Waveform inversion in triclinic anisotropic media—a resolution study

Seismic full waveform inversion (FWI) has been applied to simple elastic problems with certain symmetries, such as isotropic, transverse isotropic or vertical transversely isotropic media. In this study, the FWI concept is extended to the most general anisotropic case with 21 independent elastic material parameters and no symmetry plane (triclinic). Beside a short description of the 3-D finite-difference scheme to solve the forward problem and the FWI optimization algorithm, we present a sensitivity study for a simple anisotropic medium. This test problem consists of a homogenous triclinic anisotropic full space, which contains 21 spatially separated spheres. In each sphere one component of the elastic tensor deviates by 5 per cent from the background medium. The resolution of the different spheres, ambiguities between the different elastic parameters, as well as the effect of the acquisition geometry can be systematically investigated. Due to the high computational costs of the triclinic forward problem a few compromises have to be made regarding the acquisition geometries. Point sources are replaced by plane wave sources which lead to a limitation of incidence angles and therefore a strong decrease in resolution of the nondiagonal elastic tensor components. It is shown that, despite these limitations, a tomographic acquisition geometry would be able to resolve to some extent a monoclinic symmetry via FWI. Restricting the acquisition geometries (e.g. VSP combined with reflection seismic or reflection seismic only) significantly reduces the number of resolvable tensor elements in strict dependence of the covered incidence angles.

[1]  S. Siegesmund,et al.  Characterization of crack distribution: fabric analysis versus ultrasonic inversion , 2000 .

[2]  Changsoo Shin,et al.  Efficient calculation of a partial-derivative wavefield using reciprocity for seismic imaging and inversion , 2001 .

[3]  Ludovic Métivier,et al.  Multi-Parameter FWI - An Illustration of the Hessian Operator Role for Mitigating Trade-off between Parameter Classes , 2014 .

[4]  D. Min,et al.  Full waveform inversion strategy for density in the frequency domain , 2012 .

[5]  A. Morelli.  Inverse Problem Theory , 2010 .

[6]  A. Kurzmann.  Applications of 2D and 3D full waveform tomography in acoustic and viscoacoustic complex media , 2012 .

[7]  R. Plessix,et al.  Frequency-domain finite-difference amplitude-preserving migration , 2004 .

[8]  R. Plessix,et al.  Thematic Set: Full waveform inversion of a deep water ocean bottom seismometer dataset , 2010 .

[9]  Clara Castellanos Lopez.  Speed up and regularization techniques for seismic full waveform inversion , 2014 .

[10]  Ludovic Métivier,et al.  A guided tour of multiparameter full-waveform inversion with multicomponent data: From theory to practice , 2013 .

[11]  D. Köhn,et al.  On the influence of model parametrization in elastic full waveform tomography , 2012 .

[12]  Erik H. Saenger,et al.  Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid , 2004 .

[13]  S. Operto,et al.  Toward Gauss-Newton and Exact Newton Optimization for Full Waveform Inversion , 2012 .

[14]  Dong-Joo Min,et al.  Frequency-domain elastic full waveform inversion for VTI media , 2010 .

[15]  S. Operto,et al.  Which parameterization is suitable for acoustic vertical transverse isotropic full waveform inversion? Part 2: Synthetic and real data case studies from Valhall , 2013 .

[16]  R. Pratt,et al.  Waveform-based simulated annealing of crosshole transmission data: A semi-global method for estimating seismic anisotropy , 2014 .

[17]  S. Operto,et al.  Fast full waveform inversion with source encoding and second-order optimization methods , 2015 .

[18]  S. Shapiro,et al.  Modeling the propagation of elastic waves using a modified finite-difference grid , 2000 .

[19]  W. Rabbel,et al.  Shear wave anisotropy of laminated lower crust at the Urach geothermal anomaly , 1996 .

[20]  C. Bunks,et al.  Multiscale seismic waveform inversion , 1995 .

[21]  D. Komatitsch,et al.  An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation , 2007 .

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

[23]  T. Bohlen,et al.  Recovering Shear-wave Anisotropy of the Lower Crust: The Influence of Systematic Errors on Travel-time Inversion , 1999 .

[24]  René-Édouard Plessix,et al.  A parametrization study for surface seismic full waveform inversion in an acoustic vertical transversely isotropic medium , 2011 .

[25]  Ludovic Métivier,et al.  Full Waveform Inversion and the Truncated Newton Method , 2013, SIAM J. Sci. Comput..

[26]  Marwan Charara,et al.  Feasibility study for an anisotropic full waveform inversion of cross‐well seismic data , 2008 .

[27]  R. Plessix.  A review of the adjoint-state method for computing the gradient of a functional with geophysical applications , 2006 .

[28]  Olaf Kolditz,et al.  Impacts of the use of the geological subsurface for energy storage: an investigation concept , 2013, Environmental Earth Sciences.

[29]  W. Rabbel,et al.  Seismic Exploration of the Deep Continental Crust , 1999 .

[30]  Denes Vigh,et al.  3D Full waveform inversion on a Gulf of Mexico WAZ data set , 2010 .

[31]  Heiner Igel,et al.  Anisotropic wave propagation through finite-difference grids , 1995 .

[32]  Ying Ji,et al.  Anisotropy from full waveform inversion of multicomponent seismic data using a hybrid optimization method , 2005 .

[33]  Romain Brossier,et al.  On the footprint of anisotropy on isotropic full waveform inversion: the Valhall case study , 2011 .

[34]  Qinya Liu,et al.  Tomography, Adjoint Methods, Time-Reversal, and Banana-Doughnut Kernels , 2004 .

[35]  Ludovic Métivier,et al.  Fast Full Waveform Inversion with Source Encoding and Second Order Optimization Methods , 2013 .

[36]  Ludovic Métivier,et al.  Two-dimensional permittivity and conductivity imaging by full waveform inversion of multioffset GPR data: a frequency-domain quasi-Newton approach , 2014 .

[37]  J. Krebs,et al.  Fast full-wavefield seismic inversion using encoded sources , 2009 .

[38]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[39]  Jean Virieux,et al.  An overview of full-waveform inversion in exploration geophysics , 2009 .

[40]  Ludovic Métivier,et al.  Full waveform inversion and the truncated Newton method: quantitative imaging of complex subsurface structures , 2014 .

[41]  J. Tromp,et al.  Principal component analysis of anisotropic finite-frequency sensitivity kernels , 2009 .

[42]  S. Operto,et al.  Which parameterization is suitable for acoustic vertical transverse isotropic full waveform inversion? Part 1: Sensitivity and trade-off analysis , 2013 .

[43]  T. Bohlen,et al.  Seismic Velocities and Anisotropy of the Lower Continental Crust: A Review , 1999 .

[44]  Romain Brossier,et al.  Two-dimensional frequency-domain visco-elastic full waveform inversion: Parallel algorithms, optimization and performance , 2011, Comput. Geosci..

[45]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[46]  W. Rabbel,et al.  Seismic lamination and anisotropy of the Lower Continental Crust , 2006 .

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

[48]  C. Edward.  High-order (space And Time) Finite-difference Modeling of the Elastic Wave Equation , 1990 .