We use SPECFEM3D Cartesian 4.1.0 ( Komatitsch and Tromp, 2002; Komatitsch and Tromp, 2002; Komatitsch et al., 2023) published under the GPL 3 license.

We thank the Computational Infrastructure for Geodynamics (http://geodynamics.org) which is funded by the National Science Foundation under awards EAR-0949446, 1550901 and 2149126.

Dimitri Komatitsch, Jeroen Tromp, Rahul Garg, Hom Nath Gharti, Masaru Nagaso, Elif Oral, Daniel Peter, Michael Afanasiev, Rafael Almada, Jean Paul Ampuero, Etienne Bachmann, Kangchen Bai, Piero Basini, Stephen Beller, Jordan Bishop, François Bissey, Celine Blitz, Alexis Bottero, Ebru Bozdag, … Hejun Zhu. (2023). SPECFEM/specfem3d: SPECFEM3D v4.1.0 (v4.1.0). Zenodo. https://doi.org/10.5281/zenodo.10413988

Komatitsch, D.; Tromp, J. (2002a), Spectral-element simulations of global seismic wave propagation-I. Validation, Geophysical Journal International, 149 (2) , 390-412, doi: 10.1046/j.1365-246X.2002.01653.x, url: http://doi.wiley.com/10.1046/j.1365-246X.2002.01653.x

Komatitsch, D.; Tromp, J. (2002b), Spectral-element simulations of global seismic wave propagation–II. Three-dimensional models, oceans, rotation and self-gravitation, Geophysical Journal International, 150 (1) , 303-318.

If you compute on GPU graphics cards for acoustic or seismic wave propagation applications, please cite one or more of the following:

• Komatitsch, D. (2011), Fluid-solid coupling on a cluster of GPU graphics cards for seismic wave propagation, Comptes Rendus Mécanique, 339 (2-3) , 125-135, doi: 10.1016/j.crme.2010.11.007, url: http://linkinghub.elsevier.com/retrieve/pii/S1631072110002081
• Michéa, D.; Komatitsch, D. (2010), Accelerating a three-dimensional finite-difference wave propagation code using GPU graphics cards: Accelerating a wave propagation code using GPUs, Geophysical Journal International, 182 (1) , 389-402, doi: 10.1111/j.1365-246X.2010.04616.x, url: http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.2010.04616.x
• Komatitsch, D.; Michéa, D.; Erlebacher, G. (2009), Porting a high-order finite-element earthquake modeling application to NVIDIA graphics cards using CUDA, Journal of Parallel and Distributed Computing, 69 (5) , 451-460, doi: 10.1016/j.jpdc.2009.01.006, url: http://linkinghub.elsevier.com/retrieve/pii/S0743731509000069
• Komatitsch, D.; Erlebacher, G.; Göddeke, D.; Michéa, D. (2010), High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster, Journal of Computational Physics, 229 (20) , 7692-7714, doi: 10.1016/j.jcp.2010.06.024, url: http://linkinghub.elsevier.com/retrieve/pii/S0021999110003396

If you use this new version, which has non-blocking MPI for much better performance for medium or large runs, please cite at least one of these six articles, in which results of non -blocking MPI runs are presented:

