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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 deep target reflectors, even under a salt overhang. The effects of attenuation and anisotropy on the reflection/transmission coefficients are not yet considered.

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 satisfy this requirement. Geometrical spreading is the only consideration in most existing true-amplitude migrations (except oursd); 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. The velocity ratio at the target is obtained by subsequent least square fitting over the extracted angle-dependent reflection coefficients. The recursive nature of the 3D algorithm maens that it is computationally and memory intensive. However, for application to real seismic data, 3D true amplitude processing is necessary.

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 the (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 propose and evaluate 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.