A New Method Applied for the Determination of Relative Weight Ratios Under the TensorFlow Platform When Estimating Coseismic Slip Distribution

When estimating a coseismic slip distribution with multiple observation types, the relative weight ratios (the contribution ratios of all kinds of actual observations in the joint inversion, which should be positive by default) and regularization parameter critically impact the inversion accuracy. In this paper, we propose a new method for determining the relative weights of multiple observations of jointing inversion slip distributions. This method regards the observations and the relative weight ratios as the training data sets and training parameters, respectively; in addition, the constructed Loss function was optimized by the gradient descent method and the exponential decay learning rate method under the TensorFlow platform (GDED). We compared the GDED method with the Helmert variance component estimation method (HVCE) and Akaike's Bayesian information criterion method (ABIC) by designing eight simulation experiments. These simulations included changing the errors and resolutions of the observations, the grid size, the strike angle and the dip angle of the fault, the moment magnitudes of earthquakes, the number of observation types, and the complexity of subduction-zone earthquakes. We analyzed and discussed the characteristics of the above three methods in determining the relative weight ratios during the joint inversion process. The results of these simulation experiments showed that the GDED method and the ABIC method perform much better than the HVCE method when negative variance occurs in the HVCE method, while the accuracies of the slip distributions produced by the three methods were similar when no negative variance occurred; the GDED method can be used to prevent the occurrence of negative variance compared to the HVCE method and is more time efficient than the ABIC method. Furthermore, we applied these methods to invert the source parameters of the 2015 Mw 8.3 Illapel earthquake (in Chile), and the inversion results showed that the slip of the Illapel earthquake was mainly distributed at depths of approximately 10-50 km. The maximum slip of the Illapel earthquake was approximately 7.9 m, distributed 50-70 km northwest of the epicenter at depths of approximately 10-20 km. Plain Language Summary Different geodetic observations have distinct characteristics due to their unique observation technologies; for example, global positioning system data have a high temporal resolution but a low spatial resolution, while InSAR data have a high spatial resolution but a low temporal resolution. The spatial and temporal resolutions of the inversion results can be guaranteed by combining these two observations to invert the coseismic slip distribution. The joint estimation of the coseismic slip distribution is a research hotspot in the field of seismic source parameter inversions. However, different combinations of relative weight ratios between these two observations may lead to great differences when jointing estimation of the slip distribution. Determining the relative weight ratios of all kinds of observations (actual observations and virtual observations) during the joint inversion process is a key issue. The previous methods used to solve this problem have shortcomings such as subjectivity, low computational efficiency, and unstable effects. Herein, we developed the GDED method and compared it with the HVCE method and ABIC method through system simulation experiments and actual earthquake experiments.