaranteed to always find the optimal global answer if there are secondary minima that provide almost as good a fit as the optimal one.},
  number = {5},
  journal = {GEOPHYSICS},
  author = {Dellinger, J.},
  month = sep,
  year = {2005},
  pages = {I1-I10},
  file = {/home/kazeiv/Zotero/storage/GI2PND66/Dellinger - 2005 - Computing the optimal transversely isotropic appro.pdf}
}

@article{dupuyQuantitativeSeismicCharacterization2017,
  title = {Quantitative Seismic Characterization of {{CO2}} at the {{Sleipner}} Storage Site, {{North Sea}}},
  volume = {5},
  issn = {2324-8858},
  doi = {10.1190/INT-2017-0013.1},
  abstract = {Reliable quantification of carbon dioxide (CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$}) properties and saturation is crucial in the monitoring of CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} underground storage projects. We have focused on quantitative seismic characterization of CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} at the Sleipner storage pilot site. We evaluate a methodology combining high-resolution seismic waveform tomography, with uncertainty quantification and rock physics inversion. We use full-waveform inversion (FWI) to provide high-resolution estimates of P-wave velocity VPVP{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi mathvariant="normal"{$>$}P{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} and perform an evaluation of the reliability of the derived model based on posterior covariance matrix analysis. To get realistic estimates of CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} saturation, we implement advanced rock physics models taking into account effective fluid phase theory and patchy saturation. We determine through sensitivity tests that the estimation of CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} saturation is possible even when using only the P-wave velocity as input. After a characterization of rock frame properties based on log data prior to the CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} injection at Sleipner, we apply our two-step methodology. The FWI result provides clear indications of the injected CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} plume being observed as low-velocity zones corresponding to thin CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} filled layers. Several tests, varying the rock physics model and CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} properties, are then performed to estimate CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} saturation. The results suggest saturations reaching 30\%\textendash{}35\% in the thin sand layers and up to 75\% when patchy mixing is considered. We have carried out a joint estimation of saturation with distribution type and, even if the inversion is not well-constrained due to limited input data, we conclude that the CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} has an intermediate pattern between uniform and patchy mixing, which leads to saturation levels of approximately 25\%{$\pm$}15\%25\%{$\pm$}15\%{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}mn{$>$}25{$<$}/mn{$><$}mo{$>\%<$}/mo{$><$}mo{$>\pm{}<$}/mo{$><$}mn{$>$}15{$<$}/mn{$><$}mo form="postfix"{$>\%<$}/mo{$><$}/mrow{$><$}/math{$>$}. It is worth noting that the 2D section used in this work is located 533~m east of the injection point. We also conclude that the joint estimation of CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} properties with saturation is not crucial and consequently that knowing the pressure and temperature state of the reservoir does not prevent reliable estimation of CO2CO2{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}CO{$<$}/mi{$><$}mn{$>$}2{$<$}/mn{$><$}/msub{$><$}/mrow{$><$}/math{$>$} saturation.},
  number = {4},
  journal = {Interpretation},
  author = {Dupuy, B. and Romdhane, A. and Eliasson, P. and Querendez, E. and Yan, H. and Torres, V. and Ghaderi, A.},
  month = aug,
  year = {2017},
  pages = {SS23-SS42},
  file = {/home/kazeiv/Zotero/storage/8JDWMNRM/Dupuy et al. - 2017 - Quantitative seismic characterization of CO2 at th.pdf}
}

@misc{QuantitativeSeismicCharacterization,
  title = {Quantitative Seismic Characterization of {{CO}} 2 at the {{Sleipner}} Storage Site, {{North Sea}}},
  abstract = {ResearchGate is a network dedicated to science and research. Connect, collaborate and discover scientific publications, jobs and conferences. All for free.},
  language = {en},
  journal = {ResearchGate},
  howpublished = {https://www.researchgate.net/publication/318862999\_Quantitative\_seismic\_characterization\_of\_CO\_2\_at\_the\_Sleipner\_storage\_site\_North\_Sea}
}

@article{kazei2018,
  title = {Waveform Inversion for Orthorhombic Anisotropy with {{P}}-Waves: Feasibility \& Resolution},
  doi = {10.1093/gji/ggy034},
  journal = {Geophysical Journal International},
  author = {Kazei, Vladimir and Alkhalifah, Tariq},
  year = {2018},
  pages = {ggy034}
}

@article{poupinetObservationHighFrequency2004,
  title = {On the Observation of High Frequency {{PKiKP}} and Its Coda in {{Australia}}},
  volume = {146},
  issn = {0031-9201},
  doi = {10.1016/j.pepi.2004.05.003},
  abstract = {The seismic phase PKiKP, reflected from the inner core, and its coda give information on the short scale heterogeneities at and below the inner core boundary (ICB) of the Earth. We have collected PKiKP recorded at short distances ({$<$}45\textdegree{}) at broadband stations in Australia and at the Warramunga seismic array (WRA). Despite potential complications from a dual-passage through D{${''}$}, PKiKP is frequently observed on single traces in the frequency band 1\textendash{}5Hz. PKiKP usually has a sharp onset, but sometimes its waveforms have multiple pulses separated by times of the order of 1s. At WRA, the coda of PKiKP initially decays very rapidly after the main pulse. Thereafter, its amplitude is nearly constant and more than three times smaller than PKiKP with duration longer than 200s. Our observations differ from those of [Nature 404 (2000) 273\textendash{}275], at rather greater distances, who found that the coda is larger than PKiKP and increases slowly. We suggest that the PKiKP coda is generated near the inner core boundary by complex reverberation effects, rather than scattering through the volume of the inner core.},
  number = {3},
  journal = {Physics of the Earth and Planetary Interiors},
  author = {Poupinet, G and Kennett, B. L. N},
  month = sep,
  year = {2004},
  keywords = {Heterogeneities,Inner core,PKiKP,Seismic phase},
  pages = {497-511},
  file = {/home/kazeiv/Zotero/storage/CFGHXQYA/Poupinet_Kennett_2004_On the observation of high frequency PKiKP and its coda in Australia.pdf;/home/kazeiv/Zotero/storage/S8T8XSJX/S0031920104002225.html}
}

@article{tanakaComplexInnerCore2015,
  title = {Complex Inner Core Boundary from Frequency Characteristics of the Reflection Coefficients of {{PKiKP}} Waves Observed by {{Hi}}-Net},
  volume = {2},
  issn = {2197-4284},
  doi = {10.1186/s40645-015-0064-3},
  abstract = {Frequency-dependent reflection coefficients of P waves at the inner core boundary (ICB) are estimated from the spectral ratios of PKiKP and PcP waves observed by the high-sensitivity seismograph network (Hi-net) in Japan. The corresponding PKiKP reflection locations at the ICB are distributed beneath the western Pacific. At frequencies where noise levels are sufficiently low, spectra of reflection coefficients show four distinct sets of characteristics: a flat spectrum, a spectrum with a significant spectral hole at approximately 1 or 3~Hz, a spectrum with a strong peak at approximately 2 or 3~Hz, and a spectrum containing both a sharp peak and a significant hole. The variety in observed spectra suggests complex lateral variations in ICB properties. To explain the measured differences in frequency characteristics of ICB reflection coefficients, we conduct 2D finite difference simulations of seismic wavefields near the ICB. The models tested in our simulations include a liquid layer and a solid layer above the ICB, as well as sinusoidal and spike-shaped ICB topography with varying heights and scale lengths. We find that the existence of a layer above the ICB can be excluded as a possible explanation for the observed spectra. Furthermore, we find that an ICB topographic model with wavelengths and heights of several kilometers is too extreme to explain our measurements. However, restricting the ICB topography to wavelengths and heights of 1.0\textendash{}1.5~km can explain the observed frequency-related phenomena. The existence of laterally varying topography may be a sign of lateral variations in inner core solidification.},
  journal = {Progress in Earth and Planetary Science},
  author = {Tanaka, Satoru and Tkal{\v c}i\'c, Hrvoje},
  month = nov,
  year = {2015},
  keywords = {PKiKP,Finite difference modeling,Inner core boundary,Topography},
  pages = {34},
  file = {/home/kazeiv/Zotero/storage/ZMLVCBP8/Tanaka_Tkalčić_2015_Complex inner core boundary from frequency characteristics of the reflection.pdf;/home/kazeiv/Zotero/storage/DZTU6DAW/s40645-015-0064-3.html}
}

@article{pengInnercoreFinescaleStructure2008,
  title = {Inner-Core Fine-Scale Structure from Scattered Waves Recorded by {{LASA}}},
  volume = {113},
  issn = {2156-2202},
  doi = {10.1029/2007JB005412},
  abstract = {Recent observations of inner-core scattering (ICS) waves provide evidence that the outermost 300 km of the inner-core has strong heterogeneities with a length scale of a few kilometers. These waves follow a path similar to that of the inner-core\textendash{}reflected waves PKiKP and were originally observed in data from 16 events in the distance range 58\textdegree{} to 73\textdegree{} recorded by the Large Aperture Seismic Array (LASA). Here we present additional observations of the ICS waves from a total of 78 events recorded by LASA at distances from 18\textdegree{} to 98\textdegree. We use a modified version of the Generic Array Processing software package to identify ICS waves on the basis of travel time, back azimuth, ray parameter, amplitude, and coherence. There are 44 events that produce clear ICS waves. We then perform forward modeling of the observed ICS waves using a Monte Carlo seismic phonon method that allows for multiple scattering along the raypath. Most of the ICS waves appear without a visible PKiKP phase, initially grow in time, and have a spindle-shaped envelope. The duration, risetime, and decay rates of the observed ICS waves can be best explained by small-scale volumetric heterogeneities in the outermost few hundred kilometers of the inner core. The average Qc value for the 44 events is {$\sim$}600. Most clear ICS waves are found for raypaths sampling the Pacific Ocean and Asia, and relatively few observations are from the Atlantic Ocean, roughly consistent with the recently observed hemispheric difference in the inner-core structure.},
  language = {en},
  number = {B9},
  journal = {Journal of Geophysical Research: Solid Earth},
  author = {Peng, Zhigang and Koper, Keith D. and Vidale, John E. and Leyton, Felipe and Shearer, Peter},
  month = sep,
  year = {2008},
  keywords = {7207 Core,8124 Earth's interior: composition and state,PKiKP,8115 Core processes,coda waves,inner core},
  pages = {B09312},
  file = {/home/kazeiv/Zotero/storage/8ULZB6EY/Peng et al_2008_Inner-core fine-scale structure from scattered waves recorded by LASA.pdf;/home/kazeiv/Zotero/storage/4ZY78K7C/abstract.html}
}

@article{bolt1970,
  title = {{{PdP}} and {{PKiKP Waves}} and {{Diffracted PcP Waves}}},
  volume = {20},
  issn = {1365-246X},
  doi = {10.1111/j.1365-246X.1970.tb06080.x},
  abstract = {Travel times, listed in the I.S.S., of longitudinal waves at distances of 100\textdegree{} {$<$} {$\Delta$} {$<$} 115\textdegree{} from 16 earthquakes with depths near 100km give rather precise information on properties of the Earth (a) in the upper third of the mantle, (b) at the inner core boundary, and (c) at the bottom of the mantle. The sources are relocated using the 1968 tables of Herrin et al. Precursors to PP, called PdP, are widely reported up to about 85s before PP; few are reported at earlier times. These independent observations provide further evidence that, above a depth of at least 400 km, the upper mantle contains structural discontinuities (perhaps due to phase changes) on a global scale. PKiKP waves (reflections from the inner core) are traceable in this data sample back to 106\textdegree. The result is consistent with a sharp inner core boundary at 1220km radius. Observed PKP travel times near 113\textdegree{} are closely consistent with PKIKP times derived by Bolt for use with the 1968 P tables of Herrin et al.; the observed times for {$\Delta$} {$<$} 113\textdegree{} are about 0.5 s later than predicted. Travel times (for 100 km focal depth and 102\textdegree{} {$<$} {$\Delta$} {$<$} 110\textdegree{}) of the PcP wave which is diffracted into the shadow of the core fit the curve t= (14m 02.8{$\pm$};0.14s)+(4.60{$\pm$}0.05 s/deg)({$\Delta$}\textendash{}106\textdegree.45). This result leads to a radius for the Earth's core of 3479{$\pm$}2km; there is an indication that the P velocity may decrease by a few per cent at the base of the mantle.},
  language = {en},
  number = {4},
  journal = {Geophysical Journal of the Royal Astronomical Society},
  author = {Bolt, Bruce A.},
  month = sep,
  year = {1970},
  pages = {367-382},
  file = {/home/kazeiv/Zotero/storage/VM2MPLPR/Bolt_1970_PdP and PKiKP Waves and Diffracted PcP Waves.pdf;/home/kazeiv/Zotero/storage/NNECQST3/abstract.html}
}

