SeismicCity staff continuously participates in the research of new methods and algorithms, and over the years has contributed to the scientific progress of Geophysics through publications in scientific geophysical journals, presentations in geophysical conferences and by providing industry education programs. Below are SeismicCity staff publications.
Velocity Estimation and Model Building
Rauch-Davies M., Langton D., Bradshaw M., Bartana A., Kosloff, D., Codd J., Kessler D., Rich J., and Margrave G., 2019 Can fracture orientation and intensity be detected from seismic data? Woodford Formation, Anadarko Basin, Oklahoma investigation, The Leading Edge, Vol 38, No. 2, p.144-150
Rauch-Davies M., Sutherland S., Bradshaw M., Codd J. and Kessler D., 2018 Use of prestack depth migration for improving the accuracy of horizontal drilling in unconventional reservoirs, The Leading Edge, vol 37, No. 1, p.27-32
Kessler D., Kosloff D., Codd J. and Bartana A., SeismicCity Inc., Depth Imaging - More than PSDM, 15th International Congress of the Brazilian Geophysical Society, held in Rio de Janeiro, Brazil, 1-3 August 2017
Ammar A., Saunders R., Henry C., Wilkinson T., Frismanis M., Bradshaw M., Codd J. and Kessler D., 2015, New life to an old field - Main Pass 73 Gulf of Mexico Shelf, SEG Technical Program Expanded Abstracts 2015. 1807-1810.
Bartana A., Kosloff D. and Hollander Y., 2011 Automatic picking of delays on 3D angle gathers, SEG Expanded Abstracts 30, 3903
Bartana A., Kosloff D., Riste P., Vilenchik Y., 2009 Resolution of small velocity anomalies by wide azimuth reflection data tomography, SEG Expanded Abstracts 28, 4059
Z. Koren, I. Ravve, G. Gonzalez, and D. Kosloff. 2008 Anisotropic local tomography. Geophysics 73, 75-92
Koren Z., Ravve, I., and Tal-Ezer H., 2006 Curved rays anisotropic tomography: Local and global approaches: SEG Expanded abstracts 25, 3373-3377
Yonadav S., and Kosloff D., 2005 Sparse norm reflection tomography: Local and global approaches: SEG Expanded abstracts, 24, 2554-2557
D. Kosloff, Y. Zudeman. 2002 Uncertainties in determining interval velocities from surface reflection seismics, Geophysics, 61, 952
Yondav S., and Kosloff D., 2002 High resolution travel time tomography: SEG Expanded abstracts 21, 834-837
Koren Z., Zackhem U., and Kosloff D., 1999 3D local tomography--- residual interval velocity analysis on a depth solid model: SEG Expanded abstracts, 18 1255-1258
Kosloff D., Pecholcs P., Zackhem U. and Koren Z., 1997 Estimation of long-wavelength near-surface velocity and low-relief structural anomalies Part 2: A new near surface reconstruction method: SEG Expanded abstracts 16 1063-1065
Kosloff D., Zackhem U., and Koren Z., 1997 Subsurface velocity determination by grid tomography of depth migrated gathers: SEG Expanded abstracts 16 1815-1818 (1997)
Pecholcs P., Nguyen S., Kosloff D., and Litvin A., 1997 Estimation of long-wavelength near-surface velocity and low-relief structural anomalies Part I. A case history in central Saudi Arabia: SEG, Expanded abstracts, 16 1059-1062
Kessler D., 1997. Construction of Velocity Models for Prestack Depth Migration - Practical Aspects: Geophysical Society of Houston Data Processing SIG, Houston, Texas.
D. Kosloff, J. Sherwood, Z. Koren, E. Machet and Y. Falkovitz. 1996 Velocity and interface depth determination by tomography of depth migrated gathers. Geophysics, Vol. 61, 5, 1511-1523.
Kessler D., Canales L., and Downie A., 1995. Depth Processing Using Geophysical and Geological Tools: Interpretation workshop SIG seminar, Geophysical Society of Houston, Houston, Texas.
Roth M., Kessler D., and Sibley M., 1994. 3-D Velocity Model Building - An Accurate and Efficient Interpretive Workflow: Construction of 3-D Macro Velocity Depth Models, EAEG/SEG summer workshop, Noordwijkerhout, The Netherlands.
