Born inversion in realistic backgrounds by means of recursive Green’s functions

Abstract

The commonly applied methods for seismic inversion are based on some drastic assumptions regarding the known background or macro-velocity model and the data acquisition, that limit their applicability in geologies of realistic complexity or to realistic, noisy and incomplete, data sets. The background is usually assumed smooth, often to such a degree that the wave field can be described by simple ray theory without caustics or multipathing; the data are assumed to be complete and noise-free. Correspondingly, the algorithms for ray-based Green’s functions are, until now, mostly developed for smooth media. To be able to image in realistic backgrounds and with realistic data sets, the assumptions have to be weakened. This must be done on two fronts: the imaging formula and the Green’s functions. A new, generalized, imaging formula has been developed that takes into account that real data are incomplete, noisy and have a limited frequency band. A new approach for Green’s functions allows the backgrounds in the inversion to be non-smooth, and accounts for reflected and transmitted ray fields by organizing the ray tracing recursively. Combined, the two approaches allow a systematical target-oriented inversion, in which upper parts of the Earth model are assumed known and fixed, and the attention is concentrated on important details below. The new imaging formula, together with the realistic Green’s functions, has been successfully applied on the imaging of a complicated horst structure from the North sea.