Born inversion with a variable background velocity

Abstract

Direct, or Born, inversion has been presented as an approximate solution of the multidimensional seismic‐acoustic inverse problem (e.g., Cohen and Bleistein, 1979; Phinney and Frazer, 1978; Raz, 1981; Clayton and Stolt, 1981). The most basic assumption of the Born model is that variations, or perturbations, of some reference model remain small. This requirement of smallness is due to the fact that errors are directly related to the value of the perturbations. Both the local and overall values of the perturbation variable contribute to these errors, which are reduced if the known reference model, or background velocity, closely matches the actual medium velocity.