5:15 PM - 6:30 PM
[SSS25-P23] A multi-period inversion of broadband seismic waveforms for 3-D velocity structures
Keywords:Velocity structure model, Waveform inversion, Broadband seismic waveform, Damped least-squares method, Non-linear problem
Seismic waveforms with a period range such as 2-20 s are often used to evaluate long-period ground motions. Thus, it is important to construct a velocity structure model which well reproduces the waveforms filtered over this period range. In this study, we attempt to develop a waveform inversion method for 3-D velocity structures that are responsible for broad-period ground motions. We first divide the inverted period range into multiple period ranges such as 10-20, 5-20, and 2-20 s. We start our inversion with the waveforms with only the longer-period range (10-20 s). The solution for the current period range is used as an initial guess for the next period range, which includes the shorter period (5-20 s). The inversion is continued until the period range matches the broadest period (2-20 s). The velocity structure model is composed of homogeneous layers, and the layer thicknesses are set as model parameters, just as Hikima (2006) did. The model parameters are estimated by solving a non-linear damped least-squares problem, which is an iterative procedure. In the inversion using only longer-period waveforms (10-20 and 5-20 s), we can use coarse inversion grids (e.g., Bunks et al., 1995); in the inversion using the waveforms with the broadest period (2-20 s), a reasonable initial guess leads the iteration to achieve a fast convergence. Thus, our inversion procedure is better than conventional waveform inversions in terms of reducing the total number of 3-D forward simulations. Furthermore, we can stably estimate the model parameters for a complex velocity structure with multiple layers.
We calculate the partial derivatives with respect to model parameters using finite-difference approximation, where the difference between the unperturbed and slightly perturbed synthetic waveforms is taken. The synthetic waveforms are calculated by a 3-D finite element method with voxel meshes (Koketsu et al., 2004; Ikegami et al., 2008). We also use the modified Levenberg-Marquardt method to make the iteration stable. At each iteration, the model parameters are solved by the singular value decomposition of the Jacobian matrix. We performed several numerical experiments to confirm the validity of our inversion procedure. We will show the results and discuss the performance of the recovery of broad-period data as well as the optimal way to divide the inverted period range.