@article{zhou2015,
  title = {Full Waveform Inversion of Diving \& Reflected Waves for Velocity Model Building with Impedance Inversion Based on Scale Separation},
  volume = {202},
  doi = {10.1093/gji/ggv228},
  abstract = {Full waveform inversion (FWI) aims to reconstruct high-resolution subsurface models from the full wavefield, which includes diving waves, post-critical reflections and short-spread reflections. Most successful applications of FWI are driven by the information carried by diving waves and post-critical reflections to build the long-to-intermediate wavelengths of the velocity structure. Alternative approaches, referred to as reflection waveform inversion (RWI), have been recently revisited to retrieve these long-to-intermediate wavelengths from short-spread reflections by using some prior knowledge of the reflectivity and a scale separation between the velocity macromodel and the reflectivity. This study presents a unified formalism of FWI, named as Joint FWI, whose aim is to efficiently combine the diving and reflected waves for velocity model building. The two key ingredients of Joint FWI are, on the data side, the explicit separation between the short-spread reflections and the wide-angle arrivals and, on the model side, the scale separation between the velocity macromodel and the short-scale impedance model. The velocity model and the impedance model are updated in an alternate way by Joint FWI and waveform inversion of the reflection data (least-squares migration), respectively. Starting from a crude velocity model, Joint FWI is applied to the streamer seismic data computed in the synthetic Valhall model. While the conventional FWI is stuck into a local minimum due to cycle skipping, Joint FWI succeeds in building a reliable velocity macromodel. Compared with RWI, the use of diving waves in Joint FWI improves the reconstruction of shallow velocities, which translates into an improved imaging at deeper depths. The smooth velocity model built by Joint FWI can be subsequently used as a reliable initial model for conventional FWI to increase the high-wavenumber content of the velocity model.},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Zhou, Wei and Brossier, Romain and Operto, Stephane and Virieux, Jean},
  year = {2015},
  pages = {1535-1554},
  eprint = {http://gji.oxfordjournals.org/content/202/3/1535.full.pdf+html}
}

@book{cerveny2001seismic,
  title = {Seismic Ray Theory},
  publisher = {{Cambridge}},
  author = {\v{}Cerven\'y, V.},
  year = {2001}
}

@article{bunks1995,
  title = {Multiscale Seismic Waveform Inversion},
  volume = {60},
  doi = {10.1190/1.1443880},
  abstract = {Iterative inversion methods have been unsuccessful at inverting seismic data obtained from complicated earth models (e.g. the Marmousi model), the primary difficulty being the presence of numerous local minima in the objective function. The presence of local minima at all scales in the seismic inversion problem prevent iterative methods of inversion from attaining a reasonable degree of convergence to the neighborhood of the global minimum. The multigrid method is a technique that improves the performance of iterative inversion by decomposing the problem by scale. At long scales there are fewer local minima and those that remain are further apart from each other. Thus, at long scales iterative methods can get closer to the neighborhood of the global minimum. We apply the multigrid method to a subsampled, low-frequency version of the Marmousi data set. Although issues of source estimation, source bandwidth, and noise are not treated, results show that iterative inversion methods perform much better when employed with a decomposition by scale. Furthermore, the method greatly reduces the computational burden of the inversion that will be of importance for 3-D extensions to the method.},
  number = {5},
  journal = {Geophysics},
  author = {Bunks, Carey and Saleck, Fatimetou M. and Zaleski, S. and Chavent, G.},
  year = {1995},
  pages = {1457-1473},
  eprint = {http://geophysics.geoscienceworld.org/content/60/5/1457.full.pdf+html}
}

@article{alkhalifah2015full,
  title = {Full Model Wavenumber Inversion},
  volume = {2015},
  number = {1},
  journal = {ASEG Extended Abstracts},
  author = {Alkhalifah, Tariq A},
  year = {2015},
  pages = {1-1},
  publisher = {{CSIRO}}
}

@article{ref:kuvshinov,
  title = {The Exact Solution of the Time-Harmonic Wave Equation for a Linear Velocity Profile},
  volume = {167},
  doi = {10.1111/j.1365-246X.2006.03194.x},
  number = {2},
  journal = {Geophysical Journal International},
  author = {Kuvshinov, B. N. and Mulder, W. A.},
  year = {2006},
  pages = {659-662}
}

@article{ref:pratt99,
  title = {Two-Dimensional Velocity Models from Wide-Angle Seismic Data by Waveform Inversion},
  volume = {124},
  doi = {10.1111/j.1365-246X.1996.tb07023.x},
  number = {2},
  journal = {Geophysical Journal International},
  author = {Pratt, R[] G[] and Song, Z.-M and Williamson, P[] R[] and Warner, M[] R[]},
  year = {1996},
  pages = {323-340}
}

@article{pekeris:295,
  title = {Theory of {{Propagation}} of {{Sound}} in a {{Half}}-{{Space}} of {{Variable Sound Velocity}} under {{Conditions}} of {{Formation}} of a {{Shadow Zone}}},
  volume = {18},
  doi = {10.1121/1.1916366},
  number = {2},
  journal = {The Journal of the Acoustical Society of America},
  author = {Pekeris, C. L.},
  year = {1946},
  pages = {295-315},
  publisher = {{ASA}}
}

@book{ref:troyan,
  title = {Analysis and Processing of Data},
  publisher = {{St. Petersburg State University Press}},
  author = {Troyan, V[] N[] and Kiselev, Yuri V[]},
  year = {2010},
  note = {(in Russian)}
}

@techreport{ref:babich,
  title = {About the {{Smirnov}}-{{Sobolev}} Method for the Explicit Solution of the Problems of Mathematical Physics},
  author = {Babich, V[] M[] and Kochuguev, S[] K[]},
  howpublished = {Steklov Mathematical Institute, St. Petersburg},
  note = {(in Russian)}
}

@book{ref:chervenyheadwaves,
  title = {Theory of Seismic Head Waves},
  publisher = {{University of Toronto Press}},
  author = {\v{}Cerven\'y, Vlastislav and Ravindra, Ravi},
  year = {1971},
  urlx = {http://seis.karlov.mff.cuni.cz/papers.bin/a71vc1.pdf}
}

@article{wu:11,
  title = {Diffraction Tomography and Multisource Holography Applied to Seismic Imaging},
  volume = {52},
  doi = {10.1190/1.1442237},
  number = {1},
  journal = {Geophysics},
  author = {Wu, R.S. and Toks\"oz, M.N.},
  year = {1987},
  pages = {11-25},
  publisher = {{SEG}},
  urlx = {http://link.aip.org/link/?GPY/52/11/1}
}

@article{mora1989,
  title = {Inversion = Migration + Tomography},
  volume = {54},
  doi = {10.1190/1.1442625},
  number = {12},
  journal = {Geophysics},
  author = {Mora, Peter},
  year = {1989},
  pages = {1575-1586},
  publisher = {{SEG}},
  urlx = {http://link.aip.org/link/?GPY/54/1575/1}
}

@book{ref:akirichards,
  title = {Quantitative Seismology: {{Theory}} and Methods, {{Volume}} 1},
  publisher = {{Freeman, San Francisco}},
  author = {Aki, K[] and Richards, P[] G[]},
  year = {1980}
}

@article{Mulder,
  title = {Exploring Some Issues in Acoustic Full Waveform Inversion},
  volume = {56},
  issn = {1365-2478},
  doi = {10.1111/j.1365-2478.2008.00708.x},
  number = {6},
  journal = {Geophysical Prospecting},
  author = {Mulder, W. A. and Plessix, R.-\'E.},
  year = {2008},
  pages = {827-841},
  publisher = {{Blackwell Publishing Ltd}}
}

@article{devaney1984,
  title = {Geophysical {{Diffraction Tomography}}},
  volume = {GE-22},
  doi = {10.1109/TGRS.1984.350573},
  number = {1},
  journal = {IEEE Transactions on Geoscience and Remote Sensing},
  author = {Devaney, A. J.},
  month = jan,
  year = {1984},
  pages = {3-13},
  xissn = {0196-2892}
}

@article{gupta:122,
  title = {Reflection of Plane Waves from a Linear Transition Layer in Liquid Media},
  volume = {30},
  doi = {10.1190/1.1439528},
  number = {1},
  journal = {Geophysics},
  author = {Gupta, Ravindra N.},
  year = {1965},
  pages = {122-132},
  publisher = {{SEG}}
}

@article{Dunster,
  title = {{{BEssel Functions}} of {{Purely Imaginary Order}}, with an {{Application}} to {{Second}}-{{Order Linear Differential Equations Having}} a {{Large Parameter}}},
  volume = {21},
  doi = {10.1137/0521055},
  number = {4},
  journal = {SIAM Journal on Mathematical Analysis},
  author = {Dunster, T.},
  year = {1990},
  pages = {995-1018},
  eprint = {http://epubs.siam.org/doi/pdf/10.1137/0521055}
}

@article{iturraran-viverosValidatedArtificialNeural2018,
  title = {Validated Artificial Neural Networks in Determining Petrophysical Properties: {{A}} Case Study from {{Colombia}}},
  volume = {6},
  issn = {2324-8858},
  shorttitle = {Validated Artificial Neural Networks in Determining Petrophysical Properties},
  doi = {10.1190/INT-2018-0011.1},
  abstract = {We have applied instantaneous seismic attributes to a stacked P-wave reflected seismic section in the Tenerife field located in the Middle Magdalena Valley Basin in Colombia to estimate the volume of clay VclayVclay{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi{$>$}clay{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} and the density {$\rho\rho{}<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}mi{$>\rho{}<$}/mi{$><$}/mrow{$><$}/math{$>$} at seismic scale. The well logs and the seismic attributes associated to the seismic trace closer to one of the available wells (Tenerife-2) is the information used to train some multilayered artificial neural networks (ANN). We perform data analysis via the gamma test, a mathematically nonparametric nonlinear smooth modeling tool, to choose the best input combination of seismic attributes to train ANNs to estimate VclayVclay{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi{$>$}clay{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} and {$\rho\rho{}<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}mi{$>\rho{}<$}/mi{$><$}/mrow{$><$}/math{$>$}. Once the ANNs are trained, they are applied to predict these parameters along the seismic line. From the continuous estimations of VclayVclay{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi{$>$}clay{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$}, we distinguish two facies: sands for Vclay{$<$}0.5Vclay{$<$}0.5{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi{$>$}clay{$<$}/mi{$><$}/msub{$><$}mo{$>\&$}lt;{$<$}/mo{$><$}mn{$>$}0.5{$<$}/mn{$><$}/mrow{$><$}/math{$>$} and shales when Vclay{$\geq$}0.5Vclay{$\geq$}0.5{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi{$>$}clay{$<$}/mi{$><$}/msub{$><$}mo{$>\geq{}<$}/mo{$><$}mn{$>$}0.5{$<$}/mn{$><$}/mrow{$><$}/math{$>$}. These estimations confirm the production of the Mugrosa C-Sands zone, and we draw the brown shale that correlates with the high-amplitude attributes and the yellow sand that correlates with the low-amplitude attributes. Using the well-log information for VPVP{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi mathvariant="normal"{$>$}P{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} and the facies classification (also in the well log), two cubic polynomials that depend on time (or depth) are obtained, one for sands and the other for shales, to fit the VPVP{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi mathvariant="normal"{$>$}P{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$}. These two cubic polynomials and the facies classification obtained from the VclayVclay{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi{$>$}clay{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} at the seismic scale enable us to estimate VPVP{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi mathvariant="normal"{$>$}P{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} at the seismic scale. To validate the 2D VPVP{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi mathvariant="normal"{$>$}P{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} and {$\rho\rho{}<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}mi{$>\rho{}<$}/mi{$><$}/mrow{$><$}/math{$>$} predicted data, a forward-modeling software (the Kennett reflectivity algorithm) is used. This model calculates synthetic seismograms that are compared with the real seismograms. This comparison indicates a small misfit that suggests that the VPVP{$<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}msub{$><$}mi{$>$}V{$<$}/mi{$><$}mi mathvariant="normal"{$>$}P{$<$}/mi{$><$}/msub{$><$}/mrow{$><$}/math{$>$} and {$\rho\rho{}<$}math display="inline" overflow="scroll"{$><$}mrow{$><$}mi{$>\rho{}<$}/mi{$><$}/mrow{$><$}/math{$>$} images are representing the reservoir description characteristics and the ANN method is accurate to map these parameters.},
  number = {4},
  journal = {Interpretation},
  author = {{Iturrar\'an-Viveros}, Ursula and {Mu\~noz-Garc\'ia}, Andr\'es M. and Parra, Jorge O. and Tago, Josu\'e},
  month = aug,
  year = {2018},
  pages = {T1067-T1080},
  file = {/home/kazeiv/Zotero/storage/X28EJM5U/Iturrarán-Viveros et al. - 2018 - Validated artificial neural networks in determinin.html}
}

