Heiner Igel

(Seismology)

Department of Earth and Environmental Sciences
Geophysics
Munich University
Theresienstr. 41
80333 Munich
Germany

Room: 440
Phone: +49 (89) 2180-4204
Fax: +49 (89) 2180-4205

Publications

• Igel, H., M.-F. Nader, D. Kurrle, A.M. Ferreira, J. Wassermann, and K.U: Schreiber (2011), Observations of Earth's Toroidal Free Oscillations with a Rotation Sensor: The 2011 Magnitude 9.0 Tohoku-Oki Earthquake, Geophys. Res. Lett., doi:10.1029/2011GL049045.
• Kremers, Simon, Andreas Fichtner, Gilbert B. Brietzke, Heiner Igel, Carene Larmat, Lianjie Huang, and Martin Käser (2011), Exploring the potentials and limitations of the time-reversal imaging of finite seismic sources, Solid Earth, 95-105, doi:10.5194/se-2-95-2011.

• Blum, J., H. Igel, and M. Zumberge (2010), Observations of Rayleigh-Wave Phase Velocity and Coseismic Deformation Using an Optical Fiber, Interferometric Vertical Strainmeter at the SAFOD Borehole, California, Bull. Seis. Soc. Amer., 1879 - 1891.
• Fichtner, Andreas, Brian L. N. Kennett, Heiner Igel, and Hans-Peter Bunge (2010), Full waveform tomography for radially anisotropic structure: New insights into present and past states of the Australasian upper mantle, Earth and Planetary Science Letters, 290(3-4), 270-280.
• Kurrle, Dieter, Heiner Igel, Ana Ferreira, Joachim Wassermann, and Ulrich Schreiber (2010), Can we estimate local Love wave dispersion properties from collocated amplitude measurements of translations and rotations ?, Geophysical Research Letters, 37, L04307, doi:10.1029/2009GL042215.
• Pham, D. N., H. Igel, J. de la Puente, M. Käser, and M. A. Schoenberg (2010), Rotational motions in homogeneous anisotropic elastic media, Geophysics, 75(5), D47–D56, doi:10.1190/1.3479489.

• Bernauer, Moritz, Andreas Fichtner, and Heiner Igel (2009), Inferring Earth structure from combined measurements of rotational and translational ground motions, Geophysics, Volume 74(Issue 6), WCD41-WCD47, doi:10.1190/1.3211110.
• Ferreira, A., and H. Igel (2009), Rotational Motions of Seismic Surface Waves in a Laterally Heterogeneous Earth, Bull. Seis. Soc. Amer., 99, 1429-1436.
• Fichtner, Andreas, Heiner Igel, Hans-Peter Bunge, and Brian L. N. Kennett (2009), Simulation and inversion of seismic wave propagation on continental scales based on a spectral-element method, Journal of Numerical Analysis, Industrial and Applied Mathematics, 4(1-2), 11-22.
• Fichtner, Andreas, and Heiner Igel (2009), Sensitivity densities for rotational ground motion measurements, Bull. Seism. Soc. Am., 99, 1302-1314.
• Fichtner, Andreas, Brian L. N. Kennett, Heiner Igel, and Hans-Peter Bunge (2009), Full waveform tomography for upper-mantle structure in the Australasian region using adjoint methods, Geophys. J. Int., 179(3), 1703-1725.
• Ghayamghamian, M.R., R. Nouri, H. Igel, and T. Tobita (2009), The Effect of Torsional Ground Motion on Structural Response: Code Recommendation for Accidental Eccentricity, Bull. Seis. Soc. Amer., 99, 1261-1270.
• Igel, H., M. Käser, and M. Stupazzini (2009), Simulation of Seismic Wave Propagation in Media with Complex Geometries, in Encyclopedia of Complexity and System Science, edited by WHK Lee, Springer Verlag.
• Lee, W.H.K., M. Celebi, M.I. Todorovska, and H. Igel (2009), Introduction to the Special Issue on Rotational Seismology and Engineering Applications, Bull. Seis. Soc. Amer., 99, 945-957.
• Oeser, Jens, Hans-Peter Bunge, Marcus Mohr, and Heiner Igel (2009), Frontiers in Computational Geophysics: simulations of mantle circulation, plate tectonics and seismic wave propagation, in 100 Volumes NNFM and 40 Years Numerical Fluid Mechanics, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 100, edited by E. H. Hirschel and E. Krause, Springer, ISBN: 978-3-540-70804-9.
• Pham, D. N., H. Igel, J. Wassermann, A. Cochard, and U. Schreiber (2009), The effects of tilt on interferometric rotation sensors, BSSA, 99(2B), 1352-1365, doi:10.1785/0120080181.
• Pham, D. N., H. Igel, J. Wassermann, M. Käser, J. de la Puente, and U. Schreiber (2009), Observations and modelling of rotational signals in the P-Coda: constraints on crustal scattering, BSSA, 99(2B), 1315-1332, doi:10.1785/0120080101.
• Schreiber, U., J. Hautmann, A. Velikoseltsev, J. Wassermann, H. Igel, F. Otero, F. Vernon, and P.R. Wells (2009), Ring Laser Measurements of Ground Rotations for Seismology, Bull. Seis. Soc. Amer., 99, 1190-1198.
• Stupazzini, Marco, Josep de la Puente, Chiara Smerzini, Martin Käser, Heiner Igel, and Alberto Castellani (2009), Study of Rotational Ground Motion in the Near-Field Region, Bull. Seis. Soc. Am., 99(2B), 1271-1286, doi:10.1785/0120080153.
• Wang, H., H. Igel, F. Gallovic, and A. Cochard (2009), Source and Basin Effects on Rotational Ground Motions: Comparison with Translations, Bull. Seis. Soc. Amer., 99, 1162-1173.

