4:30 PM - 4:45 PM
[J09-2-01] Resolution analysis for earthquake kinematics inversion
Until recently, little attention has been devoted to the assessment of the quality of the solution in most geophysical inverse problems. The clear difference between optimal solutions, obtained by different proposed algorithms, has driven researchers interest to not just get a solution but to state its confidence in it. For earthquake kinematics inversion, the uncertainty quantification has been very little explored. However the research community has clearly pointed out that it is a main research topic because of the different solutions obtained in some specific benchmarks (Mai et al. (2016)).
The purpose of an earthquake kinematics inversion is to get the slip-rate time-space history using the seismograms available. A simple way to evaluate its resolution length is to perform a checkerboard test. However multiple tests must be done in order to identify the specific resolution length in different regions of the solution. Fitchner and Van Leeuwn (2015) have proposed to use random probing techniques for resolution analysis. They have pointed out that the Hessian acts as a smoother of random functions which carry information of the resolution.
In this work we show how to perform a resolution analysis for earthquake kinematics inversion based on stochastic probing of the Hessian operator. The strategy is to compute the Hessian vector product of some random vectors, then perform the autocorrelations of the product vectors and finally average all the autocorrelations to get the time and spatial resolution lengths. The Hessian vector product is done through a second-order adjoint strategy that allows to avoid the explicit Hessian computation.
The purpose of an earthquake kinematics inversion is to get the slip-rate time-space history using the seismograms available. A simple way to evaluate its resolution length is to perform a checkerboard test. However multiple tests must be done in order to identify the specific resolution length in different regions of the solution. Fitchner and Van Leeuwn (2015) have proposed to use random probing techniques for resolution analysis. They have pointed out that the Hessian acts as a smoother of random functions which carry information of the resolution.
In this work we show how to perform a resolution analysis for earthquake kinematics inversion based on stochastic probing of the Hessian operator. The strategy is to compute the Hessian vector product of some random vectors, then perform the autocorrelations of the product vectors and finally average all the autocorrelations to get the time and spatial resolution lengths. The Hessian vector product is done through a second-order adjoint strategy that allows to avoid the explicit Hessian computation.