Elastic parameter depth images

The driving force behind the current research effort is to extract as much information as possible about subsurface physical properties from seismic reflection data. The first and largest part of this effort is to reconstruct the Zoeppritz $\grave{P}\!\acute{P}$ reflection coefficients, R_pp, as a function of specular reflection angle $\theta_{pp}$ at each subsurface pixel in the designated target zone. This is accomplished by the Kirchhoff elastic prestack depth migration, which is elastic in the sense that background migration model values of V_p, V_s, and $\rho$ are specified. Our method is similar in spirit to that of Parsons (1986), which in turn is based on the methods of Beylkin (1985) and Bleistein (1987), except we consider elastodynamic wave propagation instead of acoustics. Additionally, values of the attenuation quality factor Q may be specified as a function of a single dominant frequency to approximate anelastic exponential amplitude attenuation (but not dispersion). It is a true depth migration in the sense that heterogeneous interval model properties, including lateral velocity variations, are specified as a function of spatial coordinates, in direct contrast to time migration methods.

Given the Zoeppritz specular reflectivity R_pp, information can be further extracted regarding the polarity, magnitude, and spatial distribution of relative changes in elastic parameters. Algorithmically, we achieve this inversion by defining a matrix equation relating R_pp for several specular angles to three elastic parameters using the linearized Bortfeld approximation to the nonlinear Zoeppritz $\grave{P}\!\acute{P}$ coefficient (Bortfeld, 1961). The matrix system is then inverted by Singular Value Decomposition (SVD) at each subsurface location. (For a review of the SVD method we refer the reader to Lines and Treitel, 1984.) This allows the possibility of producing elastic parameter depth images of the subsurface target zone, similar in appearance to prestack depth migrations, each exhibiting spatial variations in P or S impedance, for example. Such images will be shown in this report for synthetic data, with the corresponding field data images to be shown at a later date. Ideally, this capability will provide new or additional information about subsurface properties which may be useful in exploration and production applications.