• De la Puente, Josep, Michael Dumbser, Martin Käser, and Heiner Igel (2008), Discontinuous Galerkin Methods for Wave Propagation in Poroelastic Media, Geophysics, 73(5), T77-T97, doi:10.1190/1.2965027.
• Fichtner, Andreas, and Heiner Igel (2008), Efficient numerical surface wave propagation through the optimization of discrete crustal models - a technique based on non-linear dispersion curve matching (DCM), Geophys. J. Int., 173(2), 519-533.
• Wang, H., H. Igel, A. Cochard, and M. Ewald (2008), Quantifying Uncertainties in Earthquake Scenario Ground Motion Calculations: Finite Source Effects, Springer.

• De la Puente, J., M. Käser, M. Dumbser, and H. Igel (2007), An Arbitrary High Order Discontinuous Galerkin Method for Elastic Waves on Unstructured Meshes IV: Anisotropy, Geophysical Journal International, 169(3), 1210-1228, doi:10.1111/j.1365-246X.2007.03381.x.
• Dumbser, M., M. Käser, and J. de la Puente (2007), Arbitrary High Order Finite Volume Schemes for Seismic Wave Propagation on Unstructured Meshes in 2D and 3D, Geophysical Journal International, 171(2), 665-694, doi:10.1111/j.1365-246X.2007.03421.x.
• Evans, J. R., et al. (2007), Rotational seismology workshop of February 2006, U.S. Geol. Surv. Open File Rep., 2007-1145.
• Gallovic, F., R. Barsch, J. de la Puente, and H. Igel (2007), Digital Library for Computational Seismology, Eos Trans. AGU, 88(50).
• Igel, H., A. Cochard, J. Wassermann, A. Flaws, U. Schreiber, A. Velikoseltsev, and D. N. Pham (2007), Broad-band observations of earthquake-induced rotational ground motions, Geophys. J. Int, 168(1), 182–196, doi:10.1111/j.1365-246X.2006.03146.x.
• Igel, Heiner, Alain Cochard, Joachim Wassermann, Asher Flaws, Ulrich Schreiber, Alex Velikoseltsev, and Nguyen Pham Dinh (2007), Broad-band observations of earthquake-induced rotational ground motions, Geophysical Journal International, 168(1), 182-197, doi:10.1111/j.1365-246X.2006.03146.x.
• Käser, M., M. Dumbser, J. de la Puente, and H. Igel (2007), An Arbitrary High Order Discontinuous Galerkin Method for Elastic Waves on Unstructured Meshes III: Viscoelastic Attenuation, Geophysical Journal International, 168(1), 224-242, doi:10.1111/j.1365-246X.2006.03193.x.
• Lee, William HK, Heiner Igel, Maria Todorovska, and John Evans (2007), Rotational Seismology; AGU Session, Working Group, and Website, Technical Report 2007-1263, U.S. Geological Survey.
• Moder, Christoph, Hans-Peter Bunge, Heiner Igel, and Bernhard Schuberth (2007), Visualization in the Geosciences with Paraview and Geowall, in Proceedings of the 4th High-End Visualization Workshop, edited by Werner Benger, René Heinzl, Wolfgang Kapferer, Wolfram Schoor, Mayank Tyagi, Shalini Venkataraman and Gunther Weber, pp. 147-155, Lehmanns Media, Berlin, ISBN: 9783865412164.
• Moder, Christoph, Hans-Peter Bunge, Heiner Igel, and Bernhard Schuberth (2007), Visualization of large datasets with Paraview, in 67. Jahrestagung der Deutschen Geophysikalischen Gesellschaft, Aachen, 26.03. - 29.03.2007.
• Schuberth, B., A. Piazzoni, H. Bunge, H. Igel, G. Steinle-Neumann, C. Moder, and J. Oeser (2007), Self-consistent Synthetic Mantle Discontinuities From Joint Modeling of Geodynamics and Mineral Physics and Their Effects on the 3D Global Wave Field, in American Geophysical Union, Fall Meeting 2007, abstract #U34A-04, pp. B9+.

