Evidence of Powerlaw Flow in the Mojave Mantle

Andrew Freed and Roland Bürgmann

Introduction

Laboratory experiments suggest that rocks in the lower crust and upper mantle (shallower than  200 km) should deform by dislocation creep, characterized by a strain rate proportional to stress raised to a power, n (e.g., Kirby and Kronenberg, 1987; Carter and Tsenn, 1987). Dislocation creep has not yet been confirmed by geodetic observations. We use GPS campaign and continuous time-series data associated with 1992 Landers and 1999 Hector Mine earthquakes to infer rheologic properties of the Mojave lithosphere in southern California. The coupled nature of these earthquakes (20 km and 7 years apart) makes them ideal for a stringent rheology study in that a candidate rheologic model must satisfy the postseismic observations associated with both events. To infer the nature of viscous flow we developed a finite element model of this earthquake sequence that simulates coseismic slip associated with both events (Wald and Heaton, 1994; Dreger and Kaverina, 2000), a regional background strain rate (Savage and Svarc, 1997), and temperature dependent powerlaw rheologies (Hirth et al., 2001; Kronenberg and Tullis, 1984; Shelton and Tullis, 1981; Jaoul et al., 1984; Hansen and Carter, 1982). We consider a range of powerlaws (for felsic and mafic, wet and dry rocks) reflecting uncertainty in the mineralogy of the lithosphere and in the extrapolation from laboratory to geologic conditions. Thermal gradients are constrained from surface heat flow measurements (Williams, 1996) and regional seismic velocities (Melbourne and Helmberger, 2001). For comparison purposes, we also consider models with a Newtonian (strain rate linearly proportional to stress) rheology.

Results

Our results show that the spatial and temporal evolution of transient surface deformation following the Landers and Hector Mine earthquakes can be successfully explained by powerlaw flow (n = 3.5), predominantly in a warm and wet upper mantle. These result are characterized by model and data comparisons shown in Figure 29.1. We can rule out Newtonian flow as a reasonable explanation of both the spatial and temporal patterns of postseismic transient motions, implying that the common assumption of Newtonian flow in numerical models of ductile deformation within the crust and upper mantle (e.g., Thatcher et al., 1980; Miyashita, 1987; Deng et al., 1998; Pollitz et al., 2001, 2002) may be invalid. These results suggest that recovery-controlled dislocation creep is the dominant mechanism of viscous flow following earthquakes. The model results also preclude significant flow in the lower crust, supporting the contention that, at least beneath the Mojave Desert, the mantle is the weaker region.

The stress dependence of powerlaw flow inferred by our calculations means that the viscosity of the upper mantle changes as a function of time after an earthquake. This has implications for models of regional stress changes and fault interaction. For example, the influence of earthquake induced stress changes on neighboring faults will evolve more rapidly early on, but will last many decades longer than would be inferred from a Newtonian model. Furthermore, as viscosities are lowest where stresses are highest, a powerlaw rheology leads to a more localized shear zone beneath faults where coseismic stresses are highest. For example, our calculations show that a Newtonian model of post-Landers relaxation leads to a broad, diffuse shear zone in the mantle beneath the Landers rupture zone about 250-300 km wide. In contrast, post-Landers relaxation of a powerlaw rheology leads to a relatively narrow shear zone 70-90 km wide, with much of the shear concentrated in a central zone only 15 km wide.

Figure 29.1: Comparison of representative observed and calculated postseismic displacement time-series following the 1992 Landers and 1999 Hector Mine earthquakes. (a) Horizontal displacements at 3 continuously monitored GPS stations following 1999 Hector Mine earthquake. (b) Horizontal displacements at campaign GPS station law2 following the 1992 Landers quake (22). Inset shows campaign data at station law2 following the Hector Mine quake. (c) Vertical motions at 2 continuously monitored stations following 1999 Hector Mine earthquake. Powerlaw mantle flow model (solid black curves) is a model of aplite and wet olivine. Powerlaw crustal model (dotted black curves) is a model of wet quartzite and dry olivine. Newtonian models consider purely mantle flow with low viscosity (2.5 x 1018 Pa s, solid grey curves) and an order of magnitude higher viscosity (dotted grey curves) that match early and late time-series slopes, respectively. Curves associated with the high viscosity Newtonian model have been raised to show where the slopes match the observed time-series. These results show that a powerlaw model of flow in the mantle can satisfy that time-series data, but not a model of lower crustal or Newtonian flow.
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Acknowledgements

Funding provided by NSF grant #EAR 0207617

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