5:15 PM - 6:45 PM
[SSS09-P03] An estimation method of the estimated model parameter errors in seismic refraction analyses
Keywords:Seismic refraction analysis, estimated error , pseudo-velocity structure model set
Seismic refraction analyses are widely used around the world as one of the methods to obtain seismic velocity structures. In recent years, the number of parameters in structural models has increased, typically exceeding tens of thousands, due to the need to obtain detailed information on large structures and three-dimensional structures. When solving this problem in inversion, it is common to use iterative solution methods such as the LSQR method, because the direct solution method based on the inverse matrix is too time-consuming for computers that can be used in general laboratories.
On the other hand, since the observation data used to calculate the velocity structure contain various observation errors, the calculated seismic velocity structure also contains errors (estimated errors). To determine the estimated errors of the velocity structure, the inverse matrix must be calculated. However, as mentioned above, obtaining the inverse matrix of tens of thousands of elements is expected to take several tens of days of computation time on a laboratory computer, which is beyond the scope of realistically feasible computation time. Hence, not much work has been done to compute the estimated errors of the velocity structure.
In this study, we developed a method for the estimated errors that can be computed in realistically computable time. The procedure of the method is as follows;
1) From the obtained seismic velocity structure (optimal solution), calculate theoretical travel times. 2) add random observation errors of normal distribution to the obtained theoretical travel times, and a large number of pseudo-travel time data sets. 3) Conduct the inversion using the pseudo-travel time data sets with the initial model, make a large number of pseudo-velocity structure model sets. 4) The values of the pseudo-velocity structure model sets are expected to be scattered around the value of the optimal solution, and the degree of scattering is used as the estimated errors.
The issue with this method is how many pseudo-velocity structure model sets should be created to calculate the appropriate estimated errors. In this study, the appropriate number of the model sets was found by increasing number of the model sets by 10, calculating the standard deviation each time, and searching for the number of the model sets where the variation of the standard deviation becomes small and settles at a certain value.
In this study, we used a data set for a P-wave velocity structure around the Indian Ocean Rodriguez Triple Junction, which was obtained by Takata (master's thesis, Chiba University, 2015). We found that the variation of the standard deviation becomes small at about 200 pseudo-velocity structure model sets. Since calculation of the model sets can be performed in parallel computation, the number of 200 can be calculated in about half a day on a laboratory computer.
On the other hand, since the observation data used to calculate the velocity structure contain various observation errors, the calculated seismic velocity structure also contains errors (estimated errors). To determine the estimated errors of the velocity structure, the inverse matrix must be calculated. However, as mentioned above, obtaining the inverse matrix of tens of thousands of elements is expected to take several tens of days of computation time on a laboratory computer, which is beyond the scope of realistically feasible computation time. Hence, not much work has been done to compute the estimated errors of the velocity structure.
In this study, we developed a method for the estimated errors that can be computed in realistically computable time. The procedure of the method is as follows;
1) From the obtained seismic velocity structure (optimal solution), calculate theoretical travel times. 2) add random observation errors of normal distribution to the obtained theoretical travel times, and a large number of pseudo-travel time data sets. 3) Conduct the inversion using the pseudo-travel time data sets with the initial model, make a large number of pseudo-velocity structure model sets. 4) The values of the pseudo-velocity structure model sets are expected to be scattered around the value of the optimal solution, and the degree of scattering is used as the estimated errors.
The issue with this method is how many pseudo-velocity structure model sets should be created to calculate the appropriate estimated errors. In this study, the appropriate number of the model sets was found by increasing number of the model sets by 10, calculating the standard deviation each time, and searching for the number of the model sets where the variation of the standard deviation becomes small and settles at a certain value.
In this study, we used a data set for a P-wave velocity structure around the Indian Ocean Rodriguez Triple Junction, which was obtained by Takata (master's thesis, Chiba University, 2015). We found that the variation of the standard deviation becomes small at about 200 pseudo-velocity structure model sets. Since calculation of the model sets can be performed in parallel computation, the number of 200 can be calculated in about half a day on a laboratory computer.