Kessler D. and Reshef M., 1994. Depth Processing of Complex Seismic Data: Modern Developments in Structural Interpretation, Validation and Modeling, Geological society, London, England.
Kessler D. and Chan W.K., 1993. DMO Velocity Analysis With Jacubowicz's Dip-Decomposition Method: Geophysics, vol. 58, p. 1517-1524.
Weinstein A., Mesbey V., Isakov A., Kessler D., and Gelchinsky B., 1992. Modeling and Studying Wavefields Scattered by Fractal Interfaces: SEG 62nd. annual meeting, New Orleans, USA.
S. Keydar, Z. Koren, D. Kosloff and E. Landa. 1989 Optimum time to depth conversion. Geophysics, 54, 1001-1006.
E. Landa, D. Kosloff, S. Keydar, Z. Koren and M. Reshef. 1988 A method for determining velocity and depth from seismic reflection data. Geophysical Prospecting, Vol. 36, No. 3, 223-2438.
Kessler D., Koren Z., Reshef M., Kosloff D., and Ginzburg A., 1988. The Use of Coherency Inversion and Depth Migration for Interactive Processing: EAEG 50th. annual meeting, Hauge, The Netherlands.
Prestack Depth Migration
Langton D., Biholar A., Shaw K., Adams S., Bradshaw M., Codd J., Tan X., Bartana A. and Kessler D., 2019: Elastic imaging and its benefits —Permian Basin example. First Break, Special Topic: Data Processing, Volume 37, pages 69-77.
Horine R., Rauch-Davies M., Bradshaw M., Codd J. and Kessler D., Improved Interpretation of Over Thrust Geology using Depth Imaging Tools: Beaver Creek Field, Fermont County, Wyoming, Denver Geophysical Society Seismic Symposium Silver Anniversary, March 29, 2019
Allon Bartana*, Dan Kosloff, Brandon Warnell, Chris Connor, Jeff Codd, David Kessler, Paulius Micikevicius, Ty Mckercher, Peng Wang, Paul Holzhauer, GPU implementation of minimal dispersion recursive operators for reverse time migration, SEG Technical Program Expanded Abstracts 2015. 4116-4120.
Zvi Koren, Igor Ravve, Evgeny Ragoza, Allon Bartana and Dan Kosloff, 2008 Full-azimuth angle domain imaging, SEG Expanded Abstracts 27, 2221
Dan Kosloff, Hillel Tal-Ezer, Allon Bartana, Evgeny Ragoza and Andrei Shabelansky, 2006 Three dimensional wave equation depth migration by a direct solution method, SEG Expanded Abstracts 25, 2490
Koren Z., Xu S., and Kosloff D., 2002 Target-oriented common reflection angle migration: SEG Expanded abstracts, 21 1196-1199,
A. Bartana, D. Kosloff, and I. Ravve, Discussion and Reply On “Angle-domain common-image gathers by wavefield continuation methods” (Paul C. Sava and Sergey Fomel, 2003, Geophysics 68, 1065-1074)
Strahilevitz, R., Kosloff D., and Koren Z., 1998 Three dimensional two point ray tracing using paraxial rays in cartessian coordinates: SEG Expanded abstracts, 17 1887-1892
Kessler D., Canales L., Shih C.C., and Duncan P., 1997. Controlled Stacking for Improved Quality of Prestack Depth-Migration Results: The Leading Edge, vol. 16, No. 9, p. 994-1002.
Meshbey, V., Kosloff D., Ragoza Y., Meshbey O., Egozy U., and Cozens J., 1996 A method for computing traveltimes for an arbitrary velocity model: SEG abstracts, 15 523-526
Kessler D., and Canales L., 1995. Mixed Grid Solution of the 3D Eikonal Equation: SEG 65ft. annual meeting, Houston, Texas.
Kessler D., and Canales L., 1995. Practical Solution of the 3D Eikonal Equation On a Mixed Grid: EAEG 57th. annual meeting, Glasgow, Scotland.
Kessler D., Reshef M., Crase E., Chan W.K., Hubbard J., and Tsingas C., 1995. Depth Processing: An Example: The Leading Edge, vol. 14, No. 9, p. 949-953
Reshef M. and Kessler D., 1989. Practical Implementation of Three-Dimensional Poststack Depth Migration: Geophysics, vol. 54, p. 309-318.
