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A new 2-D true-amplitude prestack elastic depth migration algorithm compensates for anelastic attenuation and transmission losses in an isotropic medium. Geometrical spreading and its compensation are included by extrapolation of up- and down-going waves using a two-way wave equation. Intrinsic attenuation is modeled and simulated using relaxation mechanisms. Approximations to the Zoeppritz equations are used to compute and analyze the angle-dependent reflection/transmission coefficients; converted energy is included at each interface. Transmission losses are compensated, from estimated angle-dependent elastic reflectivity using a two-pass recursion. The image condition is the ratio of the compressional receiver/source wavefield amplitudes. Application to synthetic data accurately extracts P-velocity, S-velocity, density and P-wave impedance beneath target reflectors, even under a salt overhang.

The angle-dependent reflectivity of a reservoir target is crucial input for reservoir characterization. 3D prestack depth migration should be able to produce not only an accurate structural image, but also reliable angle-dependent amplitude information. However, none of the currently available 3D migration algorithms do this. Geometrical spreading is the only consideration in most existing true-amplitude migrations; intrinsic attenuation, and transmission losses also distort the wavefield amplitudes during propagation through the earth. We have implemented an integrated algorithm that compensates all three of these factors, in a two-pass recursive reverse-time 3D prestack depth migration. Examples using synthetic test data from 3D models demonstrate both production of high quality subsurface images and angle-dependent reflection coefficients.

We have tested numerical implementations of six imaging conditions for prestack reverse-time migration; these show significantly differing abilities to give accurate, angle-dependent estimates of reflection coefficients. Evaluation is in the context of a simple, one-interface acoustic model to eliminate complications associated with propagation effects. We show that only the results produced by source-normalized cross-correlation, or by by the receiver/source wavefield amplitude ratio have the correct angle dependence, scale factor and sign, and (dimensionless) units; thus, these are the only physically valid imaging condition. A prerequisite is that the source and receiver wavefield extrapolations be able to accurately reconstruct their respective wavefields at the target.

A critical factor in improving the efficiency of prestack reverse-time migration is reconstruction of the source wavefield, to avoid having to save the entire time-dependent wavefield. The latter is the most common (and most inefficient) approach; it involves computing and storing the complete wavefield during a complete forward time propagation, and then accessing the time snapshots in reverse-time order. We have evaluated cost-effective alternatives, which involve reconstruction of the source wavefield, at each time step, from boundary or initial conditions (or a combination). The advantages of reconstruction are greatest in 3-D, where the disk storage needed is reduced by approximately two orders of magnitude compared to saving all the time snapshots.

Full-wavefield inversion is another alternative to extract the P-wave anisotropic parameters that produce measured reflection coefficients for VTI, HTI and orthorhombic media. With full-wavefield inversion, both the traveltime and amplitude information in reflections are utilized simultaneously. A linearized (conjugate gradient) inversion is performed, in layer stripping mode, for parameters of overlapping pairs of layers. All layers are inverted as if they were orthorhombic; the inversion results reveal the actual anisotropic symmetry that is present in each layer.

Traveltime-based inversions cannot solve for all the anisotropic parameters for orthorhombic media. These limitations are overcome using full-wavefield inversion. Tsvankin's nine parameters and the orientation of the symmetry axis are inverted from three-component wide-azimuth synthetic datasets containing reflected P and P-S converted waves from VTI, HTI and orthorhombic models; the parameters for all three models are recovered. Effects of all the model parameters, on the reflection coefficients, are automatically included. Inversions of data with noise added gives results that are very similar to those for the noise-free data, as only the coherent signal is fitted; the residual at convergence for the noisy data corresponds to the noise level. Concurrent inversion of data from multiple sources increases the azimuthal illumination of a target.

Imaging conditions for reflection coefficients of elastic waves require decomposition of a vector wavefield into P- and S-waves at the image time and location. This can be done for vector wavefields using Helmholtz theory and the Christoffel equation. Unlike divergence and curl, which separate the wavefield into a scalar and a vector field, the decomposed P- and S- wavefields are both vector fields, with correct amplitude, phase and physical units and, if the vector components of decomposed wavefields are added, they reconstruct those of the original input wavefield. Wavefield propagation in any portions of a VTI medium that have the same polarization distribution (i.e. the same eigenvector) in the wavenumber domain, have the same decomposition operators and can be reconstructed with a single 3D Fourier transform for each operator (e.g. one for P-waves and one for S-waves). Potential practical applications include extraction of separate images for different wave types in prestack reverse-time migration, inversion, or migration velocity analysis, and calculation of wave propagation directions for common-angle gathers.

This project has so far produced six referred publications and contributed to the dissertations of three PhD students who have graduated and who are now working for ExxonMobil, GXT/ION, and Shell International. Two more manuscripts are in preparation.