Elastic Ray-Born L₂-Migration/Inversion

Abstract

The approximate ray Green's tensor in 3-D heterogeneous elastic media combined with the first-order Born approximation lead to new explicit equations for solving, modelling and inverse scattering problems. Individual wave scattering: contributions (PP. PS, SP. SS) are represented for four different linear approximations (i.e. parameter linearizations). The first-order Born appoximation yields a scattered wavefield which is linearly related to medium parameter perturbations. The linearized inverse scattering problem is solved in the space-time domain and consists of minimizing a cost function within the I , norm with a one-step conditioned gradient procedure. From uni-or multicomponent data and a reference heterogeneous background model representing adequately either the long spatial wavelengths of the medium (i.e. the smooth model), and/or its principal features (i.e. the macro-model), this operation reduces to: (1) pre-stack depth-migrating the scattered data yielding three intermediate images; and (2) deconvolving these images by an elastic Hessian correction which produces final high-resolution images representing the medium's short spatial wavelength variations convolved with the source function (e.g. P and S impedances and density maps). If the reference model and data are satisfactory, typical artefacts are due to limited aperture or insufficient coverage. Use of high-frequency and Born approximations require certain constraints. For example, the dominant wavelength must always be smaller than the characteristic length of the reference medium, but larger than the scatterer characteristic length. To increase computational efficiency, the high-frequency approximate Green's tensor is calculated by the paraxial ray method. 2-D elastic synthetic examples for surface reflection and cross-hole experiments show the ability of such a technique to delineate subsurface structure and to recover local changes in elastic properties. However, density variations are more difficult to resolve than P and S impedance or velocity changes.

Monitoring of SAGD Process: Seismic Interpretation of Ray+Born Synthetic 4D Data

“…More precisely, the (x, y, z) dimensions of the mesh must respect some criteria which depend on the significant wavelength λ of the P-wave propagated field: δx and δy are required to be less than λ/8, δz is required to be less than λ/16. In addition, several works have proved that the Born modelling is not accurate for large incidence angles [18,19,8].…”

“…To focus on the reflections generated within the reservoir zone, a 3D target-oriented modelling tool is chosen. This tool is based on the ray+Born formalism [8][9][10] which allows us to compute the P-wave elastic response, by correctly handling the seismic amplitudes as a function of source-receiver offset. In particular, the effects of the overburden and of the survey are taken into account.…”

Multi‐source least‐squares reverse time migration

“…This preconditioner enjoyed early use by Beydoun and Mendes (1989) and Luo and Schuster (1991). Plessix and Mulder (2004) provide a thorough review of its performance and properties.…”

“…In this way, the effects of the source wavelet, limited recording aperture, geometric spreading, etc, are taken into account to produce images with reduced acquisition footprints, balanced amplitudes and improved resolution. Following the work of Lailly (1984) and Beydoun and Mendes (1989), Nemeth et al (1999) proposed an iterative linear inversion method they denoted as least-squares migration (LSM).…”

“…The simplest approximation is the reciprocal of the diagonal matrix (Beydoun and Mendes, 1989;Rickett, 2003) that is applied to the image to compensate for uneven illumination. This is computationally inexpensive, but it only compensates for amplitude distortation but does not correct for aliasing artifacts or strong footprint noise.…”