3D nonlinear inversion by entropy of image contrast optimization

Abstract. An approach to solve 3D inverse problem associated with inverting seismic reflection data is presented. It exploits the a priori assumption that the reflection data, reduced properly, can be interpreted as a perturbation of a dynamical response of a certain 'reference background'. It is supposed that the corresponding perturbation of medium parameters can be treated in terms of the 'Ray + Born'- or 'Rytov + Born'- set of medium functions. This for the reflection data means that 'kinematical' part does not generate reflections, while proper reflections are caused by single-scattering perturbations. Moreover, it is guessed that the latters are cooperated in a vicinity of a certain unknown 2D smooth surface ('Interfaces'). When this a I ' information is adequate, the approach allows to recover both the low-frequency features of the medium (the background) and its discontinuities. The approach involves a new optimization criterion, called the Entropy of Image Contrast (EnIC), and a new global optimization algorithm, called Regularized Global Approximation algorithm (RGA-algorithm). It allows to choose such a background that the linerized inversion provides the most focused image of interfaces. In other words, it yields the maximum-contrast, or minimum-entropy, interface image. The method takes into account the large amounts of data that have to be processed in 3D inversion and the sparseness of input data. It is also robust with respect to the noise in the data.