Pascal Froidevaux

Insights into migration in the angle domain.

Summary We examine some aspects of the Kirchhoff migration in the angle domains. The angle domains we refer to are the scattering angle domain (both opening and azimuth of scattering), which replaces the surface related offset and azimuth of acquisition, and the illumination dip angle domain (having two components in 3D). We examine the insight given to the Kirchhoff summation and to the stationary phase approximation, by virtue of the decomposition of the migration in the illumination dip angle domain. Additionally we point out some differences between angle domain and offset domain migration.

True amplitude migration in the angle domain by regularization of illumination

We describe an approach of true amplitude Kirchhoff migration in scattering angle, based on a multi-angle regularization of illumination. The scattering angle replaces the surface related offset and azimuth of acquisition. The regularization of illumination is done in the multidimensional domain of scattering angles and illumination dip angles. We show that the regularization of illumination is in principle equivalent to the classic application of the Beylkin Jacobian, but its different implementation makes it suitable to a wider range of real-life of irregular acquisitions. We illustrate with realistic examples the issues of amplitude regularization, elimination of artifacts and removal of footprint.

Regularization of illumination in angle domains—a key to true amplitude migration

The turn of the millennium has seen the long expected affordability of 3D prestack depth migration based on wave-equation, or better said, band-limited algorithms. The success of wave-equation PreSDM (prestack depth migration) comes from the fulfillment of two, and only two, promises: correct handling of geometrical spreading and correct handling of multipathing, in complex media. Even then, the migration velocity model needs to be accurate enough to ensure the full effectiveness of this expectedly correct handling of wave propagation. How to get a complex though correct velocity model is still an open issue and is beyond our scope. There are nevertheless capabilities of Kirchhoff migration that wave-equation PreSDM cannot emulate yet, though progress is being made. On the imaging side, Kirchhoff has the well-known capability of imaging steep dips. Kirchhoff migration can also handle velocity models with various types of anisotropy. On the amplitude side, Kirchhoff migration offers better handling of irregular acquisition, better amplitude control through the theory of Beylkin, and better understanding of all illumination and regularization issues. This understanding is needed because the regularization of illumination is the key to a reduction of classic migration artifacts, to an improvement of the image quality, and to the reliability of the migration amplitudes for AVA and 4D processing.

A synthetic study to investigate the 3D structural effects on AVAZ analyses

Advances in 3D seismic acquisition and processing are providing new tools for the analysis of fractured zones. Studying the seismic wave amplitude variation as a function of azimuth is one of the current methods to determine the anisotropy parameters. Based on recent studies conducted with field data, several questions remain, notably the validity of the Amplitude Versus AZimuth (AVAZ) analysis of the seismic horizons when the preprocessing of the data oversimplifies the reality. In this paper, we use an anisotropic dynamic ray tracing to simulate the wave propagation in 3D isotropic and Horizontal Transverse Isotropic (HTI) models. Our objectives are i) to analyze the biases resulting from the use of a horizontal layering approximation in the geometrical spreading compensation and in the mapping between source-receiver offset and incidence angle and ii) to evaluate their consequences on the AVAZ curves corresponding to an HTI anisotropy. Because the true amplitude PSTM or PSDM workflows based on ray tracing include an exact geometrical spreading compensation and account for the true incidence angles, our conclusion is that these tools should be used to study the amplitudes in anisotropic media even in case of moderately inhomogeneous structures .

Elastic migration in the angle-azimuth domain: application to a seabed node experiment

Summary While the theory of true amplitude migration in the double angle-azimut domain is well known, its implementation and use in order to obtain accurate depth reflectivity cube versus angle and azimut has not yet been shown. In this paper, we review and to some extent clarify the existing theory, propose practical solutions for implementation in standard Kirchhoff algorithms and demonstrate the validity of the methods using synthetic data. Application to a seabed node type data is also shown.