Kinematic Inversion of Strong-Motion Data Using a Gaussian Parameterization for the Slip: Application to the 2008 Iwate-Miyagi, Japan, Earthquake

Abstract

Abstract We present a nonlinear technique for the purpose of estimating the distribution of the final slip and the rupture velocity on the fault plane from the inversion of strong‐motion records. In this work, the ground‐motion simulation is obtained by evaluating the representation integral in the frequency domain, through a finite‐element approach, based on a Delaunay’s triangulation of the fault plane. The slip distribution is parameterized by a linear combination of 2D overlapping Gaussian functions. This choice allows us to relate the maximum frequency in the data to the smallest resolvable wavelength on the fault plane, insuring a smooth representation for the slip function. We investigate the capability of such a representation to describe complex slip maps, and we relate the width of the Gaussian function and the overlapping to the minimum wavelength of the slip function. The inverse problem is solved by a two‐step procedure aimed at separating the computation of the rupture velocity from the evaluation of the slip distribution. While a global exploration is maintained for the rupture velocity, for each explored value of this quantity, the slip solution is computed as the best solution approaching the observations in the sense of the L2 norm. The nonlinear step is performed through the neighborhood algorithm (NA), while the linear one uses the nonnegative least‐squares (NNLS) method. The technique has been applied to retrieve the rupture history of the 2008 Iwate–Miyagi, Japan, earthquake. The slip distribution is characterized by a large slip patch extending from the hypocenter to the southern shallow part of the fault plane, with a maximum amplitude of 6 m. In addition, a relatively smaller asperity is located in the north shallow part of the fault. We found that the rupture lasted about 12 s with an average rupture velocity of about 2.0 km/s. Online Material: Figures showing synthetic inversion test results.