@article{boieroSwaveSplittingIntensity2019,
  title = {S-Wave Splitting Intensity Analysis and Inversion},
  volume = {67},
  issn = {1365-2478},
  doi = {10.1111/1365-2478.12729},
  abstract = {Analysing S-wave splitting has become a routine step in processing multicomponent data. Typically, this analysis leads to determining the principal directions of a transversely isotropic medium with a horizontal symmetry axis, which is assumed to be responsible for azimuthal anisotropy, and to the time delays between the fast and slow S-waves. These parameters are commonly estimated layer-by-layer from the top. Errors in layer stripping occurring in shallow layers might propagate to deeper layers. We propose a method for S-wave splitting analysis and compensation that consists of inverting interval values of splitting intensity to obtain a model of anisotropic parameters that vary with time and/or depth. Splitting intensity is a robust attribute with respect to structural variations and is commutative, which means that it can be summed along a ray (or throughout a sensitivity kernel volume) and can be linearly related to anisotropic perturbations at depth. Therefore, it is possible to estimate anisotropic properties within a geological formation (e.g. the reservoir) by analysing the differences of splitting intensity measured at the top and at the bottom of the layer. This allows us to avoid layer stripping, in particular, for shallow layers where anisotropic parameters are difficult to estimate due to poor coverage, and it makes S-wave splitting analysis simpler to apply. We demonstrate this method on synthetic and real data. Because the splitting intensity attribute shows usefulness in S-wave splitting analysis in transversely isotropic media, we extend the splitting intensity theory to lower symmetry classes. It enables the characterization of tilted transversely isotropic and tilted orthorhombic media, opening new opportunities for anisotropic model building.},
  language = {English},
  number = {2},
  journal = {Geophysical Prospecting},
  author = {Boiero, D. and Bagaini, C.},
  month = feb,
  year = {2019},
  pages = {362-378},
  file = {/home/kazeiv/Zotero/storage/LGQFM4BB/Boiero and Bagaini - 2019 - S-wave splitting intensity analysis and inversion.pdf}
}

@article{liDeepEarthquakesSubducting2018,
  title = {Deep Earthquakes in Subducting Slabs Hosted in Highly Anisotropic Rock Fabric},
  volume = {11},
  issn = {1752-0894, 1752-0908},
  doi = {10.1038/s41561-018-0188-3},
  language = {en},
  number = {9},
  journal = {Nature Geoscience},
  author = {Li, Jiaxuan and Zheng, Yingcai and Thomsen, Leon and Lapen, Thomas J. and Fang, Xinding},
  month = sep,
  year = {2018},
  pages = {696-700},
  file = {/home/kazeiv/Zotero/storage/RU8M39DH/Li et al. - 2018 - Deep earthquakes in subducting slabs hosted in hig.pdf}
}

@article{kazeiScatteringRadiationPattern2019,
  title = {Scattering {{Radiation Pattern Atlas}}: {{What}} Anisotropic Elastic Properties Can Body Waves Resolve?},
  journal = {JGR Solid Earth (submitted)},
  author = {Kazei, Vladimir and Alkhalifah, Tariq},
  year = {2019}
}

@article{alkhalifahVelocityAnalysisTransversely1995,
  title = {Velocity Analysis for Transversely Isotropic Media},
  volume = {60},
  number = {5},
  journal = {Geophysics},
  author = {Alkhalifah, Tariq and Tsvankin, Ilya},
  year = {1995},
  pages = {1550-1566}
}

@article{mobilenet,
  title = {Mobilenets: {{Efficient}} Convolutional Neural Networks for Mobile Vision Applications},
  journal = {arXiv preprint arXiv:1704.04861},
  author = {Howard, Andrew G. and Zhu, Menglong and Chen, Bo and Kalenichenko, Dmitry and Wang, Weijun and Weyand, Tobias and Andreetto, Marco and Adam, Hartwig},
  year = {2017}
}

@article{EZW,
  title = {Hyperspectral Image Compression: Adapting {{SPIHT}} and {{EZW}} to Anisotropic 3-{{D}} Wavelet Coding},
  volume = {17},
  number = {12},
  journal = {IEEE Transactions on Image processing},
  author = {Christophe, Emmanuel and Mailhes, Corinne and Duhamel, Pierre},
  year = {2008},
  pages = {2334-2346}
}

@inproceedings{aravkinNonlinearSparsityPromoting2011,
  title = {A Nonlinear Sparsity Promoting Formulation and Algorithm for Full Waveform Inversion},
  isbn = {2214-4609},
  booktitle = {73rd {{EAGE Conference}} and {{Exhibition}} Incorporating {{SPE EUROPEC}} 2011},
  author = {Aravkin, A. Y. and Van Leeuwen, Tristan and Burke, James V. and Herrmann, F. J.},
  year = {2011}
}

@article{kaplan2017,
  title = {Low Frequency Full Waveform Seismic Inversion within a Tree Based {{Bayesian}} Framework},
  volume = {212},
  number = {1},
  journal = {Geophysical Journal International},
  author = {Ray, Anandaroop and Kaplan, Sam and Washbourne, John and Albertin, Uwe},
  year = {2017},
  pages = {522-542}
}

@article{jpeg2000,
  title = {{{JPEG2000}}: {{Standard}} for Interactive Imaging},
  volume = {90},
  number = {8},
  journal = {Proceedings of the IEEE},
  author = {Taubman, David S. and Marcellin, Michael W.},
  year = {2002},
  pages = {1336-1357}
}

@article{laineTextureClassificationWavelet1993,
  title = {Texture Classification by Wavelet Packet Signatures},
  volume = {15},
  number = {11},
  journal = {IEEE Transactions on pattern analysis and machine intelligence},
  author = {Laine, Andrew and Fan, Jian},
  year = {1993},
  pages = {1186-1191}
}

@article{polo2018,
  title = {Deep-Learning Tomography},
  volume = {37},
  number = {1},
  journal = {The Leading Edge},
  author = {{Araya-Polo}, Mauricio and Jennings, Joseph and Adler, Amir and Dahlke, Taylor},
  year = {2018},
  pages = {58-66}
}

@book{db1992,
  title = {Ten Lectures on Wavelets},
  volume = {61},
  isbn = {1-61197-010-5},
  publisher = {{Siam}},
  author = {Daubechies, Ingrid},
  year = {1992}
}

@incollection{linSeismicFullwaveformInversion2012,
  title = {Seismic Full-Waveform Inversion Using Truncated Wavelet Representations},
  isbn = {1052-3812},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2012},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Lin, Y. and Abubakar, A. and Habashy, T. M.},
  year = {2012},
  pages = {1-6}
}

@inproceedings{liNeuralNetworksAid1998,
  title = {Neural Networks as an Aid to Iterative Optimization Methods},
  volume = {2},
  isbn = {0-7803-4778-1},
  booktitle = {{{SMC}}'98 {{Conference Proceedings}}. 1998 {{IEEE International Conference}} on {{Systems}}, {{Man}}, and {{Cybernetics}} ({{Cat}}. {{No}}. {{98CH36218}})},
  publisher = {{IEEE}},
  author = {Li, H. J. and Sung, Andrew H. and Weiss, William W. and Wo, S. C.},
  year = {1998},
  pages = {1812-1817}
}

@article{zhangVelocityGANDataDrivenFullWaveform2018,
  title = {{{VelocityGAN}}: {{Data}}-{{Driven Full}}-{{Waveform Inversion Using Conditional Adversarial Networks}}},
  journal = {arXiv preprint arXiv:1809.10262},
  author = {Zhang, Zhongping and Wu, Yue and Lin, Youzuo and Zhou, Zheng},
  year = {2018}
}

@incollection{wuInversionNetAccurateEfficient2018,
  title = {{{InversionNet}}: {{Accurate}} and Efficient Seismic Waveform Inversion with Convolutional Neural Networks},
  isbn = {1949-4645},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2018},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Wu, Yue and Lin, Youzuo and Zhou, Zheng},
  year = {2018},
  pages = {2096-2100}
}

@article{fanInverseNetSolvingInverse2017,
  title = {{{InverseNet}}: {{Solving Inverse Problems}} with {{Splitting Networks}}},
  journal = {arXiv preprint arXiv:1712.00202},
  author = {Fan, Kai and Wei, Qi and Wang, Wenlin and Chakraborty, Amit and Heller, Katherine},
  year = {2017}
}

@incollection{sunLowFrequencyExtrapolation2018,
  title = {Low Frequency Extrapolation with Deep Learning},
  isbn = {1949-4645},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2018},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Sun, Hongyu and Demanet, Laurent},
  year = {2018},
  pages = {2011-2015}
}

@inproceedings{ovcharenkoLowFrequencyDataExtrapolation2018,
  title = {Low-{{Frequency Data Extrapolation Using}} a {{Feed}}-{{Forward ANN}}},
  isbn = {2214-4609},
  booktitle = {80th {{EAGE Conference}} and {{Exhibition}} 2018},
  author = {Ovcharenko, Oleg and Kazei, Vladimir and Peter, Daniel and Zhang, Xiangliang and Alkhalifah, Tariq},
  year = {2018}
}

@inproceedings{ovcharenkoNeuralNetworkBased2017,
  title = {Neural Network Based Low-Frequency Data Extrapolation},
  booktitle = {3rd {{SEG FWI}} Workshop: {{What}} Are We Getting},
  author = {Ovcharenko, Oleg and Kazei, Vladimir and Peter, Daniel and Alkhalifah, T.},
  year = {2017}
}

@article{ivanovNormalModesOrthorhombic2018,
  title = {Normal Modes in Orthorhombic Media},
  doi = {10.1093/gji/ggy534},
  abstract = {SUMMARY.  Guided waves in a water layer overlaying an elastic half-space are known as normal modes. They are often present in seismic recordings at long offsets},
  language = {en},
  journal = {Geophysical Journal International},
  author = {Ivanov, Yuriy and Stovas, Alexey and Kazei, Vladimir},
  year = {2018},
  file = {/home/kazeiv/Zotero/storage/QB9ARUZ3/Ivanov et al. - Normal modes in orthorhombic media.pdf}
}

@article{mulderExploringIssuesAcoustic2008,
  title = {Exploring Some Issues in Acoustic Full Waveform Inversion},
  volume = {56},
  copyright = {\textcopyright{} Shell International Exploration and Production B.V.},
  issn = {1365-2478},
  doi = {10.1111/j.1365-2478.2008.00708.x},
  abstract = {The least-squares error measures the difference between observed and modelled seismic data. Because it suffers from local minima, a good initial velocity model is required to avoid convergence to the wrong model when using a gradient-based minimization method. If a data set mainly contains reflection events, it is difficult to update the velocity model with the least-squares error because the minimization method easily ends up in the nearest local minimum without ever reaching the global minimum. Several authors observed that the model could be updated by diving waves, requiring a wide-angle or large-offset data set. This full waveform tomography is limited to a maximum depth. Here, we use a linear velocity model to obtain estimates for the maximum depth. In addition, we investigate how frequencies should be selected if the seismic data are modelled in the frequency domain. In the presence of noise, the condition to avoid local minima requires more frequencies than needed for sufficient spectral coverage. We also considered acoustic inversion of a synthetic marine data set created by an elastic time-domain finite-difference code. This allowed us to validate the estimates made for the linear velocity model. The acoustic approximation leads to a number of problems when using long-offset data. Nevertheless, we obtained reasonable results. The use of a variable density in the acoustic inversion helped to match the data at the expense of accuracy in the inversion result for the density.},
  language = {en},
  number = {6},
  journal = {Geophysical Prospecting},
  author = {Mulder, W. A. and Plessix, R.-E.},
  year = {2008},
  pages = {827-841}
}

@inproceedings{kazeiSaltbodyInversionMinimum2017,
  title = {Salt-Body {{Inversion}} with {{Minimum Gradient Support}} and {{Sobolev Space Norm Regularizations}}},
  doi = {10.3997/2214-4609.201700600},
  abstract = {Full-waveform inversion (FWI) is a technique which solves the ill-posed seismic inversion problem of fitting our model data to the measured ones from the field. FWI is capable of providing high-resolution estimates of the model, and of handling wave propagation of arbitrary complexity (visco-elastic, anisotropic); yet, it often fails to retrieve high-contrast geological structures, such as salt. One of the reasons for the FWI failure is that the updates at earlier iterations are too smooth to capture the sharp edges of the salt boundary. We compare several regularization approaches, which promote sharpness of the edges. Minimum gradient support (MGS) regularization focuses the inversion on blocky models, even more than the total variation (TV) does. However, both approaches try to invert undesirable high wavenumbers in the model too early for a model of complex structure. Therefore, we apply the Sobolev space norm as a regularizing term in order to maintain a balance between sharp and smooth updates in FWI. We demonstrate the application of these regularizations on a Marmousi model, enriched by a chunk of salt. The model turns out to be too complex in some parts to retrieve its full velocity distribution, yet the salt shape and contrast are retrieved.},
  language = {English},
  booktitle = {79th {{EAGE Conference}} and {{Exhibition}} 2017},
  author = {Kazei, Vladimir and Kalita, M. and Alkhalifah, T.},
  month = jun,
  year = {2017},
  file = {/home/kazeiv/Zotero/storage/JV8FRPGI/Kazei et al. - 2017 - Salt-body Inversion with Minimum Gradient Support .pdf}
}