• Moczo, P., J.P. Ampuero, J. Kristek, S.M. Day, M. Kristekova, P. Pazak, M. Galis, and H. Igel (2006), Comparison of Numerical Methods for Seismic Wave Propagation and Source Dynamics - the SPICE Code Validation, International Symposium on the Effects of Surface Geology on Seismic Motion, 3(62), Grenoble, France.
• Wang, H., H. Igel, A. Cochard, and M. Ewald (2006), Variations of peak ground motions due to slip histories: Application to the Newport Inglewood fault, Los Angeles Basin, International Symposium on the Effects of Surface Geology on Seismic Motion, 3, Grenoble, France.
• Cochard, A., H. Igel, B. Schuberth, W. Suryanto, A. Velikoseltsev, U. Schreiber, J. Wassermann, F. Scherbaum, and D. Vollmer (2006), Rotational motions in seismology: theory, observations, simulation, in Earthquake source asymmetry, structural media and rotation effects, edited by Teisseyre et al., Springer Verlag.
• Evans, J.R., et al. (2006), A Workshop on Rotational Ground Motion, Seis. Res. Lett., submitted.
• Ewald, M., H. Igel, K.-G. Hinzen, and F. Scherbaum (2006), Basin-related effects on ground motion for earthquake scenarios in the Lower Rhine Embayment, Geophys. J. Int., 166, 197-212.
• Ewald, M. (2006), Numerical Simulations of Earthquake Scenarios in the Lower Rhine Embayment Area: Numerische Simulation von Erdbebenszenarien im Raum der Niederrheinischen Bucht, LMU Munich: Faculty of Geosciences.
• Fichtner, A., H.-P. Bunge, and H. Igel (2006), The adjoint method in seismology: I - Theory, Physics of The Earth and Planetary Interiors, 157(1-2), 86-104, doi:10.1016/j.pepi.2006.03.016.
• Fichtner, A., P. Bunge, and H. Igel (2006), The adjoint method in seismology: II - Applications: traveltimes and sensitivity functionals, Phys. Earth Planet. Int., 157(1-2), 105-123, doi:10.1016/j.pepi.2006.03.018.
• Hainzl, S., T. Kraft, J. Wassermann, and H. Igel (2006), Evidence for rain-triggered earthquake activity, Geophys. Res. Lett., 33, L19303, doi:10.1029/2006GL027642.
• Jahnke, G., M.S. Thorne, A. Cochard, and H. Igel (2006), Global SH-wave propagation using a parallel axi-symmetric finite-difference scheme, Geophysical Journal International, submitted.
• Käser, M., H. Igel, J. de la Puente, B. Schuberth, and H.P. Bunge (2006), Erdbebenforschung durch Höchstleistungsrechnen, Technical Report 02/2006, Bayerische Akademie der Wissenschaften - Akademie Aktuell.
• Kraft, T., J. Wassermann, and H. Igel (2006), High-precision relocation and focal mechanism of the 2002 rain-triggered earthquake swarms at Mt. Hochstaufen, SE-Germany, Geophys. J. Int., 167(3), 1513-1528, doi:10.1111/j.1365-246X.2006.03171.x.
• Kraft, T., J. Wassermann, E. Schmedes, and H. Igel (2006), Meteorological triggering of earthquake swarms at Mt. Hochstaufen, SE-Germany, Tectonophysics, 424(3-4), 245-258, doi:10.1016/j.tecto.2006.03.044.
• Schreiber, U., G. Stedman, H. Igel, and A. Flaws (2006), Ring Laser Gyroscopes as Rotation Sensors for Seismic Wave Studies, in Earthquake source asymmetry, structural media and rotation effects, edited by Teisseyre R., Takeo M. and Majewski E., Springer Verlag.
• Suryanto, W., H. Igel, A. Cochard, J. Wassermann, U. Schreiber, and A. Velikoseltsev (2006), Love-Wave dispersion from collocated measurements of rotations and translations, Geophys. Res. Lett., submitted.
• Suryanto, W., J. Wassermann, H. Igel, A. Cochard, D. Vollmer, F. Scherbaum, A. Velikoseltsev, and U. Schreiber (2006), First comparison of seismic array derived rotations with direct ring laser measurements of rotational ground motion, Bull. Seism. Soc. Am., 96(6), 2059-2071, doi:10.1785/0120060004.
• Suryanto, W., J. Wassermann, H. Igel, A. Cochard, D. Vollmer, B. Schuberth, F. Scherbaum, A. Velikoseltsev, and U. Schreiber (2006), First comparison of seismic array derived rotations with direct ring laser measurements of rotational ground motion, Bull. Seism. Soc. Am., 96(6), 2059-2071, doi:10.1785/0120060004.
• Thorne, M., T. Lay, E. Garnero, G. Jahnke, and H. Igel (2006), 3-D Seismic Imaging of the D" region beneath the Cocos Plate, Geophys. J. Int., submitted.

