11:00 AM - 1:00 PM
[SEM16-P02] A study of resolution test in inversion analysis using sparse regularization
Keywords:resolution test, magnetic inversion, aeromagnetic survey
When determining the subsurface structure from the magnetic anomaly data obtained from the aeromagnetic observations, the number of unknown parameters is generally larger than that of the observed data, and the equations to be solved becomes ill-posed linear equations. For this reason, it is widely used to impose constraints on the solution in order to stabilize the solution. However, the nature of the derived solution differs greatly depending on the conditions that is introduced in the inversion. It has been pointed out that when we use the smoothing condition, which has been commonly used in the previous studies, an unfocused solution that blurs the actual structure is obtained, and as the result it becomes difficult to interpret the solution to reveal the subsurface structure. On the other hand, sparse regularization methods such as Lasso (Tibshirani, 1995) have recently been attracting attention, and it is actively used in magnetic inversion analysis. This method is an optimization method that imposes the constraint for the L1 norm of the solution, that is, the absolute sum of each component of the solution vector, is minimized, and by using this method, sparse, as the result, focused solutions can be obtained.
Now, it has been pointed out that the information about the subsurface structure can be lost when the resolution of the inversion solution is not sufficient, and the degree of this information loss can be evaluated by a sort of the resolution test. A method that is commonly used for this purpose is point spread function (PSF). In this method, firstly a point magnetic source is artificially generated. Then, synthetic magnetic anomaly produced by this point source is calculated, and inversion is performed using it as an input data. Ideally, the original structure should be recovered almost completely, but in reality, deviations from the original structure occur. By setting an appropriate criterion, and by evaluating this discrepancy based on this criterion, we can identify where there is enough sensitivity to consider the resultant solution is reliable.
Until now, a resolution test using PSF has been proposed and practiced for smoothing inversion analysis (Friedel, 2003). However, in sparse inversion analysis, there are few studies that apply the PSF-based resolution test. In our presentation, we report the progress of our study on the effectiveness of the PSF-based resolution test for sparse inversion analysis.
Now, it has been pointed out that the information about the subsurface structure can be lost when the resolution of the inversion solution is not sufficient, and the degree of this information loss can be evaluated by a sort of the resolution test. A method that is commonly used for this purpose is point spread function (PSF). In this method, firstly a point magnetic source is artificially generated. Then, synthetic magnetic anomaly produced by this point source is calculated, and inversion is performed using it as an input data. Ideally, the original structure should be recovered almost completely, but in reality, deviations from the original structure occur. By setting an appropriate criterion, and by evaluating this discrepancy based on this criterion, we can identify where there is enough sensitivity to consider the resultant solution is reliable.
Until now, a resolution test using PSF has been proposed and practiced for smoothing inversion analysis (Friedel, 2003). However, in sparse inversion analysis, there are few studies that apply the PSF-based resolution test. In our presentation, we report the progress of our study on the effectiveness of the PSF-based resolution test for sparse inversion analysis.