Source Description of the 1999 Hector Mine, California, Earthquake, Part I: Wavelet Domain Inversion Theory and Resolution Analysis

We present a new procedure for the determination of rupture complexity from a joint inversion of static and seismic data. Our fault parameterization involves multiple fault segments, variable local slip, rake angle, rise time, and rupture velocity. To separate the spatial and temporal slip history, we introduce a wavelet transform that proves effective at studying the time and frequency characteristics of the seismic waveforms. Both data and synthetic seismograms are transformed into wavelets, which are then separated into several groups based on their frequency content. For each group, we use error functions to compare the wavelet amplitude variation with time between data and synthetic seismograms. The function can be an L1 + L2 norm or a correlative function based on the amplitude and scale of wavelet functions. The objective function is defined as the weighted sum of these functions. Subsequently, we developed a finite-fault inversion routine in the wavelet domain. A simulated annealing algorithm is used to determine the finite-fault model that minimizes the objective function described in terms of wavelet coefficients. With this approach, we can simultaneously invert for the slip amplitude, slip direction, rise time, and rupture velocity efficiently. Extensive experiments conducted on synthetic data are used to assess the ability to recover rupture slip details. We, also explore slip-model stability for different choices of layered Earth models assuming the geometry encountered in the 1999 Hector Mine, California, earthquake.

[1]  Egill Hauksson,et al.  Crustal structure and seismicity distribution adjacent to the Pacific and North America plate boundary in southern California , 2000 .

[2]  Luis Rivera,et al.  A note on the dynamic and static displacements from a point source in multilayered media , 2002 .

[3]  Walter H. F. Smith,et al.  Free software helps map and display data , 1991 .

[4]  Earthquake source parameters and fault kinematics in the eastern California shear zone , 1998, physics/9806031.

[5]  Robert W. Graves,et al.  Resolution analysis of finite fault source inversion using one- and three-dimensional Green's functions. 1. Strong motions , 2001 .

[6]  Thomas H. Heaton,et al.  Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake , 1983 .

[7]  Daniel H. Rothman,et al.  Automatic estimation of large residual statics corrections , 1986 .

[8]  D. Wald,et al.  Spatial and temporal distribution of slip for the 1992 Landers, California, earthquake , 1994, Bulletin of the Seismological Society of America.

[9]  Gregory C. Beroza,et al.  Slip distribution of the 1992 Landers earthquake and its implications for earthquake source mechanics , 1994 .

[10]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[11]  Pengcheng Liu,et al.  The 1994 Northridge, California, earthquake: Investigation of rupture velocity, risetime, and high‐frequency radiation , 1996 .

[12]  Mrinal K. Sen,et al.  Global Optimization Methods in Geophysical Inversion , 1995 .

[13]  Paul G. Richards,et al.  Quantitative Seismology: Theory and Methods , 1980 .

[14]  Robert W. Graves,et al.  Resolution analysis of finite fault source inversion using one- and three-dimensional Green's functions: 2. Combining seismic and geodetic data , 2001 .

[15]  Stephen H. Hartzell,et al.  INVERSION FOR SLIP DISTRIBUTION USING TELESEISMIC P WAVEFORMS: NORTH PALM SPRINGS, BORAH PEAK, AND MICHOACAN EARTHQUAKES , 1988 .

[16]  T. Heaton.  Evidence for and implications of self-healing pulses of slip in earthquake rupture , 1990 .

[17]  Mrinal K. Sen,et al.  Nonlinear one-dimensional seismic waveform inversion using simulated annealing , 1991 .

[18]  P. Spudich,et al.  What Can Strong-Motion Data Tell Us about Slip-Weakening Fault-Friction Laws? , 2000 .

[19]  Michel Campillo,et al.  Frequency domain inversion of strong motions: Application to the 1992 Landers earthquake , 1995 .

[20]  Gregory C. Beroza,et al.  Linearized inversion for fault rupture behavior: Application to the 1984 Morgan Hill, California, earthquake , 1988 .

[21]  Donald V. Helmberger,et al.  Source Estimation from Broadband Regional Seismograms , 1994 .

[22]  E. Hauksson,et al.  The 1999 Mw 7.1 Hector Mine, California, Earthquake Sequence: Complex Conjugate Strike-Slip Faulting , 2002 .

[23]  John G. Anderson,et al.  Implications of frequency-domain inversion of earthquake ground motions for resolving the space-time dependence of slip on an extended fault , 1988 .

[24]  Donald V. Helmberger,et al.  Advancement in source estimation techniques using broadband regional seismograms , 1996, Bulletin of the Seismological Society of America.

[25]  Thomas H. Heaton,et al.  Rupture model of the 1989 Loma Prieta earthquake from the inversion of strong-motion and broadband teleseismic data , 1991, Bulletin of the Seismological Society of America.

[26]  Kiyoshi Yomogida,et al.  Detection of anomalous seismic phases by the wavelet transform , 1994 .

[27]  Douglas S. Dreger,et al.  Determination of source parameters at regional distances with three‐component sparse network data , 1993 .

[28]  Gregory C. Beroza,et al.  Near-source modeling of the Loma Prieta earthquake: Evidence for heterogeneous slip and implications for earthquake hazard , 1991 .

[29]  K. Ohkitani,et al.  Orthonormal wavelet analysis of turbulence , 1991 .

[30]  Chen Ji,et al.  Source Description of the 1999 Hector Mine, California, Earthquake, Part II: Complexity of Slip History , 2002 .

[31]  Allen H. Olson,et al.  Finite faults and inverse theory with applications to the 1979 Imperial Valley earthquake , 1982 .