• Favata, F., and A. Gimenez (2005), 39th ESLAB Symposium Long lived martian geoscience observatory, Noordwijk, 39, Long lived martian geoscience observatory.
• Igel, H., U. Schreiber, A. Flaws, B. Schuberth, A. Velikoseltsev, and A. Cochard (2005), Rotational motions induced by the M8.1 Tokachi-oki earthquake, September 25, 2003, Geophys. Res. Lett., 32, L08309, doi:10.1029/2004GL022336.
• Igel, H. (2005), Ein Beben erschüttert die Welt, Technik in Bayern.
• Kraft, T., J. Wassermann, H. Igel, and E. Schmedes (2005), The 2002 Hochstaufen, SE-Germany, earthquake swarm: Cluster analysis and high precision event location, in DDG, 65. Jahrestagung, vol. SOp17, Graz, Austria.
• Kraft, T., J. Wassermann, E. Schmedes, and H. Igel (2005), The Hochstaufen project: Earthquake swarms triggered by intense rainfall?, in EGU, 2nd General Assembly 2005, Vienna, Austria, pp. EGU05–A–08617.
• Schreiber, U., H. Igel, A. Cochard, A. Velikoseltsev, A. Flaws, B. Schuberth, W. Drewitz, and F. Müller (2005), The GEOsensor Project: a new observable for seismology, in Geotechnologien, edited by BMBF, Springer Verlag.
• Schuberth, B., M. Ewald, H. Igel, M. Treml, H. Wang, and G. Brietzke (2005), Computational Seismology: Narrowing the Gap Between Theory and Observations, in High Performance Computing in Science and Engineering, Garching 2004, edited by A. Bode and F. Durst, pp. 251-262, Springer Verlag, ISBN: 978-3-540-26145-2.
• Schuberth, B., and H. Igel (2005), Challenges in Computational Seismology, inSiDE, 3(1), 6-9, ed. German Supercomputing Facilities HLRS, LRZ and NIC.