• Peter, D.; Komatitsch, D.; Luo, Y.; Martin, R.; Le Goff, N.; Casarotti, E.; Le Loher, P.; Magnoni, F.; Liu, Q.; Blitz, C.; Nissen-Meyer, T.; Basini, P.; Tromp, J. (2011), Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes: SPECFEM3D Version 2.0 'Sesame', Geophysical Journal International, 186 (2) , 721-739, doi: 10.1111/j.1365-246X.2011.05044.x, url: http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.2011.05044.x
• Komatitsch, D.; Erlebacher, G.; Göddeke, D.; Michéa, D. (2010), High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster, Journal of Computational Physics, 229 (20) , 7692-7714, doi: 10.1016/j.jcp.2010.06.024, url: http://linkinghub.elsevier.com/retrieve/pii/S0021999110003396
• Komatitsch, D.; Vinnik, L.P.; Chevrot, S. (2010), SHdiff-SVdiff splitting in an isotropic Earth, Journal of Geophysical Research, 115 (B7) , doi: 10.1029/2009JB006795, url: http://doi.wiley.com/10.1029/2009JB006795
• Komatitsch, D. (2011), Fluid-solid coupling on a cluster of GPU graphics cards for seismic wave propagation, Comptes Rendus Mécanique, 339 (2-3) , 125-135, doi: 10.1016/j.crme.2010.11.007, url: http://linkinghub.elsevier.com/retrieve/pii/S1631072110002081
• Carrington, L.; Komatitsch, D.; Laurenzano, M.; Tikir, M.M.; Michea, D.; Goff, N.L.; Snavely, A.; Tromp, J. (2008), High-frequency simulations of global seismic wave propagation using SPECFEM3D_GLOBE on 62K processors, High Performance Computing, Networking, Storage and Analysis, 2008. SC 2008. International Conference for, 1-11, doi: 10.1109/SC.2008.5215501
• Martin, R.; Komatitsch, D.; Blitz, C.; Le Goff, N. (2008), Simulation of seismic wave propagation in an asteroid based upon an unstructured MPI spectral-element method: blocking and non-blocking communication strategies, International Conference on High Performance Computing for Computational Science, 350-363.

If you work on simulations in Southern California, you may be interested in citing one or more of the following:

• Komatitsch, D. (2004), Simulations of Ground Motion in the Los Angeles Basin Based upon the Spectral-Element Method, Bulletin of the Seismological Society of America, 94 (1) , 187-206, doi: 10.1785/0120030077, url: http://bssa.geoscienceworld.org/cgi/doi/10.1785/0120030077
• Krishnan, S. (2006), Case Studies of Damage to Tall Steel Moment-Frame Buildings in Southern California during Large San Andreas Earthquakes, Bulletin of the Seismological Society of America, 96 (4a) , 1523-1537, doi: 10.1785/0120050145, url: http://www.bssaonline.org/cgi/doi/10.1785/0120050145
• Krishnan, S.; Ji, C.; Komatitsch, D.; Tromp, J. (2006), Performance of Two 18-Story Steel Moment-Frame Buildings in Southern California During Two Large Simulated San Andreas Earthquakes, Earthquake Spectra, 22 (4) , 1035-1061, doi: 10.1193/1.2360698, url: http://earthquakespectra.org/doi/abs/10.1193/1.2360698

If you use the 3D Southern California model,you may be interested in citing one or more of the following:

• Suss, M.P.; Shaw, J.H. (2003), P wave seismic velocity structure derived from sonic logs and industry reflection data in the Los Angeles basin, California, Journal of Geophysical Research: Solid Earth, 108 (B3) , 2170, Wiley Online Library, doi: 10.1029/2001JB001628
• Lovely, P.; Shaw, J.H.; Liu, Q.; Tromp, J. (2006), A structural VP model of the Salton Trough, California, and its implications for seismic hazard, Bulletin of the Seismological Society of America, 96 (5) , 1882-1896, Seismological Society of America.
• Hauksson, E. (2000), Crustal structure and seismicity distribution adjacent to the Pacific and North American plate boundary in southern California, Journal of Geophysical Research B, 105 (B6) , 13875-13903, American Geophysical Union.Zhu, L.; Kanamori, H. (2000), Moho depth variation in southern California from teleseismic receiver functions, Journal of Geophysical Research: Solid Earth, 105 (B2) , 2969-2980, Wiley Online Library.
• Dreger, D.S.; Helmberger, D.V. (1990), Broadband modeling of local earthquakes, Bulletin of the Seismological Society of America, 80 (5) , 1162-1179, Seismological Society of America.

