Multiscale resistivity inversion based on convolutional wavelet transform

Abstract

SUMMARY The resistivity imaging method, an effective geophysical technique, has been widely used in environmental, engineering and hydrological fields. The inversion method based on smooth constraint is one of the most commonly used methods. However, this method causes the resistivity to change smoothly and makes it difficult to describe geological boundaries accurately. An accurate description of the target's boundaries often requires a priori information gained with other methods (such as other geophysical methods or geological drilling). To address this issue, a multiscale inversion method is proposed for extracting boundary features and inverting feature parameters from different scales. In this method, a convolution kernel is used to extract the boundary information from the resistivity model. The model parameters are transformed from the spatial domain to the feature domain via a convolutional wavelet transform. The feature parameters of different scales can then be obtained by solving the inversion equation in the feature domain. After that, the resistivity model of the spatial domain is reconverted from the feature domain by deconvolution transform of the inversion result. Numerical simulations and experiments show that the new multiscale resistivity inversion method has the ability to locate and depict boundaries of geological targets with high accuracy.