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.

中文翻译：

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基于卷积小波变换的多尺度电阻率反演

电阻率成像方法是一种有效的地球物理技术，已广泛用于环境，工程和水文领域。基于平滑约束的反演方法是最常用的方法之一。但是，这种方法使电阻率平滑地变化并且难以准确地描述地质边界。对目标边界的准确描述通常需要先验通过其他方法（例如其他地球物理方法或地质钻探）获得的信息。为了解决这个问题，提出了一种多尺度反演方法，用于从不同尺度提取边界特征并反演特征参数。在这种方法中，使用卷积核从电阻率模型中提取边界信息。通过卷积小波变换将模型参数从空间域转换到特征域。然后可以通过在特征域中求解反演方程来获得不同尺度的特征参数。之后，通过反演结果的反卷积变换，从特征域中转换出空间域的电阻率模型。