Multiresolution Representation of Geoelectric Model and Parameter Operation in Wavelet Domain

Abstract

In this paper, an algorithm for wavelet domain geoelectric model representation and parameter manipulation is introduced, which can be utilized for multiresolution inversions of geophysical data based on tree structure. With proper wavelet choice, the model can be represented by much less parameters than traditional model representation, expecting to reduce the computational cost for inversion remarkably. The use of tree structure to represent the wavelet coefficients makes the parameter operations (e.g., perturbating model parameter and adding more details in a model) in inversion much simpler. Introducing detail in a model or removing detail from a model can be simply realized by adding nodes to or deleting nodes from the existing tree structure. The model parameter value can be perturbated by changing the tree node values. Our algorithm is general and can be applied to develop any geophysical inversions in wavelet domain with trivial additional work once the forward modeling and inversion algorithm is available.