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Time-dependent depth distribution of aftershocks: Implications for fault mechanics and crustal rheology

Frederique Rolandone, Roland Bürgmann, and Robert Nadeau


A fundamental property of the continental upper crust is the depth distribution of earthquakes. The maximum depth of seismogenic faulting is interpreted either as the brittle-ductile transition, the transition from brittle faulting to plastic flow in the continental crust, or as the transition in the frictional sliding process from unstable to stable sliding. This transition depth depends on four main factors: rock composition, temperature, strain rate, and fluid pressure (e.g., Sibson 1982, 1984; Meissner and Strehlau, 1982; Tse and Rice, 1986; Scholz, 1990). Spatial variations in the maximum depth of seismicity in southern California have been correlated with crustal temperature or lithology (e.g., Magistrale and Zhou, 1996; Williams et al., 2001). However, little has been done to examine how the maximum depth of seismogenic faulting varies locally (at the scale of a fault segment) with time during an earthquake cycle.

Many models assume a first-order transition from brittle to ductile deformation at a depth that is determined from regional estimates of the geotherm and strain rate. In the vicinity of a large fault this may be misleading because of the effects of strain localization. Strain rate values at depth around active faults are not known but recent mechanical models of strike-slip fault deformation (e.g., Chery et al., 2001; Rolandone and Jaupart, 2002) show high strain rate localization around the base of the fault. Thus the brittle-ductile transition is not a sharp and fixed discontinuity in the crust but is expected to vary near the fault with strain rate and therefore to change with time through the earthquake cycle.

The objectives of this study are to apply high-resolution earthquake relocation techniques to resolve the time-dependent depth distribution of aftershocks and thus constrain models of the brittle-ductile transition and the rheology near the base of seismogenic faults.


We investigate the time-dependent depth distribution of aftershocks following moderate to large earthquakes on strike-slip faults in southern California. Southern California offers a dense network of active strike-slip faults and high seismic activity. It is a very well instrumented area. Catalogs of seismicity provide a large observational time interval of seismicity records. We plan to examine the pattern of seismicity on different strike-slip fault segments to determine either spatially stable pattern (long-lived seismic structures) or systematic temporal variations related to recent earthquakes.

We use the 69-year catalog of the Southern California Seismic Network (SCSN) to identify target events. We use the catalog of relocated 1975-1998 earthquakes using the source specific station term method of Richards-Dinger and Shearer (2000), and the catalog of relocated events using a three-dimensional velocity model based on a joint-hypocenter-velocity (JHV) from 1981 to 2000 of Hauksson (2000) to do preliminary studies of aftershocks sequences.

Recently developed relative relocation techniques improve relative hypocenter locations (in favorable cases relative errors can be typically less than 20 m (Waldhauser et al., 1999; Waldhauser and Ellsworth, 2000) and reveal greater details of the patterns of deformation during an earthquake cycle. We apply cross-correlation techniques and the double difference method of Waldhauser and Ellsworth (2000) to relocate earthquakes in the areas of interest (with the HypoDD relocation code).

Preliminary results

We begin this study analysing the seismicity around the 1987 Superstition Hills earthquake (M$_s$=6.6) as a first test case. Figure 17.1 shows a map view of the seismicity relocated using HypoDD around Superstition Hills for the time period 1983-2000. The inside box shows the zone of our study along the surface rupture of the earthquake.

Figure 17.1: Seismicity (dots) around Superstition Hills from 1983 to 2000 relocated with HypoDD. The box indicates the seismicity used in this study around the surface rupture of the 1987 Superstition Hills earthquake (square). Active faults are shown.
\epsfig{file=frede02_1_1.eps, width=8cm}\end{center}\end{figure}

We compare the time-dependent depth distribution of seismicity given by the different published catalogs (Figure 17.2). Figure 17.3 shows our relocated earthquake catalog for different velocity models. The different catalogs and our own relocation results show large variations of hypocentral depths. These variations seem mainly related to the choice of the velocity model for the upper crust. However, a persistent feature of the depth distribution of aftershocks is that in the immediate postseismic period the aftershocks are deeper than the background seismicity and these deepest aftershocks become shallower with time following the mainshock. Preliminary analysis of other historic ruptures in the Mojave Desert show a similar pattern. In order to quantify these variations, we are working on obtaining a sharper picture of the time-dependent depth variation of the seismicity.

