We study the extent of fluid-influenced faulting in the Long Valley volcanic region to better understand the connection between earthquake production and the geothermal and magmatic system. In the analysis of earthquake data, most events are assumed to follow the double-couple (DC) model of faulting characterized by shear along a linear fault plane induced by tectonic stresses. Earthquakes with coseismic volume changes indicate that tectonic forces were not the only factor contributing to failure. In geothermal or volcanic areas, such events are thought to be influenced by fluid migration, in either liquid or gas form, or a change in the state of matter of a fluid (*Ross et al.*, 1999 ; *Dreger et al.*, 2000).

In this study, we focus on a 100 km wide circular area centered at Long Valley caldera which encompassed the Mono-Inyo craters to the north and the Sierra Nevada mountain block to the south. A comprehensive search was performed for events greater than M3.5 since 1993 with significant non-DC components, specifically compensated-linear-vector-dipole (CLVD) and isotropic components.

We model the waveforms of 128 events recorded in the NCSN catalog greater than M3.5 using four different source models: DC, DC+CLVD, DC+isotropic, and DC+CLVD+isotropic. For the DC and DC+isotropic models, a grid search method iterating over strike, dip, rake, DC moment and isotropic moment, which is equal to zero in the pure DC case, was used to find the solution which best fit the observed three-component waveforms. For the deviatoric and full moment tensor models, the second rank symmetric seismic moment tensor was solved by linearly inverting complete three-component broadband seismograms in the time domain using a weighted least squares approach. Green's functions for all four models were computed utilizing a frequency wave-number integration method and the SoCal velocity model (*Dreger and Helmberger*, 1993). A set of seven BDSN stations (BKS, CMB, KCC, MHC, ORV, PKD, and SAO) providing the best azimuthal coverage and data quality were used in this investigation. In practice, however, a solution would usually have a subset of these stations in its inversion depending on station availability and data quality issues. Both data and synthetics were bandpass filtered between 0.02 and 0.05 Hz.

Using the F test as a statistical aid, we determine which of the four models was most appropriate for each individual earthquake. Statistically significant isotropic components were determined if the improvement in fit to the data when using a more complex model was at or above the 90% significance level. We also performed several analyses to determine the stability of the solution, the depth sensitivity of the isotropic component, the recoverability of isotropic components, and the possibility of obtaining a spurious isotropic component.

Within the chosen space and time constraints, 33 events were identified that had solutions with three or more stations in their inversion (Figure 17.1). Of these 33 events, 28 had statistically insignificant non-DC components. The remaining five events had statistically significant positive volumetric components. Two of these five also had statistically significant CLVD components. All of the non-DC events were located either in the south moat of the caldera or in the Sierra Nevada block. We were not able to analyze the source process of earthquakes in or near the vicinity of the Mono-Inyo volcanic chain because events greater than M3.5 were not recorded during the time interval investigated by this study.

To test the stability of the focal mechanism solutions, we performed Jackknife tests on three events: DC event 97.12.31, DC+isotropic event 97.11.22b, and full moment tensor event 97.11.30. Each event originally had six stations in its solution. We solve for all permutations of three, four, and five station combinations and compare these results with the six station solution for each event. DC and DC+isotropic solutions are remarkably stable for solutions with four or more stations in their inversion. Solutions with three stations in the inversion are seen to be slightly more variable. The full moment tensor event showed that the P-wave radiation pattern was stable but that the orientation of the faulting planes was unstable even when using as many as five stations. However it is important to note that the DC component of this event produced only 5% of the total moment released and that the CLVD and isotropic components dominated the inversion. Thus, inversions with four or more stations can be treated with confidence. Three station inversions, while often consistent with solutions with more stations, should be understood to have more uncertainty in the solution.

Most moment tensor inversions in this study did not have good depth control. In some cases, changes in depth may produce statistically significant isotropic components. For eight events, we test for spurious isotropic components due to depth mislocation using the station combination which yielded the best solution in each case. Solutions for source depths between 2 - 11 km are calculated for the five events with significant isotropic events and three DC events (events 97.12.31, 98.06.09, and 98.07.15a). These tests illustrate the importance of accurately knowing the depth of events when attempting to identify earthquakes with significant isotropic components. For the DC events, we can see that for depths deeper than the independently determined NCSN catalog depths, the improvement in fit to the data between the DC and DC+isotropic model is statistically significant. However, the overall fit to the data decreases with depth which indicates that the isotropic components are not modeling the true source behavior. For the DC+isotropic and full moment tensor events, solutions at depths shallower than the catalog depths sometimes do not recover the significant isotropic component. For some events depths outside the allowable range can fit the data better, however, it is important to remember that with the long wavelength data used in this study, the depth of the source is not well constrained which is why NCSN catalog depths are used as an independent constraint.

To determine the stability of the isotropic component with station combination, we performed Jackknife tests on the four events with significant isotropic components that had four or more stations in their inversion. For each event, for all station combinations of three or more, we determined the statistical significance of the volumetric component. For all events, all combinations of four or more stations recovered the statistically significant isotropic component. For solutions with three station in the inversion, only four permutations out of 70 failed to recover the isotropic component. It is reasonable to assume that significant isotropic components can be recovered with as few as three, but preferably with at least four, stations in the inversion. Thus, we can be confident that there are no false negative occurrences within my set of 33 events.

We also investigate the possibility of obtaining a spurious isotropic component due to poor data coverage. For this test, we take three high quality DC inversions (events 97.12.31, 98.06.09, and 98.07.15a) and perform Jackknife tests to see if any combination of three or more stations would result in a statistically significant isotropic component at or above the 90% significance level. For their best solutions, events 97.12.31 and 98.06.09 had six stations in their inversions and event 98.07.15a had seven stations in its inversion. Of 65 four station inversions, four returned a false positive. Of 75 three station inversions, six returned a false positive. Five and six station inversions did not return false positives. Thus, from these tests, events with significant isotropic components that have four or fewer stations in their inversion should be treated with caution. This test casts doubt as to the validity of event 93.08.11 which has only three stations it its inversion.

We appreciate support for this project by NSF through contracts EAR-0087147 and EAR-0105998.

Dreger, D.S. and D.V. Helmberger, Determination of source parameters at regional distances with three-component sparse network data, *J. Geophys. Res., 98*, 8,107 - 8,125, 1993.

Dreger, D. S., H. Tkalcic, and M. Johnston, Dilational processes accompanying earthquakes in the Long Valley Caldera, *Science, 288*, 122 - 125, 2000.

Ross, A., G. R. Foulger, and B.R. Julian, Source processes of industrially-induced earthquakes at The Geysers geothermal area, California, *Geophysics, 64*, 1,877 - 1,889, 1999.

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