Alberto da Costa C., Raz S., and Kosloff D.,1989 Gaussian beam migration: SEG Expanded abstracts 8 1169-1171
Schwedersky G., and Kosloff D., 1989 Evaluation of multicomponent depth migration: SEG Expanded abstracts 8 1320-1322
Kosloff D. and Kessler D., 1987. Accurate Depth Migration by a Generalized Phase Shift Method: Geophysics, vol. 52, p. 1074-1084.
D. Kosloff, D. Kessler, 1987 Discussion On: “Accurate depth migration by a generalized phase-shift method” Geophysics, vol 52, 1074-1084
M. Reshef and D. Kosloff. 1986 Migration of common shot gathers. Geophysics, Vol. 51, 324-331.
Edwards M., Hsiung C., Kessler D., Kosloff D., and Reshef M., 1986. Three-Dimensional Depth Migration By a Generalized Phase-Shift Method: SEG 56th. annual meeting, Houston, USA.
Reshef M., and Kosloff D., 1984 Three common-shot migration methods: SEG Expanded abstracts 3 443-444
E. Baysal and D. Kosloff. 1983 Reverse time migration. Geophysics, Vol. 48, No.11, 1514-1524.
Salt Vicinity and Subsalt Imaging
Kosloff D., Bartana A., O'Connor J., Codd J. and Kessler D., 2020, Assisting geological interpretation using seismic simulation, First Break Vol. 38, pp. 73-76
Ammar A., Saunders R., Henry C., Wilkinson T., Frismanis M., Bradshaw M., Codd J., and Kessler D., 2016, Drilling Closer to salt. First Break Vol. 34, No. 9, pp. 65-71.
Hoxha F., O’Connor J., Codd J., Pignol C., and Kessler D., SeismicCity Corp., and Bridge Al., Jurick, D., Brietzke R., and Beeny K., Devon Energy Corp., 2011 Investigation of deep water GOM subsalt imaging using anisotropic model, dataset and RTM – Tempest. Geophysics 76, WB21 - WB26
O’Connor J., Hoxha F., Codd J., Pignol C., and Kessler D., SeismicCity Corp., and Bridge Al., Jurick, D., Taylor J., Seitchik A., Brietzke R., and Beeney K., Devon Energy Corp., 2010 Investigation of deep water GOM subsalt imaging using anisotropic model, dataset and RTM PSDM – Tempest. SEG Summer Research Workshop, California, USA.
Seitchik A., Jurick D., Brietzke R., and Benny K, Devon Energy Corp., and Codd J., Hoxha F., Pignol C., and Kessler D., SeismicCity Corp. 2009. The Tempest Project – Addressing challenges in deepwater Gulf of Mexico depth imaging through geologic models and numerical simulation. The Leading Edge, vol 28, p. 546-553.
Hoxha F., Kessler D., Frismanis M. and Codd J. SeismicCity Corporation. 2009. Multiple attenuation using WAZ data in VTI anisotropic media. SEG 79th annual meeting, Houston, Texas, USA.
Seitchik A., Devon Energy Corporation and Kessler D., SeismicCity Corporation, 2008 Addressing Challenges in Deep Water Gulf of Mexico Depth Imaging Through Geologic Models and Acquisition Simulation - The Tempest Project, SEG 78th annual meeting, Las Vegas, USA
Kessler D., Codd J., Hoxha F. and Pignol C., SeismicCity Corporation, Bridge A., Brietzke R., Seitchik A. and Jurick D., Devon Energy Corporation, 2008. A Realistic Deep Water Gulf of Mexico 3D Simulation and Imaging - The Tempest Simulation,Datasets and Imaging, SEG 78th annual meeting, Las Vegas, USA
Rhodes M., Statoil (Norway), Frismanis M., SeismicCity (Houston) and Dalstrom B., Statoil (London), 2005. A practical and integrated depth migration approach to prospect identification in BM-ES-11. 9th International Congress of the Brazilian Geophysical Society ,held in Salvador, Brazil, 11-14 September 2005.
Oren Peles, Allon Bartana, Dan Kosloff and Zvi Koren, 2004 Limitations of the exploding reflector model in subsalt imaging, Expanded abstract, SEG 74th Annual Meeting, 2455-2457.
