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[HTT20-P04] Time-lapse inversion of resistivity data by using sparse modeling
Keywords:Resistivity survey, Sparse modeling, Time-lapse inversion
Sparse modeling is one of the data analysis methods that assumes sparsity of solution. The sparsity means that almost all solutions are zero. In other words, the number of nonzero solutions is small. The sparsity assumption is essential to apply sparse modeling to resistivity monitoring data. Resistivity survey is a method to estimate a resistivity distribution in the ground. Although the spatial distribution of the resistivity doesn’t satisfy the sparsity assumption, the temporal change of that satisfies the sparsity assumption. For example, in the case of ground improvement, the resistivity change occurs only in a limited area that was improved. The other area that was not improved remains the same resistivity value as before ground improvement. This means almost all resistivity changes in the area are zero. That is why the sparsity assumption is established. In this study, a 2D numerical simulation was conducted to assess the effectivity of sparse modeling for time-lapse resistivity data.
Generalized LASSO (Least Absolute Shrinkage and Selection Operator) is well known as one of the typical methods of sparse modeling. There are several methos for solving LASSO problem. In this study, we employed ADMM algorithm for time-lapse resistivity inversion.
A 2D numerical analysis was conducted to test the applicability of sparse modeling. That was modeled on resistivity distribution after ground improvement. The model was set a low resistivity block into the homogeneous medium. In this numerical analysis, a conventional inversion by using least squares method was also carried out to compare with the result analyzed by sparse modeling. As a result, it was founded that sparse modeling could image the shape of anomaly more accurately compared to the conventional inversion method. However, the result of sparse modeling depended on parameters of ADMM algorithm which could be set arbitrarily. Therefore, when the actual data is inverted by using sparse modeling, a numerical simulation is necessary to determine optimal parameters in advance.
In conclusion, the sparce modeling was capable to extract the area of resistivity change more accurately compared to that obtained by the conventional inversion method.
Generalized LASSO (Least Absolute Shrinkage and Selection Operator) is well known as one of the typical methods of sparse modeling. There are several methos for solving LASSO problem. In this study, we employed ADMM algorithm for time-lapse resistivity inversion.
A 2D numerical analysis was conducted to test the applicability of sparse modeling. That was modeled on resistivity distribution after ground improvement. The model was set a low resistivity block into the homogeneous medium. In this numerical analysis, a conventional inversion by using least squares method was also carried out to compare with the result analyzed by sparse modeling. As a result, it was founded that sparse modeling could image the shape of anomaly more accurately compared to the conventional inversion method. However, the result of sparse modeling depended on parameters of ADMM algorithm which could be set arbitrarily. Therefore, when the actual data is inverted by using sparse modeling, a numerical simulation is necessary to determine optimal parameters in advance.
In conclusion, the sparce modeling was capable to extract the area of resistivity change more accurately compared to that obtained by the conventional inversion method.