@article{fdi:010063616,
  title = {{C}omputationally efficient three-dimensional acoustic finite-difference frequency-domain seismic modeling in vertical transversely isotropic media with sparse direct solver},
  author = {{O}perto, {S}. and {B}rossier, {R}. and {C}ombe, {L}. and {M}etivier, {L}. and {R}ibodetti, {A}lessandra and {V}irieux, {J}.},
  editor = {},
  language = {{ENG}},
  abstract = {{T}he computational burden of frequency-domain full-waveform inversion ({FWI}) of wide-aperture fixed-spread data is conventionally reduced by limiting the inversion to a few discrete frequencies. {I}n this framework, frequency-domain seismic modeling is performed efficiently for multiple sources by solving the linear system resulting from the discretization of the time-harmonic wave equation with the massively parallel sparse direct solver. {F}requency-domain seismic modeling based on the sparse direct solver ({DSFDM}) requires specific design finite-difference stencils of compact support to minimize the computational cost of the lower-upper decomposition of the impedance matrix in terms of memory demand and floating-point operations. {A} straightforward adaptation of such finite-difference stencil, originally developed for the (isotropic) acoustic-wave equation, is proposed to introduce vertical transverse isotropy ({VTI}) in the modeling without any extra computational cost. {T}he method relies on a fourth-order wave equation, which is decomposed as the sum of a second-order elliptic-wave equation plus an anellipticity correction term. {T}he stiffness matrix of the elliptic-wave equation is easily built from the isotropic stiffness matrix by multiplying its coefficients with factors that depend on {T}homsen's parameters, whereas the anelliptic term is discretized with a parsimonious second-order staggered-grid stencil. {V}alidation of {DSFDM} against finite-difference time-domain modeling performed in various synthetic models shows that a discretization rule of four grid points per minimum wavelength provides accurate {DSFDM} solutions. {M}oreover, comparison between real data from the {V}alhall field and {DSFDM} solutions computed in a smooth {VTI} subsurface model supports that the method can be used as a fast and accurate modeling engine to perform multiparameter {VTI} {FWI} of fixed-spread data in the viscoacoustic approximation.},
  keywords = {},
  booktitle = {},
  journal = {{G}eophysics},
  volume = {79},
  numero = {5},
  pages = {{T}257--{T}275},
  ISSN = {0016-8033},
  year = {2014},
  DOI = {10.1190/geo2013-0478.1},
  URL = {https://www.documentation.ird.fr/hor/fdi:010063616},
}