@article{esserTotalvariationRegularizationStrategies2016,
  title = {Total-Variation Regularization Strategies in Full-Waveform Inversion},
  language = {en},
  journal = {arxiv.org},
  author = {Esser, Ernie and Guasch, Lluis and {van Leeuwen}, Tristan and Aravkin, Aleksandr Y. and Herrmann, Felix J.},
  month = aug,
  year = {2016},
  file = {/home/kazeiv/Zotero/storage/2S3RANB2/Esser et al. - 2016 - Total-variation regularization strategies in full-.pdf}
}

@article{shawUseAVOAData2006,
  title = {Use of {{AVOA}} Data to Estimate Fluid Indicator in a Vertically Fractured Medium},
  volume = {71},
  issn = {0016-8033},
  doi = {10.1190/1.2194896},
  abstract = {Microstructural attributes of cracks and fractures, such as crack density, aspect ratio, and fluid infill, determine the elastic properties of a medium containing a set of parallel, vertical fractures. Although the tangential weakness  {$\Delta$}T{$\Delta$}T{$<$}math display="inline" overflow="scroll"{$><$}msub{$><$}mi{$>\Delta{}<$}/mi{$><$}mi mathvariant="normal"{$>$}T{$<$}/mi{$><$}/msub{$><$}/math{$>$}  of the fractures does not vary with the fluid content, the normal weakness  {$\Delta$}N{$\Delta$}N{$<$}math display="inline" overflow="scroll"{$><$}msub{$><$}mi{$>\Delta{}<$}/mi{$><$}mi mathvariant="normal"{$>$}N{$<$}/mi{$><$}/msub{$><$}/math{$>$}  exhibits significant dependence on fluid infill. Based on linear-slip theory, we used the ratio  g{$\Delta$}N{$\slash\Delta$}Tg{$\Delta$}N{$\slash\Delta$}T{$<$}math display="inline" overflow="scroll"{$>$} {$<$}mrow{$><$}mi{$>$}g{$<$}/mi{$>$} {$<$}msub{$><$}mi{$>\Delta{}<$}/mi{$><$}mi mathvariant="normal"{$>$}N{$<$}/mi{$><$}/msub{$>$} {$<$}mo{$>\slash{}<$}/mo{$>$} {$<$}msub{$><$}mi{$>\Delta{}<$}/mi{$><$}mi mathvariant="normal"{$>$}T{$<$}/mi{$><$}/msub{$>$} {$<$}/mrow{$>$} {$<$}/math{$>$}  \textemdash{} termed the fluid indicator \textemdash{} as a quantitative measure of the fluid content in the fractures, with g representing the square of the ratio of S- and P-wave velocity in the unfractured medium. We used a Born formalism to derive the sensitivity to fracture weakness of PP- and PS-reflection coefficients for an interface separating an unfractured medium from a vertically fractured medium. Our formulae reveal that the PP-reflection coefficient does not depend on the 2D microcorrugation/surface roughness with ridges and valleys parallel to the fracture strike, whereas the PS-reflection coefficient is sensitive to this microstructural property of the fractures. Based on this formulation, we developed a method to compute the fluid indicator from wide-azimuth PP-AVOA data. Inversion of synthetic data corrupted with 10\% random noise reliably estimates the normal and tangential fracture weaknesses and hence the fluid indicator can be determined accurately when the fractures are liquid-filled or partially saturated. As the gas saturation in the fractures increases, the quality of inversion becomes poorer. Errors of 15\%\textendash{}20\% in g do not affect the estimation of fluid indicator significantly in case of liquid infill or partial saturation. However, for gas-saturated fractures, incorrect values of g may have a significant effect on fluid-indicator estimates.},
  number = {3},
  journal = {GEOPHYSICS},
  author = {Shaw, R. and Sen, M.},
  month = may,
  year = {2006},
  pages = {C15-C24},
  file = {/home/kazeiv/Zotero/storage/UCHIDZLI/Shaw and Sen - 2006 - Use of AVOA data to estimate fluid indicator in a .pdf}
}

@article{naeiniMainComponentsFullwaveform2016,
  title = {Main Components of Full-Waveform Inversion for Reservoir Characterization},
  volume = {34},
  issn = {1365-2397},
  doi = {10.3997/1365-2397.2016015},
  abstract = {Building a 3D reservoir model, which has become a key part of reservoir management, is a challenging task. Classic seismic inversion techniques, both deterministic and stochastic, have attempted to reduce the uncertainty in reservoir modelling. However, these inversion methods are typically based just on amplitude and make a number of critical simplifying assumptions, such as that migrated data are accurate and can be modelled by 1D convolution (using reflection coefficients computed from the Zoeppritz equation or its linear approximations). Migration algorithms themselves may suffer from inadequate amplitude and multiple-scattering treatments. Full-waveform inversion (FWI), specifically designed for the direct estimation of the reservoir parameters, is proposed here as an alternative method for seismic reservoir characterization. This is clearly an ambitious goal, and it is not our intention to claim we have already achieved it. Instead, we intend to introduce the main components of such reservoir-oriented inversion and discuss a strategy for elastic, anisotropic FWI constrained by rockphysics models and facies types. Among the many challenges, we focus mostly on understanding the physics and describing some elements of an efficient forward-modelling engine. In particular, we show how analysing the radiation patterns helps to optimise the parameterisation and could reduce the null space.},
  language = {en},
  number = {2141},
  journal = {First Break},
  author = {Naeini, Ehsan Zabihi and Alkhalifah, Tariq and Tsvankin, Ilya and Kamath, Nishant and Cheng, Jiubing},
  month = nov,
  year = {2016},
  file = {/home/kazeiv/Zotero/storage/PBBYGBWI/Naeini et al. - 2016 - Main components of full-waveform inversion for res.pdf}
}

@article{vidaleFinescaleHeterogeneityEarth2000,
  title = {Fine-Scale Heterogeneity in the {{Earth}}'s Inner Core},
  volume = {404},
  issn = {0028-0836, 1476-4687},
  doi = {10.1038/35005059},
  language = {en},
  number = {6775},
  journal = {Nature},
  author = {Vidale, John E. and Earle, Paul S.},
  month = mar,
  year = {2000},
  pages = {273-275},
  file = {/home/kazeiv/Zotero/storage/K2JIK96S/Vidale and Earle - 2000 - Fine-scale heterogeneity in the Earth's inner core.pdf}
}

@article{masmoudiFullwaveformInversionAcoustic2018,
  title = {Full-Waveform Inversion in Acoustic Orthorhombic Media and Application to a {{North Sea}} Data Set},
  volume = {83},
  issn = {0016-8033},
  doi = {10.1190/geo2017-0738.1},
  abstract = {Full-waveform inversion (FWI) in anisotropic media is challenging, mainly because of the large computational cost, especially in 3D, and the potential trade-offs between the model parameters needed to describe such media. By analyzing the trade-offs and understanding the resolution limits of the inversion, we can constrain FWI to focus on the main parameters the data are sensitive to and push the inversion toward more reliable models of the subsurface. Orthorhombic anisotropy is one of the most practical approximations of the earth subsurface that takes into account the natural horizontal layering and the vertical fracture network. We investigate the feasibility of a multiparameter FWI for an acoustic orthorhombic model described by six parameters. We rely on a suitable parameterization based on the horizontal velocity and five dimensionless anisotropy parameters. This particular parameterization allows a multistage model inversion strategy in which the isotropic, then, the vertical transverse isotropic, and finally the orthorhombic model can be successively updated. We applied our acoustic orthorhombic inversion on the SEG-EAGE overthrust synthetic model. The observed data used in the inversion are obtained from an elastic variable density version of the model. The quality of the inverted model suggests that we may recover only four parameters, with different resolution scales depending on the scattering potential of these parameters. Therefore, these results give useful insights on the expected resolution of the inverted parameters and the potential constraints that could be applied to an orthorhombic model inversion. We determine the efficiency of the inversion approach on real data from the North Sea. The inverted model is in agreement with the geologic structures and well-log information.},
  number = {5},
  journal = {GEOPHYSICS},
  author = {Masmoudi, N. and Alkhalifah, T.},
  month = jun,
  year = {2018},
  pages = {C179-C193},
  file = {/home/kazeiv/Zotero/storage/FGDWBFI9/Masmoudi and Alkhalifah - 2018 - Full-waveform inversion in acoustic orthorhombic m.pdf}
}

@article{gholamiWhichParameterizationSuitable2013,
  title = {Which Parameterization Is Suitable for Acoustic Vertical Transverse Isotropic Full Waveform Inversion? {{Part}} 1: {{Sensitivity}} and Trade-off Analysis},
  volume = {78},
  issn = {0016-8033},
  shorttitle = {Which Parameterization Is Suitable for Acoustic Vertical Transverse Isotropic Full Waveform Inversion?},
  doi = {10.1190/geo2012-0204.1},
  abstract = {In most geologic environments, accounting for anisotropy is necessary to perform acoustic full waveform inversion (FWI) of wide-azimuth and wide-aperture seismic data because of the potential dependence of wave speeds on the direction of the wave propagation. In the framework of multiparameter FWI, the subsurface parameterization controls the influence of the different parameter classes on the modeled seismic data as a function of the scattering angle and hence the resolution with which the parameters can be reconstructed and the potential trade-off between different parameters. We have evaluated a numerical procedure based on computation of the scattering patterns of the different parameters to assess the sensitivity of the seismic data to different parameterizations of vertical transverse isotropic media in the acoustic approximation. Among the different categories we have tested, a monoparametric FWI was found for imaging one wave speed with a broad wavenumber content, keeping the Thomsen parameters fixed, which have a small influence on the data relative to the wave speed. This raises the question of the initial information required in the background models of the Thomsen parameters to perform reliable monoparameter FWI. Alternatively, simultaneously inverting the horizontal and vertical wave speeds introduces limited trade-off effects because these wave speeds have significant influence on the data for distinct ranges of scattering angles, while the influence of the Thomsen parameter {$\delta\delta{}<$}math display="inline" overflow="scroll"{$><$}mi{$>\delta{}<$}/mi{$><$}/math{$>$} remains weak. With such parameterization, the short-to-intermediate wavelengths of the vertical velocity are updated from the short-to-intermediate scattering angles, while the long-to-intermediate wavelengths of the horizontal velocity are updated from the wide-to-intermediate scattering angles. We concluded that the choice of the subsurface parameterization can be driven by the acquisition geometry, which controls the scattering-angle coverage and hence the resolving power of FWI, and by the accuracy of the available initial FWI models.},
  number = {2},
  journal = {GEOPHYSICS},
  author = {Gholami, Y. and Brossier, R. and Operto, S. and Ribodetti, A. and Virieux, J.},
  month = mar,
  year = {2013},
  pages = {R81-R105},
  file = {/home/kazeiv/Zotero/storage/CPP2XIB6/Gholami et al. - 2013 - Which parameterization is suitable for acoustic ve.pdf}
}

@article{cheverdaRpseudoinversesCompactOperators1995,
  title = {R-Pseudoinverses for Compact Operators in {{Hilbert}} Spaces: Existence and Stability},
  volume = {3},
  number = {2},
  journal = {Journal of Inverse and Ill-Posed Problems},
  author = {Cheverda, V. A. and Kostin, V. I.},
  year = {1995},
  pages = {131-148}
}

@article{cheverdaRpseudoinversesCompactOperators2009,
  title = {R-Pseudoinverses for Compact Operators in {{Hilbert}} Spaces: Existence and Stability},
  volume = {3},
  issn = {1569-3945},
  shorttitle = {R-Pseudoinverses for Compact Operators in {{Hilbert}} Spaces},
  doi = {10.1515/jiip.1995.3.2.131},
  number = {2},
  journal = {Journal of Inverse and Ill-Posed Problems},
  author = {CHEVERDA, V. A. and KOSTIN, V. I.},
  year = {2009},
  pages = {131--148}
}

@article{schusterFarfieldSuperresolutionImaging2014,
  title = {Far-Field Superresolution by Imaging of Resonant Multiples},
  volume = {199},
  issn = {0956-540X},
  doi = {10.1093/gji/ggu350},
  abstract = {Summary.  We show that superresolution imaging in the far-field region of the sources and receivers is theoretically and practically possible if migration of re},
  language = {en},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Schuster, Gerard T. and Huang, Yunsong},
  month = dec,
  year = {2014},
  pages = {1943-1949},
  file = {/home/kazeiv/Zotero/storage/7PLIXQ4B/Schuster and Huang - 2014 - Far-field superresolution by imaging of resonant m.pdf}
}

@article{raknes2014,
  title = {Time-Lapse Full-Waveform Inversion of Limited-Offset Seismic Data Using a Local Migration Regularization},
  volume = {79},
  number = {3},
  journal = {Geophysics},
  author = {Raknes, Espen Birger and Arntsen, B\o{}rge},
  year = {2014},
  pages = {WA117-WA128},
  publisher = {{Society of Exploration Geophysicists}}
}

