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Influence of Near-source Velocity Heterogeneity on the Recovery of Isotropic Seismic Moment Tensors

Mark Panning, Douglas Dreger, and Hrvoje Tkalcic


There has been a large amount of disagreement about source processes for earthquakes in and around Long Valley Caldera (LVC). After the Wheeler Crest earthquake on October 4, 1978, and a swarm including four magnitude 6 earthquakes in 1980, there was much debate concerning the significant non-double-couple (NDC) component of several of these (Julian and Sipkin, 1985; Wallace, 1985). More recently, another earthquake swarm in late 1997 and early 1998 consisted of several earthquakes above magnitude 4 with significant NDC components (Dreger et al., 2000) (figure 20.1).

Earlier research focused primarily on the existence and significance of a compensated-linear-vector-dipole (CLVD) component to the 1980 events. Tensile fluid fracturing, simultaneous rupture on differently oriented fault planes, or propagation anomalies due to 3D near-source structure (Wallace, 1985) were all suggested as mechanisms. High quality broadband data for the events in the 1997 swarm permitted to further invert for significant isotropic component to the moment tensor (up to 42% of the moment release, Dreger et al., 2000) This indicates possible volumetric expansion during the source process further suggesting fluid related fracturing. It does not, however, eliminate possible bias in the inversion process due to near-source structure. Because of this, we numerically analyzed the effect of 3D velocity heterogeneity on the inversion results using a elastic finite-difference code, E3D (Larsen and Schulz, 1995).

Figure 20.1: Map of the LVC showing the variation in Vp for a 6 km depth slice in the H. Benz tomographic model (written communication, 1999). Moment tensor inversion results for 4 events in 1997 are shown ( Dreger et al., 2000). Inset: configuration for the finite difference simulations. The source is the star, while the triangles are the location of receivers. The four larger triangles are the receivers used in the moment tensor inversions. Moment tensors for input source mechanisms in the finite difference simulations are shown as well.
\epsfig{file=panning00_1_1.epsi, width=8cm}\end{center}\end{figure}

Table 20.1: Comparison of input mechanism with deviatoric and full moment tensor inversion results. Percentage double-couple, CLVD, and isotropic component are shown as well as the data variance reduction for the inversions. The F ratio (see text for explanation) for each input mechanism is also shown.
Input Mechanism Deviatoric Inversion Full inversion  
Strike-slip 3 100/0/0 87/13/0 96.5 90/2/8 96.5 1.01
Strike-slip 6 100/0/0 78/22/0 96.9 78/20/2 96.9 1.00
Normal 3 100/0/0 95/5/0 94.9 77/12/11 95.2 1.06
Normal 6 100/0/0 97/3/0 92.9 91/3/7 93.2 1.04
Normal 10 100/0/0 97/3/0 92.7 98/1/1 92.7 1.00
CLVD 3 0/100/0 5/95/0 96.5 14/69/17 96.7 1.06
CLVD 6 0/100/0 32/68/0 96.3 28/67/5 96.3 1.00
DC/ISO 6 57.1/0/42.9 60/40/0 93.5 56/13/31 96.6 1.96
CLVD/ISO 6 0/57.4/42.6 84/16/0 93.9 45/23/32 96.6 1.84
DC/CLVD/ISO 6 38.2/22.9/38.9 49/51/0 90.3 29/46/26 95.3 2.10


To model the effects of LVC structure, E3D was used to calculate synthetic seismograms for a velocity model of the region derived from a local/teleseismic tomography P-wave model (H. Benz, written communication, 1999) (figure 20.1). This data was then inverted both for a deviatoric moment tensor (isotropic component constrained to zero) and a full moment tensor using a linear time-domain scheme with Green's functions calculated from 1D models. The results are shown in Table 20.1. While in general, the data fit of a model with more unknown parameters will always be better, the ratio of the variance of the deviatoric inversion to the variance of the full inversion is reported for purpose of an F test which compares two samples with different degrees of freedom. For the inversions here, the critical values for the F ratio ( $\sigma^{2}_{dev}/\sigma^{2}_{full}$) are 1.12, 1.31 and 1.47 at the 75%, 95% and 99% confidence levels respectively. With no input isotropic component, most inversions resulted in negligible isotropic components, and while one of the inversions shows an 18% isotropic component, this result only shows a slight improvement in variance reduction over the deviatoric inversion, and does not show significant improvement in data fit within the F test criteria. For the sources with isotropic component, the amount of isotropic component is actually underestimated by approximately 10%, but the full inversion shows significant improvement in fit to the data at or above the 99% confidence level compared to the deviatoric inversion.


While the NDC components of the seismic moment tensor remain difficult to resolve, the isotropic components of anomalous earthquakes in the LVC earthquake swarm of late 1997 and early 1998 appear to be real features of the source process. Finite-difference simulations of wave propagation through a 3D heterogeneous medium such as the LVC indicate that near source structure alone can not account for the observed isotropic components of some earthquakes in the region.


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

Julian, B.R., and S.A. Sipkin, Earthquake processes in the Long Valley caldera area, California, Journ. Geophys. Res., 90, 11,155-11,169, 1985.

Larsen, S., and C.A. Schulz, ELAS3D: 2D/3D elastic finite-difference wave propagation code, Technical Report No. UCRL-MA-121792, 19 pp., 1995.

Wallace, T., A reexamination of the moment tensor solutions of the 1980 Mammoth Lakes earthquakes, Journ. Geophys. Res., 90, 11,171-11,176, 1985.

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