Automatic 1D interpretation of DC resistivity sounding data

摘要

In the last few years, much of the work carried out on DC resistivity has mainly concentrated on 2D and 3D techniques for data acquisition and interpretation. However, when the resistivity changes are smooth, 1D techniques can be used to interpret the data. In the present paper, we present an automatic 1D inversion scheme for DC resistivity sounding. The inversion scheme is based on an iterative least squares procedure (ILSQP) with Singular Value Decomposition (SVD). In order to reinforce the convergence of the inversion scheme towards a global minimum, the ILSQP is combined with a logarithmic parameterization of the unknown model parameters, and splitting of the data set into parts. The data are then inverted stepwise, i.e., starting from the first data part which corresponds to the smallest electrode spacings. As the inversion continues more data parts, corresponding to increasingly larger electrode spacings, are included in the inversion until the whole data set is inverted. In this way, the shallower part of the model becomes well estimated first, and as the inversion advances and more data parts are included, the deeper structure is better resolved. The solution of the resistivity inverse problem by standard least squares procedure with SVD allows us to distinguish between well and poorly resolved linear combinations of model parameters. For a given inversion step, the construction of models that give a better data fit can be done with truncation of eigenvectors belonging to the least resolved combinations. Thus, as the iteration process advances those singular values can be activated one by one. This approach has been tested on synthetic data representing some layering that is assumed common in shallow studies. The model studies suggest that there is a strong coupling between the resolving power of DC resistivity data and their random errors. For high to moderate data quality, the resolution power of the scheme is generally good, depending upon the degree of complexity of the model. For larger error levels, however, there is a loss of resolution. The inversion scheme is suitable for fast interpretation of data that are collected in shallow studies in connection with environmental, hydrogeological and geotechnical investigations if the lateral changes in the study area are smooth. The method may also be used as a first interpretation prior to a 2D or 3D survey.