Jurick D., Codd, J., Hoxha F., Naumenko J., and Kessler D., 2003. Gulf of Suez Acquisition Design Using 2D and 3D Full Wave Equation Simulation. SEG 73rd annual meeting, Dallas, USA
Subsalt Challenges, Seismic Gymnastics Provide View, The AAPG Explorer, June 2002. Publication courtesy of the American Association of Petroleum Geologists (AAPG)
Kessler D., Codd J., Hoxha F., Drummond J., Walraven D., and Mehlhop A., 2002. Interpretation of Subsalt Converted Waves: SEG 72nd annual meeting., Salt Lake City, USA.
Kessler D., 1998. Depth Processing of Mississippi Salt Basin: Geological Society of Mississippi and Geophysical Society of Jackson SIG, Jackson, Mississippi.
Ridges Build Walls, Concept Shakes Mississippi Salt, The AAPG Explorer, November 1997. Publication courtesy of the American Association of Petroleum Geologists (AAPG)
Kessler D., Canales L., Shih C.H., and Duncan P, 1996. On Accurate Imaging of Steep Salt: SEG 66th. annual meeting, Denver, USA.
Kessler D., Canales L., Shih C.H., and Duncan P, 1996. Accurate Imaging and Positioning of Steep Salt Flanks by Controlled Stacking: EAEG 58th. annual meeting, Amsterdam, The Netherlands.
Kessler D., Canales L., and Shih C.H., 1996. Controlled stacking: CSEG 1996 Annual National Convention, Calgary, Alberta, Canada.
D. Kosloff, J. Carcione. 2010 Two-dimensional simulation of Rayleigh waves with staggered sine/cosine transforms and variable grid spacing. Geophysics 75, 133-140,
D. Kosloff, R. Pestana, H. Tal-Ezer. 2010 Acoustic and elastic numerical wave simulations by recursive spatial derivative operators. Geophysics 75, 167-174
Kosloff D, Pestana R. and Tal-Ezer H., 2008 Numerical solution of the constant density acoustic wave equation by implicit spatial derivative operators: SEG Expanded abstract, SEG 27, 2057-2061
E. Tessmer and D. Kosloff, 1994 3-D elastic modeling with surface topography by a Chebychev spectral method, Geophysics, Vol. 59, No. 3 P 464-473, 11 FIGS
H. Tal Ezer and D. Kosloff. A modified Chebyshev pseudo spectral method with (N-1) time step restriction. Journal of Computational Physics, Vol. 104, No. 2, 1993.
Kessler D. and Kosloff D., 1993. 3-D Elastic Simulation of Wave Propagation using Cylindrical Coordinates: Jour. Seis. Expl., vol 2., p. 173-188.
Tessmer E., Kessler D., Kosloff D. and Behle A., 1992. Multi-Domain Chebychev-Fourier Method for the Solution of the Equations of Motion of Dynamic Elasticity: Jour. Comp. Phys., vol 100, p. 355-363.
E. Tessmer, D. Kosloff and A. Behle. 1992 Elastic wave propagation simulation in the presence of surface topography. Geophysics. J. 108.
J. M. Carcione, D. Koslloff, A. Behle, and G. Seriani 1992 A spectral scheme for wave propagation I 3-D elastic anisotropic media. Geophysics, vol 57, No. 12 P. 1593-1607
Kessler D. and Kosloff D., 1991. Elastic Wave Propagation using Cylindrical Coordinates: Geophysics, vol. 56, p. 2080-2089.
J.M. Carcione, D. Kosloff and A. Behle. 1991 Long wave anisotropy stratified media: A numerical test. Geophysics. Vol. 56, 245-254..
Kessler D. and Kosloff D., 1991. 3-D Elastic Wave Propagation for VSP Geometry: SEG 61st. annual meeting, Houston, USA.
Tessmer E., and Kosloff D., 1991 3-D elastic modeling with surface topography by a Chebychev spectral method: SEG Expanded abstracts 10 1565-1568
Kosloff D., Kessler D., Filho A. Q., Tessmer E., Behlle A. and Strahilevits R., 1990. Solutions of the Equations of Dynamic Elasticity by a Chebychev Spectral Method: Geophysics, vol. 55, p. 734-748.
Kosloff D. and Kessler D., 1990. Seismic Numerical Modeling: Oceanographic and Geophysical Tomography: Elsevier Science Publishers, p. 251-312.
Kessler D. and Kosloff D.,1990. Acoustic Wave Propagation in 2-D Cylindrical Coordinates: Geophys. Jour. Int., vol. 103, p. 577-587.
