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Coseismic Slip Distribution of the Mw 7.1 Hector Mine Earthquake from Space Geodetic Techniques

Evelyn Price and Roland Bürgmann


The October 16, 1999 Mw 7.1 Hector Mine earthquake ruptured only 30 km to the east of the 1992 Mw 7.3 Landers earthquake in a region where individual faults experience large earthquakes every 1,500 to 5,000 years (Sauber et al., 1994; Wesnousky, 1986 and references therein). The proximity of these two earthquakes in space and time suggests that they are mechanically related (Parsons and Dreger, 2000; Scientists, 2000). A detailed estimate of the distribution of coseismic slip on the earthquake rupture provides constraints on models describing inter-earthquake, inter-fault, and intra-fault mechanics.

The deformation of the Earth's surface in the region surrounding the Hector Mine rupture was measured by Global Positioning System (GPS) and Interferometric Synthetic Aperture Radar (InSAR) techniques. Using GPS, we can measure vector displacements of the Earth's surface at locations where GPS antennas exist. Geodetic measurements were made at 35 geodetic markers within a 50 km radius of the fault rupture using campaign GPS, at 144 stations maintained by the Southern California Integrated GPS Network (SCIGN), and at 60 meter postings using InSAR (Figure 0.26). Using InSAR, we obtain a spatially dense map of the displacements of the Earth's surface in the direction of the SAR satellite's line-of-sight (LOS). The InSAR data used in this study was collected during descending passes of the European Space Agency's ERS-1 and ERS-2 satellites whose LOS direction has an azimuth of 103$^\circ $and is 23$^\circ $from vertical.

Inversion of Geodetic Data for Earthquake Slip Distribution

We combine the geodetic data sets in a damped linear least-squares inversion to infer the distribution of slip on the Hector Mine earthquake rupture. The physics of the problem are described by a homogeneous, linear elastic half-space Earth model containing a vertical cut. This cut is the synthetic earthquake rupture whose trace, at the surface of the half-space, follows the geometry of the rupture mapped at Earth's surface by geologists (Figures 0.26 and 17.2). We parameterize the rupture using planar patches enabling us to use the formulation of Okada, (1985) to describe the displacements at the surface of the half-space caused by offsets across each patch. The forward problem is to predict the displacements at the Earth's surface caused by the displacements across the patches. The inverse problem concerns determination of the offsets on patches from the geodetically measured displacements at the surface.

We infer the distribution of slip on the earthquake rupture by solving the following system of equations for the elements of $\stackrel{\rightarrow}{\mathbf m}$, $\mathit c$, $\mathit s_e$, and $\mathit s_n$:

\begin{displaymath}\left [
C_g\Sigma_{gps}^{-\frac{1}{2}} [ \...
...{\mathit sar} \vspace{2pt} \\
\mathbf 0 \end{array} \right ]

where $\mathit C_g$ is the relative weight of GPS data; $\mathit C_s$ is the relative weight of InSAR data; $\Sigma_{\mathit gps}$ is the GPS data covariance matrix; $\Sigma_{\mathit sar}$ is the InSAR data covariance matrix; $\mathbf G_{\mathit gps}$ is the GPS design matrix; $\mathbf G_{\mathit sar}$ is the InSAR design matrix; P allows for a regional tilt in the InSAR displacement map; $\mathit \beta$ penalizes roughness in the model; L is a Laplacian filter; $\stackrel{\rightarrow}{\mathbf m}$ contains the distributed slip model; $\mathit c$, $\mathit s_e$, $\mathit s_n$ are, respectively, a constant offset, east slope and north slope in the InSAR displacement map; $\stackrel{\rightarrow}{\mathbf d}_{\mathit gps}$ contains the GPS displacements; and $\stackrel{\rightarrow}{\mathbf d}_{\mathit sar}$ contains the InSAR displacements. The design matrices contain the Green's functions which relate displacements at geodetic measurement locations to slip on rupture patches.