• Brietzke, G., H. Igel, G. Jahnke, M. Treml, M. Ewald, H. Wang, A. Cochard, and G. Wang (2004), Computational wave propagation: advances in global and regional seismology, in High-Performance Computing in Science and Engineering, Springer Verlag.
• Fohrmann, M., H. Igel, G. Jahnke, and Y. Ben-Zion (2004), Guided Waves from Sources Outside Faults: An Indication for Shallow Fault Zone Structure?, Pure appl. geophysics, 161, 2125-2137, doi:10.1007/s00024-004-2553-y.
• Igel, H., and Team SPICE (2004), New European Training Network to Improve Young Scientists' Capabilities in Computational Wave Propagation, EOS, Transactions of the American Geophysical Union, 85(28).
• Kraft, T., E. Schmedes, and H. Igel (2004), Seismo-meteorological monitoring of an earthquake swarm, in EGU, 1st General Assembly, vol. EGU04-A-04410, Nice, France.
• Kraft, T., J. Wassermann, E. Schmedes, and H. Igel (2004), Observations of induced seismicity near Bad Reichenhall, SE-Germany., in ESC, XXIX General Assembly, Potsdam, Germany, vol. SCC-2, pp. 146.
• Wang, G.-Q., D. M. Boore, H. Igel, and X.-Y. Zhou (2004), Comparisons of ground motions from five aftershocks of the 1999 Chi-Chi, Taiwan earthquake with empirical predictions largely based on data from California, Bull. Seism. Soc. Am., 94(6), 2198-2212.

• Ionescu, D., and H. Igel (2003), Transparent Boundary Conditions for Wave Propagation on Unbounded Domains, in Lecture Notes in Computer Science, vol. Vol. 2659, pp. 807-816, Springer Verlag.
• Kraft, T., E. Schmedes, and H. Igel (2003), A new study on the influence of fluid related and meteorological parameters on the behavior of earthquake swarms., in 29. Sitzung der AG-Seismologie, Fürstenfeldbruck, Germany.
• Ripperger, J., H. Igel, and J. Wassermann (2003), Seismic wave simulation in the presence of real volcano topography, J. Volcanol. Geotherm. Res., 128(1-3), 31-44.
• Schmedes, E., T. Kraft, and H. Igel (2003), Das Bayern-Netz: Erdbebenüberwachung in Bayern, in 29. Sitzung der AG-Seismologie, Fürstenfeldbruck, Germany.
• Schreiber, K. U., A. Velikoseltsev, H. Igel, A. Cochard, A. Flaws, W. Drewitz, and F. Müller (2003), The GEOsensor: A new instrument for seismology, in GEOTECHNOLOGIEN Science Report No. 3: “Observation of the System Earth from Space”, Status Seminar, Bavarian State Mapping Agency (BLVA), Munich, 12-13 June 2003, Programme & Abstracts.
• Wang, G.-Q, D. M. Boore, H. Igel, and X. Y. Zhou (2003), Some observations on colocated and closely-spaced strong ground motion records of the 1999, Chi-Chi, Taiwan Earthquake, Bull. Seism. Soc. Am., 93(2), 674-693.

• Fohrmann, M., H. Igel, G. Jahnke, and Y. Ben-Zion (2002), Guided waves from sources outside faults: an indication for shallow fault zone structure?, in Proceedings of 3rd ACES Workshop 2002, Geoprint, ISBN: 0-9750394-0-7.
• Igel, H., G. Brietzke, M. Ewald, M. Fohrmann, G. Jahnke, T. Nissen-Meyer, J. Ripperger, M. Strasser, M. Treml, and G. Wang (2002), 3-D Seismic Wave Propagation on a Global and Regional Scale: Earthquakes, Fault Zones, Volcanoes, in High Performance Computing in Science and Engineering 2002. Transactions of the First Joint HLRB and KONWIHR Result and Reviewing Workshop, October 10th and 11th, 2002, Technical University of Munich, HPC in Science and Engineering, Springer.
• Igel, H., G. Jahnke, and Y. Ben-Zion (2002), Numerical Simulation of Fault Zone Guided Waves: Accuracy and 3-D Effects, Pure and Applied Geophysics, 9(2067-2083), doi:2002PApGe.159.2067I.
• Igel, H., G. Jahnke, and Y. Ben-Zion (2002), Numerical simulation of fault zone trapped waves: accuracy and 3-D effects, Pure Appl. Geophys., 159, 2067-2083.
• Igel, H., T. Nissen-Meyer, and G. Jahnke (2002), Wave propagation in 3D spherical sections. Effects of subduction zones, Phys. Earth Planet. Int., 132(1-3), 219-234.
• Igel, H., and others (2002), 3D Seismic Wave Propagation on a Global and Regional Scale: Earthquakes, Fault Zones, Volcanoes, in High Performance Computing in Science and Engineering, Springer Verlag, Heidelberg, ISBN 3-540-00474-2.
• Igel, H. (2002), Erdbeben und die Struktur des tiefen Erdinnern, Einsichten.
• Jahnke, G., H. Igel, and Y. Ben-Zion (2002), Three-dimensional calculations of fault zone guided waves in various irregular structures, Geophys. J. Int., 151(2), 416-426.
• Kraft, T., E. Schmedes, H. Igel, P. Danecek, and J. Ripperger (2002), The swarmquake area Bad Reichenhall, southeast Germany., in EGS, XXVII General Assembly, vol. EGS02-A-04914, Nice, France.
• Kraft, T., E. Schmedes, and H. Igel (2002), Erdbebenschwärme in Bayern, wir sind auf der Jagd nach ihnen., in Münchner Wissenschaftstage, Lebendige Erde, München, Germany.
• Wang, G.-Q, X. Y. Zhou, P. Z. Zhang, and H. Igel (2002), Characteristics of amplitude and duration for near fault strong ground motion from the 1999 Chi-Chi, Taiwan, Earthquake, Soil Dyn. Earthquake Eng., 22, 73-96.

