A critical appraisal of asymptotic 3D-to-2D data transformation in full-waveform seismic crosshole tomography

ABSTRACTSeismic full-waveform inversion (FWI) is often based on forward modeling in the computationally attractive 2D domain. This implies the assumption of a line source extended in the out-of-plane medium invariant direction, with far-field amplitudes decaying inversely with the square root of distance. Realistic point sources, however, generate amplitudes that decay approximately with the inverse of distance. Conventionally, practitioners correct for this amplitude difference and the associated phase shift by transforming the recorded 3D field data to the approximate 2D equivalent by using simplistic asymptotic filter algorithms. Such filters assume straight raypaths, a constant velocity medium, and far-field recordings. We have assessed the validity of 3D-to-2D data transformation in the context of crosshole seismic full-waveform tomography by propagating 3D and 2D wavefields through 2D media and comparing 2D reference synthetics with their filtered 3D equivalent. The filter performs well in simple si...

[1]  Olaf Schenk,et al.  Solving unsymmetric sparse systems of linear equations with PARDISO , 2004, Future Gener. Comput. Syst..

[2]  Fuchun Gao,et al.  Integrating 3D Full Waveform Inversion Into Depth Imaging Projects , 2011 .

[3]  Johan O. A. Robertsson,et al.  Finite-difference modeling of wave propagation in a fluid-solid configuration , 2002 .

[4]  Bing Zhou,et al.  Computing the Sensitivity Kernels for 2.5-D Seismic Waveform Inversion in Heterogeneous, Anisotropic Media , 2011 .

[5]  Hansruedi Maurer,et al.  Frequency and spatial sampling strategies for crosshole seismic waveform spectral inversion experiments , 2009 .

[6]  Stefano Marelli,et al.  Receiver-coupling effects in seismic waveform inversions , 2012 .

[7]  R. Clayton,et al.  Finite-difference seismograms for SH waves , 1985 .

[8]  2D Acoustic Full Waveform Inversion of a Land Seismic Line , 2010 .

[9]  F. Wenzel,et al.  Simulating three-dimensional seismograms in 2.5-dimensional structures by combining two-dimensional finite difference modelling and ray tracing , 2008 .

[10]  S. Marelli,et al.  Validity of the acoustic approximation in full-waveform seismic crosshole tomography , 2012 .

[11]  P. Williamson,et al.  Frequency-domain acoustic-wave modeling and inversion of crosshole data; Part 1, 2.5-D modeling method , 1995 .

[12]  S. Greenhalgh,et al.  Crosshole seismic inversion with normalized full‐waveform amplitude data , 2003 .

[13]  Jean Virieux,et al.  Velocity model building by 3D frequency-domain, full-waveform inversion of wide-aperture seismic data , 2008 .

[14]  Z. Bing,et al.  Crosshole acoustic velocity imaging with full-waveform spectral data: 2.5-D numerical simulations , 1998 .

[15]  R. Pratt,et al.  Reflection waveform inversion using local descent methods: Estimating attenuation and velocity over a gas-sand deposit , 2001 .

[16]  Yibing Zheng,et al.  Anisotropic Perfectly Matched Layers for Elastic Waves in Cartesian and Curvilinear Coordinates , 2002 .

[17]  Binzhong Zhou,et al.  Radio frequency tomography trial at Mt Isa Mine , 1998 .

[18]  N. Bleistein Two-and-One-Half Dimensional In-Plane Wave Propagation. , 1984 .

[19]  A. Tarantola Inversion of seismic reflection data in the acoustic approximation , 1984 .

[20]  Jean Virieux,et al.  Uniform asymptotic conversion of Helmholtz data from 3D to 2D , 2012 .

[21]  S. Greenhalgh,et al.  Wavenumber Sampling Issues in 2.5D Frequency Domain Seismic Modelling , 2011, Pure and Applied Geophysics.

[22]  M. Abramowitz,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[23]  S. Greenhalgh,et al.  2.5-D acoustic wave modelling in the frequency-wavenumber domain , 1997 .