To estimate the distribution of slip on the earthquake rupture surface, we address several technical issues regarding model smoothing and data combination. We first infer the slip distribution using GPS and InSAR measurements seperately and analyze groups of distributed slip models in which the smoothness of the members differ. As the smoothness of a model increases, the misfit between the observations and the surface displacements predicted by the model increases. We choose, from each group of models, an optimal member which retains enough detail, is reasonably smooth, and maintains an acceptable level of misfit. Optimal members of the InSAR and GPS groups are shown in the top two panels of Figure 17.2. After we have chosen the optimal group members, we weight the data sets in a joint inversion of both data sets such that the amount of smoothing specified by the above analysis is maintained for each data type. Using this weighting scheme, we infer the slip distribution shown in the third panel of Figure 17.2.

Figure 17.1: The geodetic data and regional faults. Each color cycle is 28 mm of displacement in the LOS direction. Arrows indicate horizontal GPS displacements with 95%-confidence error ellipses. The magenta lines are the Landers (west) and Hector Mine (east) earthquake ruptures, the black lines are mapped faults, and the stars are at the epicenters of earthquakes with magnitudes > 6 that have happened in the last seven years.
\epsfig{file=price00_1.eps, width=7cm}\begin{flushleft}\end{flushleft}\end{center}\end{figure}

Results and Discussion

The distribution of slip inferred from InSAR data alone covers a much greater area of the rupture plane than that inferred from GPS data alone and predicts an earthquake moment release nearly twice that predicted by the GPS data. It also leads us to infer deep slip on the rupture and major concentrations of slip to the north of the hypocenter. The slip distribution determined by the joint inversion is bilateral with concentrations of slip on either side of the hypocenter and confined to the upper 15 km of the rupture plane.

The differences between the slip distributions obtained by InSAR and GPS separately could be due to several factors. Some of the deep slip inferred by InSAR may be postseismic afterslip down-dip of the rupture plane or may reflect a tilt in the InSAR displacement map caused by errors in the estimation of SAR satellite orbital positions. Shallow differences between the two slip distributions could be effected by vertical displacements being mapped into horizontal ones in the InSAR inversion and the greater and more even spatial sampling of the InSAR data. The majority of the GPS displacements are to the west of the rupture and the concentration of slip south of the hypocenter is in a region poorly resolved by the GPS data. Despite these differences, a more reasonable slip distribution is obtained by combining the two data sets. The GPS data constrain the long-wavelength surface deformation and the InSAR data allow us to resolve details in the slip distribution.

Figure 17.2: The distributed slip models. The fault length is 58 km, its depth is 20 km, and each patch has dimensions of 2 km by 2 km.
\epsfig{file=price00_2.eps, width=7cm}\end{center}\end{figure}

The geodetically obtained slip distribution is similar to that obtained seismically using strong ground motion data by Kaverina et al., (2000). Both geodetic and seismic slip distributions are bilateral and confined to the upper 15 km of the crust. Also, they both taper to the south. The similarity of the two slip distributions implies that most of the earthquake slip was localized and transformed into ground motion measurable by seismometers.


Kaverina, A., D. Dreger, and E. Price, Source process of the October 16, 1999 Hector Mine Earthquake (Mw7.2) from the inversion of broadband regional data, to be submitted, 2000.

Parsons, T., and D.S. Dreger, Static-stress impact of the 1992 Landers earthquake sequence on nucleation and slip at the site of the 1999 M=7.1 Hector Mine earthquake, southern California, Geophys. Res. Lett., 27 1949-1952, 2000.

Okada, Y., Surface deformation due to shear and tensile faults in a half-space, Bull. Seism. Soc. Am., 75, 1135-1154, 1985.

Sauber, J., W. Thatcher, S.C. Solomon, and M. Lisowski, Geodetic slip rate for the eastern California shear zone and the recurrence time of Mojave desert earthquakes, Nature, 367 264-266, 1994.

Scientists from the U.S. Geological Survey, Southern California Earthquake Center, and California Division of Mines and Geology, Seism. Res. Lett., 71 11-23, 2000.

Wesnousky, S.G., Earthquakes, Quaternary Faults, and Seismic Hazard in California, J. Geophys. Res., 91, 12,587-12631, 1986.

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