Inversion of Seismic Wavefield Data for P- and S-wave Velocity

Described and illustrated are seismic inversion formulas derived by Tarantola (1987) and Mora (1987d). The formulas are based on nonlinear least squares iterations to find the elastic properties of the Earth corresponding to the synthetic wavefield that best matches the seismic observations. Primary P- and S-wave reflections, mode converted waves and Rayleigh waves are all theoretically useful in the inversions. Beginning with a starting guess, the Earth properties are iteratively updated using a preconditioned conjugate-gradient algorithm. The gradient direction is cast in terms of two wave propagations which can be easily implemented on fast fine grain parallel computers such as the ‘Connection Machine’ (see Hillis (1986)).

The method is tested by inverting a shot profile. The wave propagations are done, using elastic finite differences to allow for Earth models of realistic complexity. The results verify the theoretical predictions of Mora (1987c) that the iterative elastic inversion formulas are capable of obtaining all wavenumbers of the compressional and shear wavespeeds that are resolvable separately by prestack elastic migration and elastic reflection tomography.