Figure 17.2: Time-dependent depth distribution of the seismicity from (1) the Richards-Dinger and Shearer catalog (2000), and from (2) the Hauksson catalog. (3) Detail of the distribution of seismicity from the Hauksson catalog from November 24 1987 to the end of 1987.
\epsfig{file=frede02_1_2.eps, width=16cm}\end{center}\end{figure*}

Figure 17.3: (1) Velocity structures used for relocation with HypoDD: (a) derived from Shearer (1997), (b) derived from Fuis et al. (1982). (2) Our relocation results obtained for velocity model (a), and (3) for velocity model (b). Note the difference in the depth scale with Figure 17.2.
\epsfig{file=frede02_1_3.eps, width=16cm}\end{center}\end{figure*}

Future work

Temporal changes in depth of seismicity may serve to increase our knowledge of (1) the depth to which upper crustal deformation is coupled to deformation within the lower crust, (2) the mechanics of fault zones near the base of the seismogenic zone where large earthquakes tend to nucleate and (3) of the transient deformation processes and their rheological parameters that are active during the postseismic period.

We are working on developing numerical finite-element models to compare these observations and the mechanical evolution of strike-slip faults and to infer fault slip and rheologic stratification. Our objective is to relate the depth distribution of hypocenters during an earthquake cycle to the evolution of the brittle-ductile transition to place constraints on strain rate at depth and on the partitioning of deformation between brittle faulting and distributed deformation.


Chery, J., M.D. Zoback, and R. Hassani, An integrated mechanical model of the San Andreas Fault in central and northern California, J. Geophys. Res., 106, 22,051-22,066, 2001.

Hauksson E., Crustal structure and seismicity distribution adjacent to the Pacific and North America plate boundary in southern California, J. Geophys. Res., 105, 13,875-13,903, 2000.

Magistrale, H. and H. Zhou, Lithologic control of the depth of earthquakes in southern California, Science, 273, 639-642, 1996.

Meissner, R. and J. Strehlau, Limits of stresses in continental crusts and their relation to the depth-frequency distribution of shallow earthquakes, Tectonics, 1, 73-79, 1982.

Richards-Dinger, K.B. and P. Shearer, Earthquake locations in southern California obtained using source-specific station terms, J. Geophys. Res., 105, 10,939-10,960, 2000.

Rolandone F. and C. Jaupart, The distribution of slip rate and ductile deformation in a strike-slip shear zone, Geophys. J. Int., 148, 179-192, 2002.

Scholz, C.H., The mechanics of earthquakes and faulting, pp. 439, Cambridge University Press, 1990.

Sibson, R.H., Fault zone models, heat flow, and the depth distribution of earthquakes in the continental crust of the United States, Bull. Seismol. Soc. Am., 68, 1421-1448, 1982.

Sibson, R.H., Roughness at the base of the seismogenic zone: contributing factors, J. Geophys. Res., 89, 5791-5799, 1984.

Tse, S.T. and J.R. Rice, Crustal earthquake instability in relation to the depth variation of frictional slip properties, J. Geophys. Res., 91, 9452-9472, 1986.

Waldhauser, F., W.L. Ellsworth, and A. Cole, Slip-parallel seismic lineations on the northern Hayward fault, California, Geophys. Res. Lett., 26, 3525-3528, 1999.

Waldhauser, F. and W. L. Ellsworth, A double-difference earthquake location algorithm: method and application to the northern Hayward fault, California, Bull. Seismol. Soc. Am., 90, 1353-1368, 2000.

Williams, C.F., L.A. Beyer, F.V. Grubb, S. Galanis, Heat Flow and the Seismotectonics of the Los Angeles and Ventura Basins of southern California, Eos Trans. AGU, 82(47), Fall Meet. Suppl., Abstract S11A-0534, 2001.

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