If you use anisotropy, you may be interested in citing one or more of the following:

• Chen, M.; Tromp, J. (2007), Theoretical and numerical investigations of global and regional seismic wave propagation in weakly anisotropic earth models, Geophysical Journal International, 168 (3) , 1130-1152, doi: 10.1111/j.1365-246X.2006.03218.x, url: http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.2006.03218.x
• Ji, C. (2005), Rayleigh-Wave Multipathing along the West Coast of North America, Bulletin of the Seismological Society of America, 95 (6) , 2115-2124, doi: 10.1785/0120040180, url: http://bssa.geoscienceworld.org/cgi/doi/10.1785/0120040180
• Chevrot, S.; Favier, N.; Komatitsch, D. (2004), Shear wave splitting in three-dimensional anisotropic media, Geophysical Journal International, 159 (2) , 711-720, doi: 10.1111/j.1365-246X.2004.02432.x, url: http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.2004.02432.x
• Favier, N.; Chevrot, S.; Komatitsch, D. (2004), Near-field influence on shear wave splitting and traveltime sensitivity kernels, Geophysical Journal International, 156 (3) , 467-482, doi: 10.1111/j.1365-246X.2004.02178.x, url: http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.2004.02178.x
• Ritsema, J.; Rivera, L.A.; Komatitsch, D.; Tromp, J.; van Heijst, H.-J. (2002), Effects of crust and mantle heterogeneity on PP/P and SS/S amplitude ratios, Geophysical Research Letters, 29 (10) , 72-1-72-4, doi: 10.1029/2001GL013831, url: http://doi.wiley.com/10.1029/2001GL013831
• Tromp, J.; Komatitsch, D. (2000), Spectral-element simulations of wave propagation in a laterally homogeneous Earth model, Problems in Geophysics for the New Millennium, INGV, 351-372, Ingv.

If you use topography, you may be interested in citing one or more of the following:

• Lee, S.-J.; Komatitsch, D.; Huang, B.-S.; Tromp, J. (2009), Effects of Topography on Seismic-Wave Propagation: An Example from Northern Taiwan, Bulletin of the Seismological Society of America, 99 (1) , 314-325, doi: 10.1785/0120080020, url: http://www.bssaonline.org/cgi/doi/10.1785/0120080020
• Lee, S.-J.; Chan, Y.-C.; Komatitsch, D.; Huang, B.-S.; Tromp, J. (2009), Effects of Realistic Surface Topography on Seismic Ground Motion in the Yangminshan Region of Taiwan Based Upon the Spectral-Element Method and LiDAR DTM, Bulletin of the Seismological Society of America, 99 (2a) , 681-693, doi: 10.1785/0120080264, url: http://www.bssaonline.org/cgi/doi/10.1785/0120080264
• Lee, S.-J.; Chen, H.-W.; Liu, Q.; Komatitsch, D.; Huang, B.-S.; Tromp, J. (2008), Three-Dimensional Simulations of Seismic-Wave Propagation in the Taipei Basin with Realistic Topography Based upon the Spectral-Element Method, Bulletin of the Seismological Society of America, 98 (1) , 253-264, doi: 10.1785/0120070033, url: http://www.bssaonline.org/cgi/doi/10.1785/0120070033
• Godinho, L.; Amado Mendes, P.; Tadeu, A.; Cadena-Isaza, A.; Smerzini, C.; Sanchez-Sesma, F.J.; Madec, R.; Komatitsch, D. (2009), Numerical Simulation of Ground Rotations along 2D Topographical Profiles under the Incidence of Elastic Plane Waves, Bulletin of the Seismological Society of America, 99 (2b) , 1147-1161, doi: 10.1785/0120080096, url: http://www.bssaonline.org/cgi/doi/10.1785/0120080096
• van Wijk, K.; Komatitsch, D.; Scales, J.A.; Tromp, J. (2004), Analysis of strong scattering at the micro-scale, The Journal of the Acoustical Society of America, 115 (3) , 1006, doi: 10.1121/1.1647480, url: http://scitation.aip.org/content/asa/journal/jasa/115/3/10.1121/1.1647480

If you use the C-PML absorbing layer capabilities of the code, please cite at least one article written by the developers of the package, for instance:

• Xie, Z.; Komatitsch, D.; Martin, R.; Matzen, R. (2014), Improved forward wave propagation and adjoint-based sensitivity kernel calculations using a numerically stable finite-element PML, Geophysical Journal International, 198 (3) , 1714-1747, doi: 10.1093/gji/ggu219, url: http://gji.oxfordjournals.org/cgi/doi/10.1093/gji/ggu219
• Xie, Z.; Matzen, R.; Cristini, P.; Komatitsch, D.; Martin, R. (2016), A perfectly matched layer for fluid-solid problems: Application to ocean-acoustics simulations with solid ocean bottoms, jasa, 140 (1) , 165-175, doi: 10.1121/1.4954736

If you use the attenuation (anelastic/viscoelastic) capabilities of the code, please cite at least one article written by the developers of the package, for instance:

• Blanc, E.; Komatitsch, D.; Chaljub, E.; Lombard, B.; Xie, Z. (2016), Highly accurate stability-preserving optimization of the Zener viscoelastic model, with application to wave propagation in the presence of strong attenuation, Geophysical Journal International, 205 (1) , 427-439, doi: 10.1093/gji/ggw024, url: http://gji.oxfordjournals.org/content/205/1/427.abstract

If you use the kernel capabilities of the code, please cite at least one article written by the developers of the package, for instance:

• Tromp, J.; Komatitsch, D.; Liu, Q. (2008), Spectral-element and adjoint methods in seismology, Communications in Computational Physics, 3 (1) , 1-32.
• Peter, D.; Komatitsch, D.; Luo, Y.; Martin, R.; Le Goff, N.; Casarotti, E.; Le Loher, P.; Magnoni, F.; Liu, Q.; Blitz, C.; Nissen-Meyer, T.; Basini, P.; Tromp, J. (2011), Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes: SPECFEM3D Version 2.0 'Sesame', Geophysical Journal International, 186 (2) , 721-739, doi: 10.1111/j.1365-246X.2011.05044.x, url: http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.2011.05044.x
• Liu, Q.; Tromp, J. (2006), Finite-Frequency Kernels Based on Adjoint Methods, Bulletin of the Seismological Society of America, 96 (6) , 2383-2397, doi: 10.1785/0120060041, url: http://www.bssaonline.org/cgi/doi/10.1785/0120060041
• Morency, C.; Luo, Y.; Tromp, J. (2009), Finite-frequency kernels for wave propagation in porous media based upon adjoint methods, Geophysical Journal International, 179 (2) , 1148-1168, doi: 10.1111/j.1365-246X.2009.04332.x, url: http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.2009.04332.x

If you use attenuation, you may be interested in citing one or more of the following:

• Savage, B.; Komatitsch, D.; Tromp, J. (2010), Effects of 3D Attenuation on Seismic Wave Amplitude and Phase Measurements, Bulletin of the Seismological Society of America, 100 (3) , 1241-1251, doi: 10.1785/0120090263, url: http://www.bssaonline.org/cgi/doi/10.1785/0120090263
• Komatitsch, D.; Tromp, J. (2002), Spectral-element simulations of global seismic wave propagation-I. Validation, Geophysical Journal International, 149 (2) , 390-412, doi: 10.1046/j.1365-246X.2002.01653.x, url: http://doi.wiley.com/10.1046/j.1365-246X.2002.01653.x
• Komatitsch, D.; Tromp, J. (1999), Introduction to the spectral element method for three-dimensional seismic wave propagation, Geophysical Journal International, 139 (3) , 806-822, doi: 10.1046/j.1365-246x.1999.00967.x, url: http://doi.wiley.com/10.1046/j.1365-246x.1999.00967.x

If you are not using a regular release, that is you have cloned from master on the github repository, we recommend that you make the following changes to the citation reference:

• substitute the download year, YYYY, for 9999
• substitute the git short hash for the doi: git: GITHASH8
• append the download date: downloaded on DD MON YYYY

For previous versions, please substitute the appropriate version and year in the above.

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