• Käser, M., H. Igel, M. Sambridge, and J. Braun (2001), A Comparative Study of Explicit Differential Operators on Arbitrary Grids, Journal of Computational Acoustics, 9(3), 1111-1125, doi:10.1142/S0218396X01000838.
• Käser, M., and H. Igel (2001), Numerical simulation of 2D wave propagation on unstructured grids using explicit differential operators, Geophysical Prospecting, 49(5), 607-619, doi:10.1046/j.1365-2478.2001.00276.x.
• Lang, O., H. Igel, B. Rabus, S. Dech, and R. Bamler (2001), Einsatz interferometrischer Radarfernerkundung zur Erfassung von Naturkatastrophen, Petermanns Geographische Mitteilungen, 28-36.
• Nissen-Meyer, T., G. Brietzke, and H. Igel (2001), Numerische Simulationen von Wellenausbreitung in seismisch aktiven Zonen, KONWIHR Quarterly, 31(3).

• Igel, H., N. Takeuchi, R. J. Geller, C. Megnin, H.P. Bunge, E. Clevede, J. Dalkolmo, and B. Romanowicz (2000), The COSY Project: verification of global seismic modeling algorithms, Phys. Earth Planet. Int., 119(1-2), 3-23.
• Thomas, C., H. Igel, M. Weber, and F. Scherbaum (2000), Acoustic simulation of P-wave propagation in a heterogeneous spherical Earth: numerical method and application to precursor waves to PKPdf, Geophys. J. Int., 141(2), 307-320.

• Igel, H. (1999), Wave propagation in spherical sections by the Chebyshev spectral method, Geophys. J. Int., 136(3), 559-566.

• Igel, H., Y. Ben-Zion, and P. C. Leary (1997), Simulation of SH- and P-SV wave propagation in fault zones, Geophys. J. Int., 128(3), 533-546.
• Igel, H., and O. Gudmundsson (1997), Frequency-dependent effects on travel times and waveforms of long-period S waves: implications for the scale of mantle heterogeneity, Phys. Earth Plan. Int., 104(1-3), 229-246.
• Igel, H., and J. Ita (1997), The effects of subduction zones on teleseismic SH waves: a numerical study, in Upper Mantle Heterogeneities from Active and Passive Seismology, edited by K. Fuchs, pp. 333-341, Kluwer Academic Publishers.

• Igel, H., H. Djikpesse, and A. Tarantola (1996), Waveform inversion of marine reflection seismograms for P-impedance and Poisson's ratio, Geophys. J. Int., 124(2), 363-371.
• Igel, H., and M. Weber (1996), P-SV wave propagation in the Earth's mantle using finite differences: Application to heterogeneous lowermost mantle structure, Geophys. Res. Lett., 23, 415-418.

• Igel, H., P. Mora, and B. Riollet (1995), Anisotropic wave propagation through FD grids, Geophysics, 60(4), 1203-1216.
• Igel, H., and M. Weber (1995), SH-wave propagation in the whole mantle using high-order finite differences, Geophys. Res. Lett., 22(6), 731-734.