H. Tal-Ezer, J.M. Carcione and D. Kosloff. 1990 An accurate and efficient scheme for wave propagation in linear viscoelastic media. Geophysics, Vol. 55, 1366-1379.
Kessler D. and Kosloff D., 1990. Wave Propagation in the Vicinity of a Cylindrical Object: SEG 60th. annual meeting, San Francisco, USA.
Carcione J., and Kosloff D., 1990 Long-wave anisotropy in periodically layered media: A numerical test: SEG Expanded abstracts 9 1582-1585
Tessmer E., Tessmer G., Kosloff D., and Behle A., 1990 3-D elastic modeling by a Chebychev spectral method: SEG Expanded abstracts 9 1049-1052
D. Kosloff, A. Filho, E. Tessmer and A. Behle. 1989 Numerical solution of the acoustic and elastic wave equations by a new rapid expansion method. Geophysical Prospecting 37, 383-394.
Kosloff D., Carcione J., Rommel B., and Beble A., 1989 Three-dimensional wave propagation simulation in elastic – Anisotropic media: SEG Expanded abstracts 8 1016-1018
M. Reshef, M. Edwards, C. Hsuing and D. Kosloff. 1988 Three dimensional acoustic modelling by the acoustic Fourier method. Part I, Acoustic Case. Geophysics, Vol. 53, No. 9, 1175-1183.
M. Reshef, M. Edwards, C. Hsuing and D. Kosloff. 1988 Three dimensional elastic modelling by the acoustic Fourier method. Part II, Elastic Case. Geophysics, Vol. 53, No. 9, 1184-1193.
J.M. Carcione, D. Kosloff and R. Kosloff. 1988 Viscoacoustic wave propagation simulation in the Earth. Geophysics, Vol. 53, No. 6, 769-777.
J.M. Carcione, D. Kosloff and R. Kosloff. 1988 Wave propagation simulation in a linear viscoacoustic medium. Geophys. Jour. 93, 393-407.
J.M. Carcione, D. Kosloff and R. Kosloff. 1988 Wave propagation simulation in an elastic anisotropic (Transversely Isotropic) solid. Quat. Jour. Mech. Appl. Math. 41, 320-345.
J.M. Carcione, D. Kosloff and R. Kosloff. 1988 Wave propagation simulation in a linear viscoelastic medium. Geophys. Jour., 95, 597-611.
Edwards M., Kosloff D., Reshef M., and Tessmer E., 1987 Three-dimensional solutions of equations of dynamic elasticity by a new rapid expansion method (REM): SEG Expanded abstracts 6 536-538
H. Tal Ezer, D. Kosloff and Z. Koren. 1987 An accurate scheme for seismic forward modeling. Geophysical Prospecting, Vol. 35, No. 5, 479-490.
R. Kosloff and D. Kosloff.986 Absorbing boundaries for wave propagation problems. Journal of Computational Physics, 63, 363-376,.
D. Kosloff and R. Kosloff.1986 A non-periodic Fourier method for the solution of the classical wave equation. Computer Physics Communications, 30, 333-336.
C. Cerjan, D. Kosloff, R. Kosloff and M. Reshef. 1985 A non-reflecting boundary condition for discrete acoustic and elastic wave equations. Geophysics, Vol. 50, No. 5, 705-708.
M. Reshef and D. Kosloff. 1985 Application of elastic forward modeling to seismic interpretation. Geophysics, Vol. 50, 1266-1272.
Edwards M., Hsiung C., Kosloff D., and Reshef M., 1985 Elastic 3-D forward modeling by the Fourier method: SEG Expanded abstracts 4 534-535
D. Kosloff, M. Reshef and D. Loewenthal. 1984 Elastic wave calculations by the Fourier method. Bull. Seis. Soc. Amer. Vol. 74, No. 3, 875-891.