@article{podgornovaResolutionVTIAnisotropy2018,
  title = {Resolution of {{VTI}} Anisotropy with Elastic Full-Waveform Inversion: Theory and Basic Numerical Examples},
  issn = {0956-540X},
  doi = {10.1093/gji/ggy116},
  abstract = {Extracting medium properties from seismic data faces some limitations due to the finite frequency content of the data and restricted spatial positions of the sources and receivers. Some distributions of the medium properties make low impact on the data (including none). If these properties are used as the inversion parameters, then the inverse problem becomes over-parametrized, leading to ambiguous results. We present an analysis of multiparameter resolution for the linearized inverse problem in the framework of elastic full-waveform inversion. We show that the spatial and multiparameter sensitivities are intertwined and non-sensitive properties are spatial distributions of some non-trivial combinations of the conventional elastic parameters. The analysis accounts for the Hessian information and frequency content of the data; it is semi-analytical (in some scenarios analytical), easy to interpret, and enhances results of the widely used radiation pattern analysis. Single-type scattering is shown to have limited sensitivity, even for full-aperture data. Finite-frequency data lose multiparameter sensitivity at smooth and fine spatial scales. Also, we establish ways to quantify a spatial-multiparameter coupling and demonstrate that the theoretical predictions agree well with the numerical results.},
  journal = {Geophysical Journal International},
  author = {Podgornova, O and Leaney, S and Liang, L},
  month = mar,
  year = {2018},
  pages = {ggy116-ggy116}
}

@article{snieder3DLinearizedScattering1986,
  title = {3-{{D}} Linearized Scattering of Surface Waves and a Formalism for Surface Wave Holography},
  volume = {84},
  issn = {0956-540X},
  doi = {10.1111/j.1365-246X.1986.tb04372.x},
  abstract = {Scattering of surface waves by lateral heterogeneities is analysed in the Born approximation. It is assumed that the background medium is either laterally homogeneous, or smoothly varying in the horizontal direction. A dyadic representation of the Green's function simplifies the theory tremendously. Several examples of the theory are presented. The scattering and mode conversion coefficients are shown for scattering of surface waves by the root of an Alpine-like crustal structure. Furthermore a `great circle theorem' in a plane geometry is derived. A new proof of Snell's law is given for surface wave scattering by a quarter-space. It is shown how a stationary phase approximation can be used to simplify the Fourier synthesis of the scattered wave in the time domain. Finally a procedure is suggested to do `surface wave holography'.},
  language = {en},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Snieder, Roel},
  month = mar,
  year = {1986},
  pages = {581-605},
  file = {/home/kazeiv/Zotero/storage/G32I56CG/Snieder - 1986 - 3-D linearized scattering of surface waves and a f.pdf;/home/kazeiv/Zotero/storage/QM8HKTYZ/Snieder_1986_3-D linearized scattering of surface waves and a formalism for surface wave.pdf}
}

@incollection{kalitaRegularizedFullwaveformInversion2018,
  series = {{{SEG Technical Program Expanded Abstracts}}},
  title = {Regularized Full-Waveform Inversion for Salt Bodies},
  abstract = {Full-waveform inversion (FWI) aims to resolve an ill-posed non-linear optimization problem in order to retrieve unknown subsurface model parameters with high resolution from seismic data. The non-linearity, in the absence of low frequencies from the recorded seismic signal, tends to increase, especially for large-velocity structures, like salt bodies and the sediments beneath them, and often prevents the inversion from obtaining an adequate model. To alleviate the ill-posedness of FWI for salt-bodies, we propose to utilize model regularization in order to promote a limited variation in the inverted model and a salt-flooding regularization from the top of the salt (without picking). On that account, we split the optimization problem into two parts: first, we minimize the data misfit and the total variation in the model, seeking to achieve an inverted model with sharp interfaces; and second, we penalize sharp velocity drops in the model by a computational flooding of the velocity field. Unlike conventional industrial salt flooding, our proposed technique requires minimal human intervention and no information whatsoever about the top of the salt. Those features are demonstrated on a dataset of the Sigsbee2A model in which the lowest available frequency is 3~Hz. We retrieve most of the salt region and also some of the fine sedimentary layering beneath the salt.Presentation Date: Monday, October 15, 2018Start Time: 1:50:00 PMLocation: 207C (Anaheim Convention Center)Presentation Type: Oral},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2018},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Kalita, M. and Kazei, V. and Choi, Y. and Alkhalifah, T.},
  month = aug,
  year = {2018},
  pages = {1043-1047},
  doi = {10.1190/segam2018-2995963.1}
}

@article{alkhalifahFullmodelWavenumberInversion2016,
  title = {Full-Model Wavenumber Inversion: {{An}} Emphasis on the Appropriate Wavenumber Continuation},
  volume = {81},
  issn = {0016-8033},
  shorttitle = {Full-Model Wavenumber Inversion},
  doi = {10.1190/geo2015-0537.1},
  abstract = {A model of the earth can be described using a Fourier basis represented by its wavenumber content. In full-waveform inversion (FWI), the wavenumber description of the model is natural because our Born-approximation-based velocity updates are made up of wavefields. Our objective in FWI is to access all the model wavenumbers available in our limited aperture and bandwidth recorded data that are not yet accurately present in the initial velocity model. To invert for those model wavenumbers, we need to locate their imprint in the data. Thus, I review the relation between the model wavenumber buildup and the inversion process. Specifically, I emphasize a focus on the model wavenumber components and identified their individual influence on the data. Missing the energy for a single vertical low-model wavenumber from the residual between the true Marmousi model and some initial linearly increasing velocity model produced a worse least-squares fit to the data than the initial model itself, in which all the residual model wavenumbers were missing. This stern realization validated the importance of wavenumber continuation, specifically starting from the low-model wavenumbers, to higher (resolution) wavenumbers, especially those attained in an order dictated by the scattering angle filter. A numerical Marmousi example determined the important role that the scattering angle filter played in managing the wavenumber continuation from low to high. An application on the SEG2014 blind test data set with frequencies lower than 7~Hz muted out further validated the versatility of the scattering angle filtering.},
  number = {3},
  journal = {GEOPHYSICS},
  author = {Alkhalifah, T.},
  month = apr,
  year = {2016},
  pages = {R89-R98},
  file = {/home/kazeiv/Zotero/storage/QGYB89PR/Alkhalifah - 2016 - Full-model wavenumber inversion An emphasis on th.pdf}
}

@article{opertoEfficient3DFrequencydomain2015,
  title = {Efficient 3-{{D}} Frequency-Domain Mono-Parameter Full-Waveform Inversion of Ocean-Bottom Cable Data: Application to {{Valhall}} in the Visco-Acoustic Vertical Transverse Isotropic Approximation},
  volume = {202},
  issn = {0956-540X},
  shorttitle = {Efficient 3-{{D}} Frequency-Domain Mono-Parameter Full-Waveform Inversion of Ocean-Bottom Cable Data},
  doi = {10.1093/gji/ggv226},
  abstract = {Abstract.  Computationally efficient 3-D frequency-domain full waveform inversion (FWI) is applied to ocean-bottom cable data from the Valhall oil field in the},
  language = {en},
  number = {2},
  journal = {Geophysical Journal International},
  author = {Operto, S. and Miniussi, A. and Brossier, R. and Combe, L. and M\'etivier, L. and Monteiller, V. and Ribodetti, A. and Virieux, J.},
  month = aug,
  year = {2015},
  pages = {1362-1391},
  file = {/home/kazeiv/Zotero/storage/3V3WKM8I/Operto et al. - 2015 - Efficient 3-D frequency-domain mono-parameter full.pdf}
}

@article{sieminskiFinitefrequencySensitivitySurface2007,
  title = {Finite-Frequency Sensitivity of Surface Waves to Anisotropy Based upon Adjoint Methods},
  volume = {168},
  issn = {0956-540X},
  doi = {10.1111/j.1365-246X.2006.03261.x},
  abstract = {SUMMARY We calculate finite-frequency anisotropic traveltime sensitivity kernels for Rayleigh and Love waves using the recently developed combination of the adjoint method with spectral-element modelling of seismic wave propagation. We describe anisotropy following the ?natural? 13 elastic parameters for surface waves (A, C, F, L, N, Bc,s, Hc,s, Gc,s and Ec,s) complemented by eight ?body-wave parameters? (Jc,s, Kc,s, Mc,s and Dc,s). Along the ray path, the adjoint spectral-element computations agree well with asymptotic theory, but also expose the limitations of the asymptotic description. The adjoint spectral-element method is an efficient and flexible numerical tool, but it does not allow one to identify the various wave propagation phenomena contributing to the observed sensitivity. To decipher the numerical results, we apply Born scattering theory together with a surface-wave mode-coupling formulation. We identify a strong effect due to mode coupling. The sensitivity of Rayleigh waves for some of the anisotropic parameters is affected by Love?Rayleigh coupling, while Love-wave sensitivity is affected by cross-branch coupling. In addition, and very specific to anisotropy, the directional dependence of the sensitivity to azimuthal anisotropy may strongly distort the kernels, rendering them highly path-dependent. Because of these combined effects, the anisotropic sensitivity kernels can deviate substantially from the simple elliptical kernels used in recent isotropic finite-frequency tomography.},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Sieminski, Anne and Liu, Qinya and Trampert, Jeannot and Tromp, Jeroen},
  month = mar,
  year = {2007},
  keywords = {Fréchet derivatives,adjoint methods,scattering,seismic anisotropy,sensitivity,surface waves},
  pages = {1153-1174},
  file = {/home/kazeiv/Zotero/storage/GAIDJIVG/Sieminski et al. - 2007 - Finite-frequency sensitivity of surface waves to a.pdf}
}

@article{sieminskiFinitefrequencySensitivityBody2007,
  title = {Finite-Frequency Sensitivity of Body Waves to Anisotropy Based upon Adjoint Methods},
  volume = {171},
  issn = {1365-246X},
  doi = {10.1111/j.1365-246X.2007.03528.x},
  abstract = {We investigate the sensitivity of finite-frequency body-wave observables to mantle anisotropy based upon kernels calculated by combining adjoint methods and spectral-element modelling of seismic wave propagation. Anisotropy is described by 21 density-normalized elastic parameters naturally involved in asymptotic wave propagation in weakly anisotropic media. In a 1-D reference model, body-wave sensitivity to anisotropy is characterized by `banana\textendash{}doughnut' kernels which exhibit large, path-dependent variations and even sign changes. P-wave traveltimes appear much more sensitive to certain azimuthally anisotropic parameters than to the usual isotropic parameters, suggesting that isotropic P-wave tomography could be significantly biased by coherent anisotropic structures, such as slabs. Because of shear-wave splitting, the common cross-correlation traveltime anomaly is not an appropriate observable for S waves propagating in anisotropic media. We propose two new observables for shear waves. The first observable is a generalized cross-correlation traveltime anomaly, and the second a generalized `splitting intensity'. Like P waves, S waves analysed based upon these observables are generally sensitive to a large number of the 21 anisotropic parameters and show significant path-dependent variations. The specific path-geometry of SKS waves results in favourable properties for imaging based upon the splitting intensity, because it is sensitive to a smaller number of anisotropic parameters, and the region which is sampled is mainly limited to the upper mantle beneath the receiver.},
  language = {en},
  number = {1},
  journal = {Geophysical Journal International},
  author = {Sieminski, Anne and Liu, Qinya and Trampert, Jeannot and Tromp, Jeroen},
  year = {2007},
  keywords = {Fréchet derivatives,adjoint methods,seismic anisotropy,sensitivity,body waves,shear-wave splitting},
  pages = {368-389},
  file = {/home/kazeiv/Zotero/storage/V7EIP5BW/Sieminski et al. - 2007 - Finite-frequency sensitivity of body waves to anis.pdf}
}

@article{chenTheoreticalNumericalInvestigations2007,
  title = {Theoretical and Numerical Investigations of Global and Regional Seismic Wave Propagation in Weakly Anisotropic Earth Models},
  volume = {168},
  issn = {0956-540X},
  doi = {10.1111/j.1365-246X.2006.03218.x},
  abstract = {SUMMARY Smith and Dahlen demonstrated that in a weakly anisotropic earth model the relative surface wave phase-speed perturbation {$\delta$}c/c may be written in the form , where An and Bn are frequency-dependent depth integrals and ? denotes the ray azimuth. In this approximation, surface wave anisotropy is governed by 13 elastic parameters and the azimuthal dependence of the phase speed is represented by an even Fourier series in ? involving degrees zero (five elastic parameters), two (six elastic parameters), and four (two elastic parameters). Jech and Ps?enc?\'ik demonstrated that in such a weakly anisotropic earth model the relative compressional-wave phase-speed perturbation may be expressed as {$\delta$}c/c= (2c2)?1B33, whereas the relative shear wave phase-speed perturbations are given by {$\delta$}c/c= (4c2)?1\{B11+B22{$\pm$}[(B11?B22)2+ 4B212]1/2\}. We demonstrate that the coefficients B33, B11, B22, and B12 may be written in the generic form , where ? denotes the local azimuth and i the local angle of incidence. For B11, B22 and B33 the coefficients an(i) and bn(i) are an even Fourier series of degrees zero, two and four in i, but for B12 they are an odd Fourier series of degrees one and three. Like surface waves, the azimuthal (?) dependence of body waves involves even degrees zero (five elastic parameters), two (six elastic parameters), and four (two elastic parameters), but, unlike surface waves, it also involves the odd degrees one (six elastic parameters) and three (two elastic parameters). Thus, weakly anisotropic body-wave propagation involves all 21 independent elastic parameters. We use spectral-element simulations of global and regional seismic wave propagation to assess the validity of these asymptotic body and surface wave results. The numerical simulations and asymptotic predictions are in good agreement for anisotropy at the 5 per cent level.},
  number = {3},
  journal = {Geophysical Journal International},
  author = {Chen, Min and Tromp, Jeroen},
  month = mar,
  year = {2007},
  keywords = {surface waves,body waves,phase-speed perturbations,spectral-element simulations,weakly anisotropic earth model},
  pages = {1130-1152},
  file = {/home/kazeiv/Zotero/storage/FJ79XKWG/Chen and Tromp - 2007 - Theoretical and numerical investigations of global.pdf}
}