[24]  W. Rodi,et al.  Nonlinear waveform tomography applied to crosshole seismic data , 1996 .

[25]  Mark Noble,et al.  Robust elastic nonlinear waveform inversion: Application to real data , 1990 .

[26]  Cengiz Esmersoy,et al.  Reverse-time wave-field extrapolation, imaging, and inversion , 1988 .

[27]  S. Deregowski,et al.  A THEORY OF ACOUSTIC DIFFRACTORS APPLIED TO 2-D MODELS* , 1983 .

[28]  Denes Vigh,et al.  3D prestack plane-wave, full-waveform inversion , 2008 .

[29]  H. Maurer,et al.  Stochastic regularization: Smoothness or similarity? , 1998 .

[30]  S. Greenhalgh,et al.  Wavenumber sampling strategies for 2.5-D frequency-domain seismic wave modelling in general anisotropic media , 2012 .

[31]  Hiroshi Takenaka,et al.  Quasi-cylindrical 2.5D wave modeling for large-scale seismic surveys , 2003 .

[32]  A. Levander,et al.  A stochastic view of lower crustal fabric based on evidence from the Ivrea Zone , 1992 .

[33]  P. Mora Nonlinear two-dimensional elastic inversion of multioffset seismic data , 1987 .

[34]  R. Pratt Seismic waveform inversion in the frequency domain; Part 1, Theory and verification in a physical scale model , 1999 .

[35]  Y. Kravtsov,et al.  Geometrical optics of inhomogeneous media , 2019, Geometrical Optics of Weakly Anisotropic Media.

[36]  A. Tarantola A strategy for nonlinear elastic inversion of seismic reflection data , 1986 .

[37]  Zhou Bing,et al.  Explicit expressions and numerical calculations for the Fréchet and second derivatives in 2.5D Helmholtz equation inversion , 1999 .

[38]  A. Chopra,et al.  Perfectly matched layers for time-harmonic elastodynamics of unbounded domains : Theory and finite-element implementation , 2003 .

[39]  S. Operto,et al.  Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion , 2009 .

[40]  A. Pica,et al.  Nonliner inversion of seismic reflection data in a laterally invariant medium , 1990 .

[41]  Lúcio T. Santos,et al.  2.5D finite‐difference solution of the acoustic wave equation , 2005 .

[42]  Thomas Bohlen,et al.  Paralel 3-D viscoelastic finite difference seismic modelling , 2002 .

[43]  M. Warner,et al.  Anisotropic 3D full-waveform inversion , 2013 .

[44]  J. Hole,et al.  Applying waveform inversion to wide-angle seismic surveys , 2009 .

[45]  A. Fichtner Full Seismic Waveform Modelling and Inversion , 2011 .

[46]  Jacques R. Ernst,et al.  Application of a new 2D time-domain full-waveform inversion scheme to crosshole radar data , 2007 .

[47]  R. Shipp,et al.  Two-dimensional full wavefield inversion of wide-aperture marine seismic streamer data , 2002 .

[48]  Vlastislav Cerveny,et al.  Seismic Ray Theory , 2003 .

[49]  R. Pratt,et al.  Short Note A critical review of acoustic wave modeling procedures in 2.5 dimensions , 1995 .

[50]  D. J. Verschuur,et al.  Amplitude preprocessing of single and multicomponent seismic data , 1992 .

[51]  Niklas Linde,et al.  Full-waveform inversion of cross-hole ground-penetrating radar data to characterize a gravel aquifer close to the Thur River, Switzerland , 2010 .

[52]  Klaus Holliger,et al.  Inversion of crosshole seismic data in heterogeneous environments: Comparison of waveform and ray-based approaches , 2009 .

[53]  Norman Bleistein,et al.  Mathematical Methods for Wave Phenomena , 1984 .

[54]  S. Greenhalgh,et al.  Exploitation of data-information content in elastic-waveform inversions , 2012 .