E. Baysal, D. Kosloff and J. Sherwood. 1984 A two-way nonreflecting acoustic wave equation. Geophysics, 49, 132.
Kosloff D., and Kosloff R., 1984 A nonreflecting boundary condition for discrete acoustic and elastic wave calculations: SEG Abstracts 3 627-628
D. Kosloff and E, Baysal. 1983 Migration with the full acoustic wave equation. Geophysics, Vol. 48, No. 6, 677-687.
Kosloff D., Reshef M., and Loewenthal D., 1983 Elastic forward modeling by the fourier method: SEG Expanded abstracts 2 336-337
D. Kosloff and E. Baysal. 1982 Forward modelling by a Fourier method. Geophysics, 47 No.10, 1402-1412.
Allon Bartana, Ronnie Kosloff and David J. Tannor, 2001 Laser Cooling of Molecules by Dynamically Traped States, Chem. Phys., 267, 195
Guy Ashkenazi, Uri Banin, Allon Bartana, Ronnie Kosloff and Sanford Ruhman, 1997 Quantum Description of the Impulsive Photo dissociation Dynamics of in Solution, Adv. Chem. Phys., 100, 229-315
Allon Bartana, Ronnie Kosloff and David J. Tannor, 1997 Laser Cooling of Internal Degrees of Freedom II. J. Chem. Phys., 106, 1435-1448.
Uri Banin, Allon Bartana, Sanford Ruhman and Ronnie Kosloff, 1994 Impulsive Excitation of Coherent Vibrational Motion Ground Surface Dynamics Induced by Intense Short Pulses, J. Chem. Phys. 101, 8461-8481.
Allon Bartana, Uri Banin, Sanford Ruhman and Ronnie Kosloff, 1994 Intensity Effect on Impulsive Excitation of Ground Surface Coherent Vibrational Motion: A “V” Jump Simulation, Chem. Phys. Lett., 229, 211-217.
Allon Bartana, Ronnie Kosloff and David J. Tannor, 1993 Laser Cooling of Molecular Internal Degrees of Freedom by a Series of Shaped Pulses, J. Chem. Phys., 99, 196-210 (1993).
E. Heyman, R. Strahileritz and D. Kosloff. Pulsed beam reflection and transmission of a planar interface, exact solution and coral models. Wave Motion, 18.
R.H. Bisseling, R. Kosloff and D. Kosloff. 1987 Fast Sinc interpolation and differentiation by preprocessing of sampled data. Proc. Image. Analysis and Processing. Plenum Publishing Corp., N.Y. De Gefu, Editor.
R.H. Bisseling, R. Kosloff and D. Kosloff. 1986 Multi-dimensional interpolation and differentiation based on an accelerated Sinc interpolation procedure. Computer Physics Communications 39, 313-332.
D. Kosloff and R. Kosloff. 1983 A Fourier method solution of the time dependent Schrodinger equation as a tool in molecular dynamics. Journal of Computational Physics, 52: p.35.
R. Kosloff and D. Kosloff. 1983 A Fourier method solution for the time dependent Schrodinger equation: A study of the reaction H+- H2, D+- H2 and D+ + H2. Journal of Chemical Physics, 79(4), 1823-1833.
H.P. Liu and D. Kosloff. 1981 Numerical evaluation of the Hilbert transform by the Fast Fourier Transform (FFT) technique. Geophysical Journal, 67, 791-799.
D. Kosloff, R.F. Scott and J. Scranton. 1980 Finite element simulation of Wilmington oil field subsidence, I. Linear Modelling. Tectonophys. 64, 339-368.
D. Kosloff, R.F. Scott and J. Scranton. 1980 Finite element simulation of Wilmington oil field subsidence, II. Nonlinear Modelling. Tectonophys. 70, 159-183.
D. Kosloff and H.P. Liu. 1980 Reformulation and discussion of the mechanical behavior of the velocity dependent friction law proposed by Dietrich. Geophysical Research Letters, Vol. 7, No. 11, 913-916.
L.H. Ping and D. Kosloff. 1978 Flexer of the lithosphere in the vicinity of island arcs and seamounts. Tectonophysics 50 (2/3): 249.
D. Cole, D. Kosloff and J.B. Minister. 1978 A numerical boundary integral method for elastodynamics. Bull. Seism. Soc. Am. 65: 1331.
D. Kosloff. 1977 Numerical simulation of tectonic processes in Southern California, Geophysical J. 51(2): 487-502.
D. Kosloff, G.A. Frazier. 1977 Treatment of hourglass modes in low order finite element codes. Intl. J. for Numerical and Analytical Methods in Geomechanics 2: 57-72.
D. Kosloff. 1975 A perturbation scheme for obtaining partial derivatives of long- wave group velocity dispersion. Bull. Seism. Soc. Am. 65: 1753-1760.