@article{berettaAVOAVAInversion2002,
  title = {{{AVO}} and {{AVA}} Inversion for Fractured Reservoir Characterization},
  volume = {67},
  issn = {0016-8033},
  doi = {10.1190/1.1451802},
  abstract = {Seismic wave reflection amplitudes are used to detect fluids and fracture properties in reservoirs. This paper studies the characterization of a vertically fractured fluid-filled reservoir by analyzing the reflection amplitudes of P-waves with varying incident and azimuthal angles. The reservoir is modeled as a horizontal transversely isotropic medium embedded in an isotropic background, and the linearized P-waves reflection coefficient are considered. The conditioning of the inverse problem is analyzed, and fracture density is found to be the best conditioned parameter. Using diffraction tomography under the Born approximation, an inversion procedure is proposed in the transformed k\textendash{$\omega$} domain to detect fracture density variations within the reservoir. Seismic data are rearranged in pairs of incident and reflected plane waves, enlightening only one spectral component of the fracture density field at a time. Only the observable spectral components are inverted. Moreover, working in the transformed domain, picking reflection amplitudes is not required. An example of the inversion applied to a synthetic data set is presented. The limitation of source and receiver numbers and the finite bandwidth of the wavelet produce a loss of resolution, but the overall fracture density variations are recovered correctly.},
  number = {1},
  journal = {GEOPHYSICS},
  author = {Beretta, M. and Bernasconi, G. and Drufuca, G.},
  month = jan,
  year = {2002},
  pages = {300-306},
  file = {/home/kazeiv/Zotero/storage/XQCD7IU2/Beretta et al. - 2002 - AVO and AVA inversion for fractured reservoir char.pdf}
}

@article{KazeiHeada,
  title = {P341 {{On}} the {{Contribution}} of {{Head Waves}} to {{Full Waveform Inversion}}},
  journal = {presented as poster P341 at the annual EAGE meeting in Copenhagen},
  author = {Kazei, Vladimir and Ponomarenko, A. V. and Troyan, V. N. and Kashtan, B. M. and Mulder, W. A.},
  year = {2012},
  publisher = {{EAGE}}
}

@article{KazeiHead,
  title = {On the {{Contribution}} of {{Head Waves}} to {{Full Waveform Inversion}}},
  author = {Kazei, Vladimir and Ponomarenko, A. V. and Troyan, V. N. and Kashtan, B. M. and Mulder, W. A.},
  year = {2012},
  howpublished = {74th EAGE Conference & Exhibition incorporating SPE EUROPEC 2012, Extended Abstracts, P341, Copenhagen, Denmark}
}

@inproceedings{kazeiCenteredDifferentialWaveform2017,
  title = {Centered {{Differential Waveform Inversion}} with {{Minimum Support Regularization}}},
  doi = {10.3997/2214-4609.201701336},
  abstract = {Time-lapse full-waveform inversion has two major challenges. The first one is the reconstruction of a reference model (baseline model for most of approaches). The second is inversion for the time-lapse changes in the parameters. Common model approach is utilizing the information contained in all available data sets to build a better reference model for time lapse inversion. Differential (Double-difference) waveform inversion allows to reduce the artifacts introduced into estimates of time-lapse parameter changes by imperfect inversion for the baseline-reference model. We propose centered differential waveform inversion (CDWI) which combines these two approaches in order to benefit from both of their features. We apply minimum support regularization commonly used with electromagnetic methods of geophysical exploration. We test the CDWI method on synthetic dataset with random noise and show that, with Minimum support regularization, it provides better resolution of velocity changes than with total variation and Tikhonov regularizations in time-lapse full-waveform inversion.},
  language = {English},
  booktitle = {79th {{EAGE Conference}} and {{Exhibition}} 2017},
  author = {Kazei, Vladimir and Alkhalifah, T.},
  month = jun,
  year = {2017},
  file = {/home/kazeiv/Zotero/storage/BT26VAGR/Kazei and Alkhalifah - 2017 - Centered Differential Waveform Inversion with Mini.pdf}
}

@inproceedings{kazei2013spectral,
  title = {Spectral {{Sensitivity Analysis}} of {{FWI}} in a {{Constant}}-Gradient {{Background Velocity Model}}},
  doi = {10.3997/2214-4609.20130599},
  booktitle = {75th {{EAGE Conference}} \& {{Exhibition}} Incorporating {{SPE EUROPEC}} 2013},
  author = {Kazei, Vladimir and Kashtan, B. M. and Troyan, V. N. and Mulder, W. A.},
  year = {2013}
}

@book{voigtLehrbuchKristallphysikMit1910,
  title = {Lehrbuch Der Kristallphysik:(Mit Ausschluss Der Kristalloptik)},
  volume = {34},
  publisher = {{BG Teubner}},
  author = {Voigt, Woldemar},
  year = {1910}
}

@book{zotero-202,
  type = {Book}
}

@misc{PhysRev90,
  title = {Phys. {{Rev}}. {{B}} 90, 224104 (2014) - {{Necessary}} and Sufficient Elastic Stability Conditions in Various Crystal Systems},
  howpublished = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.90.224104}
}

@misc{LicensingMITVs,
  title = {Licensing - {{MIT}} vs {{GPL}} License},
  journal = {Stack Overflow},
  howpublished = {https://stackoverflow.com/questions/3902754/mit-vs-gpl-license}
}

@article{panEstimationElasticConstants2016,
  title = {Estimation of Elastic Constants for {{HTI}} Media Using {{Gauss}}-{{Newton}} and Full-{{Newton}} Multiparameter Full-Waveform Inversion},
  volume = {81},
  issn = {0016-8033},
  doi = {10.1190/geo2015-0594.1},
  abstract = {In seismic full-waveform inversion (FWI), subsurface parameters are estimated by iteratively minimizing the difference between the modeled and the observed data. We have considered the problem of estimating the elastic constants of a fractured medium using multiparameter FWI and modeling naturally fractured reservoirs as equivalent anisotropic media. Multiparameter FWI, although promising, remains exposed to a range of challenges, one being the parameter crosstalk problem resulting from the overlap of Fr\'echet derivative wavefields. Parameter crosstalk is strongly influenced by the form of the scattering pattern for each parameter. We have derived 3D radiation patterns associated with scattering from a range of elastic constants in general anisotropic media. Then, we developed scattering patterns specific to a horizontal transverse isotropic (HTI) medium to draw conclusions about parameter crosstalk in FWI. Bare gradients exhibit crosstalk, as well as artifacts caused by doubly scattered energy in the data residuals. The role of the multiparameter Gauss-Newton (GN) Hessian in suppressing parameter crosstalk is revealed. We have found that the second-order term in the multiparameter Hessian, which is associated with multiparameter second-order scattering effects, can be constructed with the adjoint-state technique. We have examined the analytic scattering patterns for HTI media with a 2D numerical example. We have examined the roles played by the first- and second-order terms in multiparameter Hessian to suppress parameter crosstalk and second-order scattering artifacts numerically. We have also compared the multiparameter GN and full-Newton methods as methods for determining the elastic constants in HTI media with a two-block-layer model.},
  number = {5},
  journal = {Geophysics},
  author = {Pan, W. and Innanen, K. and Margrave, G. and Fehler, M. and Fang, X. and Li, J.},
  month = jul,
  year = {2016},
  pages = {R275-R291},
  file = {/home/kazeiv/Zotero/storage/Y5YW2XSC/Pan et al_2016_Estimation of elastic constants for HTI media using Gauss-Newton and.pdf}
}

@incollection{kotsi4DFullwaveformMetropolis2018,
  series = {{{SEG Technical Program Expanded Abstracts}}},
  title = {{{4D}} Full-Waveform Metropolis Hastings Inversion Using a Local Acoustic Solver},
  abstract = {Time lapse seismic monitoring usually involves looking for small changes in localized regions. Quantifying the uncertainty related to these changes is important because it affects exploration and production decisions. Traditional methods that use pixel by pixel quantification with large models are computationally infeasible. We use a local acoustic solver in the area of interest, which allows for fast computation of the wavefield solves. This allows us to use a Metropolis Hastings algorithm in a Bayesian inversion to address the uncertainty that is present in the estimation of 4D velocity changes. Presentation Date: Tuesday, October 16, 2018 Start Time: 8:30:00 AM Location: 204C (Anaheim Convention Center) Presentation Type: Oral},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2018},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Kotsi, M. and Malcolm, A. and Ely, G.},
  month = aug,
  year = {2018},
  pages = {5323-5327},
  doi = {10.1190/segam2018-2997858.1}
}

@article{zhuLDMNetLowDimensional2017,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1711.06246},
  primaryClass = {cs},
  title = {{{LDMNet}}: {{Low Dimensional Manifold Regularized Neural Networks}}},
  shorttitle = {{{LDMNet}}},
  abstract = {Deep neural networks have proved very successful on archetypal tasks for which large training sets are available, but when the training data are scarce, their performance suffers from overfitting. Many existing methods of reducing overfitting are data-independent, and their efficacy is often limited when the training set is very small. Data-dependent regularizations are mostly motivated by the observation that data of interest lie close to a manifold, which is typically hard to parametrize explicitly and often requires human input of tangent vectors. These methods typically only focus on the geometry of the input data, and do not necessarily encourage the networks to produce geometrically meaningful features. To resolve this, we propose a new framework, the Low-Dimensional-Manifold-regularized neural Network (LDMNet), which incorporates a feature regularization method that focuses on the geometry of both the input data and the output features. In LDMNet, we regularize the network by encouraging the combination of the input data and the output features to sample a collection of low dimensional manifolds, which are searched efficiently without explicit parametrization. To achieve this, we directly use the manifold dimension as a regularization term in a variational functional. The resulting Euler-Lagrange equation is a Laplace-Beltrami equation over a point cloud, which is solved by the point integral method without increasing the computational complexity. We demonstrate two benefits of LDMNet in the experiments. First, we show that LDMNet significantly outperforms widely-used network regularizers such as weight decay and DropOut. Second, we show that LDMNet can be designed to extract common features of an object imaged via different modalities, which proves to be very useful in real-world applications such as cross-spectral face recognition.},
  journal = {arXiv:1711.06246 [cs]},
  author = {Zhu, Wei and Qiu, Qiang and Huang, Jiaji and Calderbank, Robert and Sapiro, Guillermo and Daubechies, Ingrid},
  month = nov,
  year = {2017},
  keywords = {Computer Science - Computer Vision and Pattern Recognition},
  file = {/home/kazeiv/Zotero/storage/P65LZCFC/Zhu et al_2017_LDMNet.pdf}
}

@article{osypovModelUncertaintyQuantification2013,
  title = {Model-uncertainty Quantification in Seismic Tomography: Method and Applications},
  volume = {61},
  issn = {1365-2478},
  shorttitle = {Model-uncertainty Quantification in Seismic Tomography},
  doi = {10.1111/1365-2478.12058},
  language = {en},
  number = {6},
  journal = {Geophysical Prospecting},
  author = {Osypov, Konstantin and Yang, Yi and Fournier, Aim\'e and Ivanova, Natalia and Bachrach, Ran and Yarman, Can Evren and You, Yu and Nichols, Dave and Woodward, Marta},
  month = nov,
  year = {2013},
  pages = {1114-1134},
  file = {/home/kazeiv/Zotero/storage/YBDCY5BT/Osypov et al_2013_Model‐uncertainty quantification in seismic tomography.pdf}
}

