4:15 PM - 4:30 PM
[STT34-04] Automatic estimation of regression curves indicating average depths of causative layers from power spectrum of gravity anomaly or gravity gradient (gzz) data
Keywords:Gravity anomaly, Power spectrum, Automatic estimation of average depth of causative layer
In this study, we propose a method of automatically estimating regression lines or curves indicating the average depths of causative layers from the power spectrum of gravity anomaly or gravity gradient data (gzz).
To estimate the average depth of a causative layer, we select a frequency range and apply linear or curve approximation to the power spectrum of gravity anomaly or gravity gradient data and estimate the optimum regression line or curve for the data. In general, the frequency range is selected by an analyst; therefore, the analysis depends on the skill level of the analyst. If the effective-frequency range for each causative layer can be automatically determined from the power spectrum according to a suitable index, we can estimate the regression line or curve more objectively. If a technique for the automatic and direct determination of the regression curve from the data with one indicator is developed, it would be the best way for performing quantitative analysis of gravity anomaly or gravity gradient data.
In this study, we focused on estimating the regression line and employed the coefficient of determination (R2) as the indicator. R2 was used to measure the goodness of fit for the regression line. It generally distributes in the range of less than 1.0; the closer R2 is to 1.0, the better the explanation of data by the estimated regression line.
In the analysis, the data in all the frequency zones were set as the initial data, and the regression line indicating the depth of the deepest layer was first estimated. The regression lines were estimated by sequentially reducing data from the higher frequency side, and R2 was also calculated each time the regression line was estimated. When R2 of one line assumed the highest value, we used the line as the optimum regression line. Next, we applied the same process to the residual data (high-frequency side) and obtained the regression line indicating the second-deepest layer. By repeating these processes, we automatically determined the number of causative layers and the regression lines indicating the layer depths.
The radial average of the power spectrum of gravity is known to draw a relatively smooth curve. Instead of L2 norm minimisation (least square method), we employed L1 norm minimisation, which is robust, for estimating the regression line from these data. R2 has been used to measure the goodness of fit for the regression line via the least square method and is not a suitable indicator for evaluating the goodness of fit for the regression line provided by L1 minimisation but only an indicator. However, as shown in Fig. 1, we could extract the regression lines indicating the average depths in the regional, local, and noise frequency zones by evaluating R2.
To estimate the average depth of a causative layer, we select a frequency range and apply linear or curve approximation to the power spectrum of gravity anomaly or gravity gradient data and estimate the optimum regression line or curve for the data. In general, the frequency range is selected by an analyst; therefore, the analysis depends on the skill level of the analyst. If the effective-frequency range for each causative layer can be automatically determined from the power spectrum according to a suitable index, we can estimate the regression line or curve more objectively. If a technique for the automatic and direct determination of the regression curve from the data with one indicator is developed, it would be the best way for performing quantitative analysis of gravity anomaly or gravity gradient data.
In this study, we focused on estimating the regression line and employed the coefficient of determination (R2) as the indicator. R2 was used to measure the goodness of fit for the regression line. It generally distributes in the range of less than 1.0; the closer R2 is to 1.0, the better the explanation of data by the estimated regression line.
In the analysis, the data in all the frequency zones were set as the initial data, and the regression line indicating the depth of the deepest layer was first estimated. The regression lines were estimated by sequentially reducing data from the higher frequency side, and R2 was also calculated each time the regression line was estimated. When R2 of one line assumed the highest value, we used the line as the optimum regression line. Next, we applied the same process to the residual data (high-frequency side) and obtained the regression line indicating the second-deepest layer. By repeating these processes, we automatically determined the number of causative layers and the regression lines indicating the layer depths.
The radial average of the power spectrum of gravity is known to draw a relatively smooth curve. Instead of L2 norm minimisation (least square method), we employed L1 norm minimisation, which is robust, for estimating the regression line from these data. R2 has been used to measure the goodness of fit for the regression line via the least square method and is not a suitable indicator for evaluating the goodness of fit for the regression line provided by L1 minimisation but only an indicator. However, as shown in Fig. 1, we could extract the regression lines indicating the average depths in the regional, local, and noise frequency zones by evaluating R2.