Born Inv ersion in Realistic Backgrounds by Means of Recursive Green ’ s Functions

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 wav e field can be described by simple ray theory without caustics or multipathing; the data are assumed to be complete and noise-free. Correspondingly,t he algorithms for ray-based Green'sf unctions are, until now, mostly developed for smooth media. To bea ble to image in realistic backgrounds and with realistic data sets, the assumptions have tobeweakened. This must be done on twofronts: the imaging formula and the Green'sfunctions. A new, generalized, imaging formula has been developed that takes into account that real data are incomplete, noisy and have a limited frequencyb and. A newa pproach for Green'sf unctions allows the backgrounds in the inversion to be non-smooth, and accounts for reflected and transmitted ray fields by organizing the ray tracing recursively.C ombined, the twoa pproaches allowas ystematical 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 newi maging formula, together with the realistic Green'sf unctions, has been successfully applied on the imaging of a complicated horst structure from the North sea. 1Introduction As eismic inversion in a realistic background remains a challenge evenf or 2D problems, because of the absence of anyap riori symmetry.A na dvanced inversion formula, reducing inversion to a sort of migration, has been suggested by Beylkin ([2], [3]), and applied with relative success ([7], and others). Nevertheless, this formula has a limited applicability in areas with a realistic complexity,o rf or realistic seismic data acquisitions. The inversion is based on the generalized Radon transform, which supposes that for a givenb ackground and a givens ource/receiver acquisition, there exists a one-to-one correspondence between a record sample and the parameters of an isochron crossing a background point. Even in a layered background this supposition fails due to existence of up-and downgoing rays, crossing the background point. Besides, the inversion formula is not valid for incomplete data (for instance, reflection data from a narrowa perture acquisition), also it is hard to adapt the formula for data from a fews ource/receiverp airs, noisy data, narrowf requencyb and signal, etc. Also, its …