@article{devaneyNonuniquenessInverseSource1982,
  title = {Nonuniqueness in Inverse Source and Scattering Problems},
  volume = {30},
  issn = {0018-926X},
  doi = {10.1109/TAP.1982.1142902},
  abstract = {The fields radiated by spherically symmetric time-harmonic sources are used to illustrate how little can be learned about a source from knowledge of the radiated field outside of the source volume. It is shown that even if it is known that the source is spherically symmetric, it is not possible to determine its radial structure. Moreover, even if the radial structure of the source is known apart from a constant amplitude and a finite radius, it is not possible to evaluate those two unknowns independently. These examples are applied to demonstrate explicitly that two methods that have been claimed to produce exact unique solutions to inverse-source and inverse-scattering problems do not yield the claimed results.},
  number = {5},
  journal = {IEEE Transactions on Antennas and Propagation},
  author = {Devaney, A. and Sherman, G.},
  month = sep,
  year = {1982},
  keywords = {Acoustic scattering,Antenna radiation patterns,Apertures,Current distribution,Electromagnetic scattering; inverse problem,H infinity control,Inverse scattering problem,Iterative methods,Magnetic resonance,Notice of Violation,Phased arrays,Sampling methods,Scattering},
  pages = {1034-1037},
  file = {/home/kazeiv/Zotero/storage/CAQZRR47/Devaney and Sherman - 1982 - Nonuniqueness in inverse source and scattering pro.pdf}
}

@article{SimultaneousNonlinearReconstruction,
  title = {Simultaneous Nonlinear Reconstruction of Two-Dimensional Permittivity and Conductivity},
  volume = {29},
  issn = {1944-799X},
  doi = {10.1029/93RS03448},
  abstract = {A new inversion algorithm for the simultaneous reconstruction of permittivity and conductivity recasts the nonlinear inversion as the solution of a coupled set of linear equations. The algorithm is iterative and proceeds through the minimization of two cost functions. At the initial step the data are matched through the reconstruction of the radiating or minimum norm scattering currents; subsequent steps refine the nonradiating scattering currents and the material properties inside the scatterer. Two types of basis functions are constructed for the nonradiating currents: ``invisible'' (global) basis functions, which are appropriate for discrete measurements and nonradiating (local) basis functions, which are useful in studying the limit of continuous measurements. Reconstructions of square cylinders from multiple source receiver measurements at a single frequency show that the method can handle large contrasts in material properties.},
  language = {en},
  number = {4},
  journal = {Radio Science},
  pages = {1101-1118},
  file = {/home/kazeiv/Zotero/storage/VH22U6CZ/Simultaneous nonlinear reconstruction of two-dimen.pdf}
}

@article{bergContrastSourceInversion1997,
  title = {A Contrast Source Inversion Method},
  volume = {13},
  issn = {0266-5611},
  doi = {10.1088/0266-5611/13/6/013},
  abstract = {This paper describes a simple algorithm for reconstructing the complex index of refraction of a bounded object immersed in a known background from a knowledge of how the object scatters known incident radiation. The method described here is versatile accommodating both spatially and frequency varying incident fields and allowing a priori information about the scatterer to be introduced in a simple fashion. Numerical results show that this new algorithm outperforms the modified gradient approach which until now has been one of the most effective reconstruction algorithms available.},
  language = {en},
  number = {6},
  journal = {Inverse Problems},
  author = {van den Berg, Peter M. and Kleinman, Ralph E.},
  year = {1997},
  pages = {1607},
  file = {/home/kazeiv/Zotero/storage/DAN8RZ64/Berg and Kleinman - 1997 - A contrast source inversion method.pdf}
}

@incollection{schusterApproximateInverseL2spaces2007,
  series = {Lecture {{Notes}} in {{Mathematics}}},
  title = {Approximate Inverse in {{L}}2-Spaces},
  isbn = {978-3-540-71226-8 978-3-540-71227-5},
  language = {en},
  booktitle = {The {{Method}} of {{Approximate Inverse}}: {{Theory}} and {{Applications}}},
  publisher = {{Springer, Berlin, Heidelberg}},
  author = {Schuster, Thomas},
  year = {2007},
  pages = {11-24},
  file = {/home/kazeiv/Zotero/storage/YKB5ERNY/Schuster - 2007 - Approximate inverse in Emphasis Type=ItalicL.pdf},
  doi = {10.1007/978-3-540-71227-5_2}
}

@article{bleisteinNonuniquenessInverseSource1977,
  title = {Nonuniqueness in the Inverse Source Problem in Acoustics and Electromagnetics},
  volume = {18},
  issn = {00222488},
  doi = {10.1063/1.523256},
  language = {en},
  number = {2},
  journal = {Journal of Mathematical Physics},
  author = {Bleistein, Norman and Cohen, Jack K.},
  year = {1977},
  pages = {194},
  file = {/home/kazeiv/Zotero/storage/DZ39PDG7/Bleistein and Cohen - 1977 - Nonuniqueness in the inverse source problem in aco.pdf}
}

@article{rudinNonlinearTotalVariation1992,
  title = {Nonlinear Total Variation Based Noise Removal Algorithms},
  volume = {60},
  issn = {0167-2789},
  doi = {10.1016/0167-2789(92)90242-F},
  abstract = {A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lanrange multipliers. The solution is obtained using the gradient-projection method. This amounts to solving a time dependent partial differential equation on a manifold determined by the constraints. As t {$\rightarrow$} {$\infty$} the solution converges to a steady state which is the denoised image. The numerical algorithm is simple and relatively fast. The results appear to be state-of-the-art for very noisy images. The method is noninvasive, yielding sharp edges in the image. The technique could be interpreted as a first step of moving each level set of the image normal to itself with velocity equal to the curvature of the level set divided by the magnitude of the gradient of the image, and a second step which projects the image back onto the constraint set.},
  number = {1},
  journal = {Physica D: Nonlinear Phenomena},
  author = {Rudin, Leonid I. and Osher, Stanley and Fatemi, Emad},
  month = nov,
  year = {1992},
  pages = {259-268},
  file = {/home/kazeiv/Zotero/storage/H4P2SVN4/Rudin et al_1992_Nonlinear total variation based noise removal algorithms.pdf}
}

@article{fons2013,
  title = {Broadband Seismic Data ? {{The}} Importance of Low Frequencies},
  volume = {78},
  doi = {10.1190/geo2012-0294.1},
  number = {2},
  journal = {GEOPHYSICS},
  author = {Ten Kroode, Fons and Bergler, Steffen and Corsten, Cees and {de Maag}, Jan Willem and Strijbos, Floris and Tijhof, Henk},
  year = {2013},
  pages = {WA3-WA14},
  eprint = {http://dx.doi.org/10.1190/geo2012-0294.1}
}

@article{kohnInfluenceModelParametrization2012,
  title = {On the Influence of Model Parametrization in Elastic Full Waveform Tomography},
  volume = {191},
  issn = {0956-540X},
  doi = {10.1111/j.1365-246X.2012.05633.x},
  abstract = {Elastic Full Waveform Tomography (FWT) aims to reduce the misfit between recorded and modelled data, to deduce a very detailed model of elastic material parameters in the underground. The choice of the elastic model parameters to be inverted affects the convergence and quality of the reconstructed subsurface model. Using the Cross-Triangle-Squares (CTS) model three elastic parametrizations, Lam\'e parameters m1 = [{$\lambda$}, {$\mu$}, {$\rho$}], seismic velocities m2 = [Vp, Vs, {$\rho$}] and seismic impedances m3 = [Ip, Is, {$\rho$}] for far-offset reflection seismic acquisition geometries with explosive point sources and free-surface condition are studied. In each CTS model the three elastic parameters are assigned to three different geometrical objects that are spatially separated. The results of the CTS model study reveal a strong requirement of a sequential frequency inversion from low to high frequencies to reconstruct the density model. Using only high-frequency data, cross-talk artefacts have an influence on the quantitative reconstruction of the material parameters, while for a sequential frequency inversion only structural artefacts, representing the boundaries of different model parameters, are present. During the inversion, the Lam\'e parameters, seismic velocities and impedances could be reconstructed well. However, using the Lam\'e parametrization -artefacts are present in the {$\lambda$} model, while similar artefacts are suppressed when using seismic velocities or impedances. The density inversion shows the largest ambiguity for all parametrizations. However, the artefacts are again more dominant, when using the Lam\'e parameters and suppressed for seismic velocity and impedance parametrization. The afore mentioned results are confirmed for a geologically more realistic modified Marmousi-II model. Using a conventional streamer acquisition geometry the P-velocity, S-velocity and density models of the subsurface were reconstructed successfully and are compared with the results of the Lam\'e parameter inversion.},
  language = {en},
  number = {1},
  journal = {Geophysical Journal International},
  author = {K\"ohn, D. and De Nil, D. and Kurzmann, A. and Przebindowska, A. and Bohlen, T.},
  month = oct,
  year = {2012},
  pages = {325-345},
  file = {/home/kazeiv/Zotero/storage/KU9Z3R3L/Köhn et al_2012_On the influence of model parametrization in elastic full waveform tomography.pdf}
}

@article{hoop1997,
  title = {Generalized {{Radon}} Transform Inversions for Reflectivity in Anisotropic Elastic Media},
  volume = {13},
  number = {3},
  journal = {Inverse problems},
  author = {De Hoop, Maarten V and Bleistein, Norman},
  year = {1997},
  pages = {669},
  publisher = {{IOP Publishing}}
}

@article{hoop1999,
  title = {The Resolving Power of Seismic Amplitude Data: {{An}} Anisotropic Inversion/Migration Approach},
  volume = {64},
  number = {3},
  journal = {Geophysics},
  author = {De Hoop, Maarten V and Spencer, Carl and Burridge, Robert},
  year = {1999},
  pages = {852-873},
  publisher = {{Society of Exploration Geophysicists}}
}

@inproceedings{blaseCharacterizationDentalTissue2018,
  title = {Characterization of Dental Tissue by Reflection and Transmission Ultrasound Microscopy},
  volume = {10600},
  doi = {10.1117/12.2300510},
  abstract = {Ultrasound (US) is a widely used modality for medical imaging, since it is non-invasive and relatively inexpensive. The ability of US imaging to detect internal structures, like tissue interfaces or lesion sites makes it a promising candidate for dental imaging. So far, the inherent technical difficulties of US imaging in tissues and organs with very heterogeneous (acoustic) properties and limited access have prevented its widespread use. In this study, we characterized the acoustic properties of sectioned teeth by scanning acoustic microscopy in reflection and transmission modes. The spatial distribution of sound velocity was measured in sections of extracted human teeth by use of a scanning acoustic microscope (SAM). Freshly extracted teeth were fixed in 4\% formaldehyde solution and embedded in a polymer block (PMMA). Sections of approximately 1 mm thickness were cut along the coronal-apical axis. Radio frequency (RF) data of teeth were collected in a scan region of 15 \× 15 mm\textsuperscript{2} by a SAM operating at 30 MHz with a lateral step size of 50 {$\mathrm{\mu}$}m and a sampling rate of 500 MSa/s. Sound velocity was determined from the time resolved reflection and transmission signals. Values for sound velocity from transmission mode were about 20\% lower than that from the reflection mode, if thickness information from reflection mode was used. If thickness was determined from the transmission mode, sound velocities from transmission were very close to those obtained from the reflection mode. Transmission mode is less sensitive to artifacts caused by the inclination of the specimen.},
  booktitle = {Health {{Monitoring}} of {{Structural}} and {{Biological Systems XII}}},
  publisher = {{International Society for Optics and Photonics}},
  author = {Blase, Christopher and Amjad, Umar and Kundu, Tribikram and {Bereiter-Hahn}, J\"urgen and Blume, Maximilian and Sader, Robert},
  month = mar,
  year = {2018},
  pages = {106000W},
  file = {/home/kazeiv/Zotero/storage/RJT43GIL/Blase et al_2018_Characterization of dental tissue by reflection and transmission ultrasound.pdf}
}

@article{vinnikObservationalEvidenceDiffracted1989,
  title = {Observational Evidence for Diffracted {{SV}} in the Shadow of the {{Earth}}'s Core},
  volume = {16},
  number = {6},
  journal = {Geophysical Research Letters},
  author = {Vinnik, Lev P. and Farra, Veronique and Romanowicz, Barbara},
  year = {1989},
  pages = {519-522}
}

@article{vinnikSeismicAnisotropyLayer1995,
  title = {Seismic Anisotropy in the {{D}} {${''}$}layer},
  volume = {22},
  number = {13},
  journal = {Geophysical Research Letters},
  author = {Vinnik, Lev and Romanowicz, Barbara and Le Stunff, Yves and Makeyeva, Larissa},
  year = {1995},
  pages = {1657-1660}
}

@article{boerConstructingDiscreteFracture2018,
  title = {Constructing a Discrete Fracture Network Constrained by Seismic Inversion Data},
  volume = {66},
  issn = {1365-2478},
  doi = {10.1111/1365-2478.12527},
  language = {en},
  number = {1},
  journal = {Geophysical Prospecting},
  author = {den Boer, Lennert D. and Sayers, Colin M.},
  month = jan,
  year = {2018},
  pages = {124-140},
  file = {/home/kazeiv/Zotero/storage/GU8N9K6U/Boer_Sayers_2018_Constructing a discrete fracture network constrained by seismic inversion data.pdf}
}

