Marwan Charara

The domain of applicability of acoustic full-waveform inversion for marine seismic data

Marine reflection seismic data inversion is a compute-intensive process, especially in three dimensions. Approximations often are made to limit the number of physical parameters we invert for, or to speed up the forward modeling. Because the data often are dominated by unconverted P-waves, one popular approximation is to consider the earth as purely acoustic, i.e., no shear modulus. The material density sometimes is taken as a constant. Nonlinear waveform seismic inversion consists of iteratively minimizing the misfit between the amplitudes of the measured and the modeled data. Approximations, such as assuming an acoustic medium, lead to incorrect modeling of the amplitudes of the seismic waves, especially with respect to amplitude variation with offset (AVO), and therefore have a direct impact on the inversion results. For evaluation purposes, we have performed a series of inversions with different approximations and different constraints whereby the synthetic data set to recover is computed for a 1D elastic medium. A series of numerical experiments, although simple, help to define the applicability domain of the acoustic assumption. Acoustic full-wave inversion is applicable only when the S-wave velocity and the density fields are smooth enough to reduce the AVO effect, or when the near-offset seismograms are inverted with a good starting model. However, in many realistic cases, acoustic approximation penalizes the full-wave inversion of marine reflection seismic data in retrieving the acoustic parameters.

Anisotropic elastic full-waveform inversion of walkaway VSP data from the Arabian Gulf

Borehole seismic addresses the need for high-resolution images and elastic parameters of the subsurface. Full-waveform inversion of vertical seismic profile data is a promising technology with the potential to recover quantitative information about elastic properties of the medium. Full-waveform inversion has the capability to process the entire wavefield and to address the wave propagation effects contained in the borehole data—multi-component measurements; anisotropic effects; compressional and shear waves; and transmitted, converted, and reflected waves and multiples. Full-waveform inversion, therefore, has the potential to provide a more accurate result compared with conventional processing methods. We present a feasibility study with results of the application of high-frequency (up to 60 Hz) anisotropic elastic full-waveform inversion to a walkaway vertical seismic profile data from the Arabian Gulf. Full-waveform inversion has reproduced the majority of the wave events and recovered a geologically plausible layered model with physically meaningful values of the medium.

The state of affairs in inversion of seismic data: An OVSP example

Comment: I value very high this work made by my old students Marwan Charara and Christophe Barnes, as it is a very serious demonstration that complex seismic waveform fitting is possible. The price to pay, of course, is the use of a very realistic (so expensive) simulation of the propagation of the elastic waves (including attenuation), and an inversion process where there is a nontrivial use of Monte Carlo techniques (otherwise, it is not possible to discover in which region of the model space the actual Earth is). Note that even a very simple medium (here, it was not extremely far from a layered medium), the observed seismograms can be very complex. At the time these two complementary studies had to be terminated (a Ph.D. diploma is to be obtained in a finite time), a complete assessment of the uncertainties in the obtained solution had not yet been made. Albert Tarantola

Multiscale time‐domain full‐waveform inversion for anisotropic elastic media

We study the feasibility of the full-waveform inversion method in the time domain with sequential iterations in frequency bandwidths for anisotropic elastic media. This sequential approach appears to be less dependent on the choice of an initial model than a nonsequential approach, performing the inversion for the whole range of frequencies at once. We report on numerical experiments with multicomponent synthetic crosswell data for isotropic and VTI anisotropic media and present cases where the sequential algorithm converges while the nonsequential case fails. In case of convergence, the resolution of medium parameters is acceptable for both approaches (sequential and nonsequential); however, the results for anisotropic media are not as good as for isotropic ones due to the coupling between parameters.

Boundary conditions and the source term for one‐way acoustic depth extrapolation

The one-way acoustic wave equations can be derived, using eigenvalue decomposition of the two-way wave equation in the Fourier domain, in such a manner that the source term and the free-surface boundary condition are explicitly introduced. The proposed form of the one-way wave equations is well adapted to seismic reflection modeling because it allows a pressure field recorded at the surface to be extrapolated directly in depth. A numerical example illustrates the appropriate implementation of the source term and the free-surface boundary conditions. A comparison with a two-way modeling shows a good agreement of the computed wavefields.

Elastic Full Waveform Inversion for Land Walkaway VSP Data from British Columbia, Canada

Full waveform inversion (FWI) is capable of handling multicomponent borehole seismic data and reveals quantitative values of the subsurface medium properties, including compressional and shear-wave velocities. Careful treatment of the source wavelet is crucial for FWI success and is challenging task for land data because of the high variability of downgoing wavelets for different source positions caused by variations of near surface conditions. We present a feasibility study of anisotropic elastic FWI for the land walkaway vertical seismic profiling (VSP) data acquired in northeast British Columbia, Canada, with a vibrator source. FWI explained the data at medium frequencies and recovered a layered structure of the subsurface that agrees with reasonable accuracy with sonic measurements. The inverted source signature and shallow part of the model compensated for the variations of the downgoing wavelet.

Simulation of sonic logging for deviated wells in anisotropic formations

Interpretation of sonic logging data acquired in environments with complex anisotropy is a difficult problem attracting attention of researchers and oil industry. In order to better understand physics of wave propagation in highly anisotropic medium and be able explaining observations from field data there is a need for fast and accurate numerical modeling capability. To address such challenge, we developed an efficient and accurate numerical algorithm for the simulation of sonic logging experiments in highly anisotropic formation. The basis of the approach is a heterogeneous spectral element method implemented on multi-GPU applied to acoustic-elastic wave equation. The approach was designed to simulate wave propagation in 3D arbitrary anisotropic elastic media with attenuation for a constant quality factor via standard linear solid using the tau-method. Due to the use of an unstructured grid, the spectral element algorithm enables handling tools in a fluid-filled borehole with surrounding geological mode...