Christophe Barnes

Simulation of anisotropic wave propagation based upon a spectral element method

We introduce a numerical approach for modeling elastic wave propagation in 2-D and 3-D fully anisotropic media based upon a spectral element method. The technique solves a weak formulation of the wave equation, which is discretized using a high-order polynomial representation on a finite element mesh. For isotropic media, the spectral element method is known for its high degree of accuracy, its ability to handle complex model geometries, and its low computational cost. We show that the method can be extended to fully anisotropic media. The mass matrix obtained is diagonal by construction, which leads to a very efficient fully explicit solver. We demonstrate the accuracy of the method by comparing it against a known analytical solution for a 2-D transversely isotropic test case, and by comparing its predictions against those based upon a finite difference method for a 2-D heterogeneous, anisotropic medium. We show its generality and its flexibility by modeling wave propagation in a 3-D transversely isotropic medium with a symmetry axis tilted relative to the axes of the grid.

Wave propagation near a fluid‐solid interface: A spectral‐element approach

We introduce a spectral-element method for modeling wave propagation in media with both fluid (acoustic) and solid (elastic) regions, as for instance in offshore seismic experiments. The problem is formulated in terms of displacement in elastic regions and a velocity potential in acoustic regions. Matching between domains is implemented based upon an interface integral in the framework of an explicit prediction-multicorrection staggered time scheme. The formulation results in a mass matrix that is diagonal by construction. The scheme exhibits high accuracy for a 2-D test case with known analytical solution. The method is robust in the case of strong topography at the fluid-solid interface and is a good alternative to classical techniques, such as finite differencing.

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.

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

Full-waveform inversion results when using acoustic approximation instead of elastic medium

Seismic marine data inversion is a very heavy process, especially for the 3D seismic case. Often approximations are made to limit the number of physical parameters or to speed up the forward modeling. Because the data are often dominated by uncoverted P waves, one popular approximation is to consider the earth as purely acoustic: no shear modulus; even sometimes with constant density. Nonlinear waveform seismic inversion consists in iteratively minimizing the misfit between the amplitudes of the measured and the modeled data.

Anisotropic Anelastic Full Waveform Inversion: Application to North Sea Offset VSP Data

In sedimentary basin, elastic anisotropy can be described by a transverse isotropic medium and the attenuation in the seismic bandwidth can be approximated by a quasiconstant quality factor. Very few full waveform inversions were conducted for such realistic media to show the feasibility and the benefit of this approach. For illustration, we have chosen two offset VSP datasets from the North Sea displaying attenuated phases and where the medium is known to be transverse isotropic. By inverting elastic parameters, anisotropy, shear attenuation and source functions, we have been able to find an Earth model reproducing fairly the real data. By exploiting all the information in the seismograms, full waveform inversion allows us to localize and characterize the Brent gas reservoir target.

Contribution to the understanding of field‐specific seismic attenuation

The quantitative use of the seismic amplitude information during the interpretation is a key point for many prospect evaluations and almost all reservoir characterization studies. The local amplitude information of interest is always affected by a series of signal attenuators along the propagation of the incident and reflected wavefield which are highly dependent upon the geological context, structural shape, lithologies and fluids.

High Frequency Losses – Stripping Various Causes

The quantitative use of the seismic amplitude information during the interpretation is a key point for many prospect evaluations and almost all reservoir characterization studies. The local amplitude information of interest is always affected by a series of signal attenuators along the propagation of the incident and reflected wavefield which are highly dependent upon the geological context, structural shape, lithologies and fluids. Also, incident amplitude effects might or might not have frequency dependence as well as phase or dispersion characteristics. These many causes of attenuation are often pragmatically treated by a combination of a few well-known tools: spherical divergence compensation, surface-consistent or volumic time and frequency-dependent compensations. Cases where severe amplitude attenuation effects cannot be treated using usual approaches are a serious issue, in particular for seismic characterization of reservoirs. In this paper, we present some ways to study the impact and the relevance of specific attenuation processes. Alternative mechanisms and tools for a quantitative assessment of these processes are proposed. Some results are shown from field case studies including VSP data and 3D surface acquisition, standard and broadband. We also attempt to point out the impact of the bandwidth in the identification and quantification of possible attenuation causes.

A Priori Model Estimation for FWI from Constrained Kinematic Inverse Problem

Exploration inverse methods such as Monte Carlo could provide the general solution for the fullwaveform inversion (FWI) inverse problem allowing incorporating complex a priori information and data with arbitrary noise distributions. Such an approach applied directly to the FWI problem is computationally not tractable. The alternative is to solve the highly non-linear part of the problem with a fast forward problem such as traveltime with a constrained random exploration. The obtained a priori models and uncertainties help greatly in solving the FWI. This approach was successfully applied to an offset vertical seismic profile (OVSP) case.

Contribution to the Discrimination of Field-specific Seismic Amplitude Attenuation Causes

The quantitative use of the seismic amplitude information during the interpretation is a key point for many prospect evaluations and almost all reservoir characterization studies. The local amplitude information of interest is always affected by a series of signal attenuators along the propagation of the incident and reflected wavefield which are highly dependent upon the geological context, structural shape, lithologies and fluids. These many causes of attenuation are often pragmatically treated by a combination of a few well-known tools: spherical divergence compensation, surface-consistent or volumic time & frequency-dependent compensations. Cases where severe amplitude attenuation effects cannot be treated using usual approaches are a serious issue, in particular for seismic characterization of reservoirs. In this paper, a methodology adapted to the study of the impact and relevance of specific attenuation processes is presented; Alternative mechanisms and tools for a quantitative assessment of these processes are proposed. This methodology is illustrated through a field case study, using vertical incidence VSP and 3D surface data. The seismic amplitude attenuation analysis uses the VSP data to validate the modeling of measurable effects and to propose possible causes for the remaining strong attenuation, such as diffuse gas.