@article{ohOptimalFullWaveform2018,
  title = {Optimal Full Waveform Inversion Strategy for Marine Data in Azimuthally Rotated Elastic Orthorhombic Media},
  issn = {0016-8033},
  doi = {10.1190/geo2017-0762.1},
  abstract = {The orthorhombic anisotropic description of Earth layers can allow the capture many of the Earth's anisotropic complexity. The inversion for high-resolution azimuthal variation of anisotropy is important for reservoir characterization, among other applications. A high-resolution description of the azimuth of fractures can help us predict flow preferences. To verify the feasibility of multi-parameter full waveform inversion for marine data assuming azimuthally rotated elastic orthorhombic media, we analyze the radiation patterns and gradient directions of orthorhombic parameters to the reflection data. We first express the gradient direction of the orthorhombic parameters considering the azimuthal rotation of the symmetric planes. Then, to support our observations in the gradient direction, the radiation patterns of the partial derivative wavefields from each parameter perturbation are also derived under the rotated elastic orthorhombic assumption. To find an optimal parameterization, we compare three different parameterizations: monoclinic, velocity-based and hierarchical parameterizations. Then, we suggest an optimal multi-stage update strategy by analyzing the behavior of the rotation angle as an FWI target. To analyze the trade-off among parameters in different parameterizations, we calculate the gradient direction from a hockey puck model, in which each parameter is perturbed at the different location on a horizontal layer. The trade-off analysis supports that the hierarchical parameterization provides us with more opportunities to build up subsurface models with less trade-off between parameters and less influence of the azimuthal rotation of orthorhombic anisotropy. The feasibility of the proposed FWI strategy is examined using synthetic marine streamer data from a simple 3D reservoir model with a fractured layer.},
  journal = {GEOPHYSICS},
  author = {Oh, J. and Alkhalifah, T.},
  month = mar,
  year = {2018},
  pages = {1-61},
  file = {/home/kazeiv/Zotero/storage/5D9YUJDZ/Oh_Alkhalifah_2018_Optimal full waveform inversion strategy for marine data in azimuthally rotated.pdf}
}

@article{chang3D3CFullwavefield2009,
  title = {{{3D}} 3-{{C}} Full-Wavefield Elastic Inversion for Estimating Anisotropic Parameters: {{A}} Feasibility Study with Synthetic Data},
  volume = {74},
  issn = {0016-8033},
  shorttitle = {{{3D}} 3-{{C}} Full-Wavefield Elastic Inversion for Estimating Anisotropic Parameters},
  doi = {10.1190/1.3204766},
  abstract = {Traveltime-based inversions cannot solve for all of the anisotropy parameters for orthorhombic media. Vertical velocities cannot be recovered simultaneously with the dimensionless anisotropy parameters. Also, the density cannot be solved because it does not affect the normal moveout of P and S reflections. These limitations can be overcome using full-wavefield inversion for anisotropy parameters for orthorhombic media and for transversely isotropic media with vertical and horizontal symmetry axes. Tsvankin's parameters and the orientation of the local (anisotropic) coordinates are inverted from three-component, wide-azimuth data sets containing P reflected and PS converted waves. The inversions are performed in two steps. The first step uses only reflections from the top of an anisotropic layer, whichdoes not constrain the trade-offs between the vertical velocities, the anisotropies, and density, as shown by parameter correlation analysis. The results from the first step are refined by using them as the starting model for the second step, which fits reflections from the top and bottom of the layer. The properties of the target layer influence the amplitudes of top and bottom reflections as well as the traveltime of the bottom reflections; when all these data are used, the inversion is highly overdetermined and all model parameters are estimated accurately. When Gaussian noise is added, the inversion results are very similar to those for the noise-free data because only the coherent signal is fitted. The residual at convergence for the noisy data corresponds to the noise level. Concurrent inversion of data from multiple sources increases the azimuthal illumination of a target.},
  number = {6},
  journal = {GEOPHYSICS},
  author = {Chang, H. and McMechan, G.},
  month = nov,
  year = {2009},
  pages = {WCC159-WCC175},
  file = {/home/kazeiv/Zotero/storage/FFIARNEE/Chang_McMechan_2009_3D 3-C full-wavefield elastic inversion for estimating anisotropic parameters.pdf}
}

@inproceedings{ohOptimalFullWaveform2017,
  title = {Optimal {{Full Waveform Inversion Strategy}} in {{Azimuthally Rotated Elastic Orthorhombic Media}}},
  doi = {10.3997/2214-4609.201701232},
  abstract = {The elastic orthorhombic assumption is one of the most practical Earth models that takes into account the horizontal anisotropic layering and vertical fracture network. In this model, the rotation angle of the vertical planes of symmetry is a crucial parameter needed to increase the convergence of an anisotropic full waveform inversion (FWI) as well as to provide the fracture geometry along azimuthal direction. As an initial step, we investigate the possibility of recovering the azimuth angle via FWI, which may offer high-resolution information. We first utilize our new parameterization with deviation parameters, which provides the opportunity for multi-stage FWI. Based on the radiation patterns and gradient directions of each parameter, we show that the azimuth angle mainly affects the parameters that have azimuth-dependent radiation patterns, so that we can hierarchically build up the subsurface model from isotropic to VTI to azimuthally rotated orthorhombic models with less trade-offs. From the numerical example for a synthetic 3D model, we expect that both a deviation parameter and the azimuth angle can be recovered in the last stage of FWI with minimum trade-offs.},
  language = {English},
  booktitle = {79th {{EAGE Conference}} and {{Exhibition}} 2017},
  author = {Oh, J. W. and Alkhalifah, T.},
  month = jun,
  year = {2017},
  file = {/home/kazeiv/Zotero/storage/EVQVJD4K/Oh_Alkhalifah_2017_Optimal Full Waveform Inversion Strategy in Azimuthally Rotated Elastic.pdf}
}

@inproceedings{routhFullWavefieldInversion2012,
  series = {{{SEG Technical Program Expanded Abstracts}}},
  title = {Full {{Wavefield Inversion}} of {{Time}}-{{Lapse Data}} for {{Improved Imaging}} and {{Reservoir Characterization}}},
  abstract = {We apply full wavefield inversion (FWI) to determine from time-lapse data the changes in the subsurface due to production. It is well recognized that a significant velocity change between the baseline and monitor survey introduces a time shift in the seismic data. Current practices are to apply time-shift analysis or to perform time-shift inversion to interpret such changes. These changes can be large enough that the background velocity model needs to be updated between the base and the monitor survey. Ideally if the velocity models can be estimated for both the base and monitor surveys, then these large changes can be interpreted. The FWI framework is ideally suited to accomplish this task. The objective of this paper is to demonstrate this concept and its impact on imaging time-lapse data. A synthetic 2D example is used to demonstrate the solution to this problem.},
  booktitle = {{{SEG Technical Program Expanded Abstracts}} 2012},
  publisher = {{Society of Exploration Geophysicists}},
  author = {Routh, P. and Palacharla, G. and Chikichev, I. and Lazaratos, S.},
  month = sep,
  year = {2012},
  pages = {1-6},
  doi = {10.1190/segam2012-1043.1}
}

@article{zuberiMitigatingNonlinearityFull2018,
  title = {Mitigating Nonlinearity in Full Waveform Inversion Using Scaled-{{Sobolev}} Pre-Conditioning},
  volume = {213},
  issn = {0956-540X},
  doi = {10.1093/gji/ggx549},
  abstract = {The Born approximation successfully linearizes seismic full waveform inversion if the background velocity is sufficiently accurate. When the background velocity is not known it can be estimated by using model scale separation methods. A frequently used technique is to separate the spatial scales of the model according to the scattering angles present in the data, by using either first- or second-order terms in the Born series. For example, the well-known `banana-donut' and the `rabbit ear' shaped kernels are, respectively, the first- and second-order Born terms in which at least one of the scattering events is associated with a large angle. Whichever term of the Born series is used, all such methods suffer from errors in the starting velocity model because all terms in the Born series assume that the background Green's function is known. An alternative approach to Born-based scale separation is to work in the model domain, for example, by Gaussian smoothing of the update vectors, or some other approach for separation by model wavenumbers. However such model domain methods are usually based on a strict separation in which only the low-wavenumber updates are retained. This implies that the scattered information in the data is not taken into account. This can lead to the inversion being trapped in a false (local) minimum when sharp features are updated incorrectly. In this study we propose a scaled-Sobolev pre-conditioning (SSP) of the updates to achieve a constrained scale separation in the model domain. The SSP is obtained by introducing a scaled Sobolev inner product (SSIP) into the measure of the gradient of the objective function with respect to the model parameters. This modified measure seeks reductions in the L2 norm of the spatial derivatives of the gradient without changing the objective function. The SSP does not rely on the Born prediction of scale based on scattering angles, and requires negligible extra computational cost per iteration. Synthetic examples from the Marmousi model show that the constrained scale separation using SSP is able to keep the background updates in the zone of attraction of the global minimum, in spite of using a poor starting model in which conventional methods fail.},
  language = {en},
  number = {1},
  journal = {Geophysical Journal International},
  author = {Zuberi, M. Ah and Pratt, R. G.},
  month = apr,
  year = {2018},
  pages = {706-725},
  file = {/home/kazeiv/Zotero/storage/E7UFW6HS/Zuberi_Pratt_2018_Mitigating nonlinearity in full waveform inversion using scaled-Sobolev.pdf}
}

@article{choi2012,
  title = {Application of Multi-source Waveform Inversion to Marine Streamer Data Using the Global Correlation Norm},
  volume = {60},
  issn = {0016-8025},
  doi = {10.1111/j.1365-2478.2012.01079.x},
  abstract = {ABSTRACT Conventional multi?source waveform inversion using an objective function based on the least?square misfit cannot be applied to marine streamer acquisition data because of inconsistent acquisition geometries between observed and modelled data. To apply the multi?source waveform inversion to marine streamer data, we use the global correlation between observed and modelled data as an alternative objective function. The new residual seismogram derived from the global correlation norm attenuates modelled data not supported by the configuration of observed data and thus, can be applied to multi?source waveform inversion of marine streamer data. We also show that the global correlation norm is theoretically the same as the least?square norm of the normalized wavefield. To efficiently calculate the gradient, our method employs a back?propagation algorithm similar to reverse?time migration based on the adjoint?state of the wave equation. In numerical examples, the multi?source waveform inversion using the global correlation norm results in better inversion results for marine streamer acquisition data than the conventional approach.},
  number = {4},
  journal = {Geophysical Prospecting},
  author = {Choi, Yunseok and Alkhalifah, Tariq},
  month = jun,
  year = {2012},
  keywords = {Global correlation,Marine streamer data,Modelled},
  pages = {748-758},
  file = {/home/kazeiv/Zotero/storage/FLF79QSI/Choi Yunseok_Alkhalifah Tariq_2012_Application of multi‐source waveform inversion to marine streamer data using.pdf}
}

@article{wuSimultaneousInversionBackground2015,
  title = {Simultaneous Inversion of the Background Velocity and the Perturbation in Full-Waveform Inversion},
  volume = {80},
  issn = {0016-8033},
  doi = {10.1190/geo2014-0365.1},
  abstract = {The gradient of standard full-waveform inversion (FWI) attempts to map the residuals in the data to perturbations in the model. Such perturbations may include smooth background updates from the transmission components and high wavenumber updates from the reflection components. However, if we fix the reflection components using imaging, the gradient of what is referred to as reflected-waveform inversion (RWI) admits mainly transmission background-type updates. The drawback of existing RWI methods is that they lack an optimal image capable of producing reflections within the convex region of the optimization. Because the influence of velocity on the data was given mainly by its background (propagator) and perturbed (reflectivity) components, we have optimized both components simultaneously using a modified objective function. Specifically, we used an objective function that combined the data generated from a source using the background velocity, and that by the perturbed velocity through Born modeling, to fit the observed data. When the initial velocity was smooth, the data modeled from the source using the background velocity will mainly be reflection free, and most of the reflections were obtained from the image (perturbed velocity). As the background velocity becomes more accurate and can produce reflections, the role of the image will slowly diminish, and the update will be dominated by the standard FWI gradient to obtain high resolution. Because the objective function was quadratic with respect to the image, the inversion for the image was fast. To update the background velocity smoothly, we have combined different components of the gradient linearly through solving a small optimization problem. Application to the Marmousi model found that this method converged starting with a linearly increasing velocity, and with data free of frequencies below 4~Hz. Application to the 2014 Chevron Gulf of Mexico imaging challenge data set demonstrated the potential of the proposed method.},
  number = {6},
  journal = {GEOPHYSICS},
  author = {Wu, Z. and Alkhalifah, T.},
  month = sep,
  year = {2015},
  pages = {R317-R329},
  file = {/home/kazeiv/Zotero/storage/4EHNR4MS/Wu_Alkhalifah_2015_Simultaneous inversion of the background velocity and the perturbation in.pdf}
}

license: MIT

license_type: permissive

branch_name: refs/heads/master

extension: bib