On the resolution of shallow mantle viscosity structure using postearthquake relaxation data: Application to the 1999 Hector Mine, California, earthquake

[1] Most models of lower crust/mantle viscosity inferred from postearthquake relaxation assume one or two uniform‐viscosity layers. A few existing models possess apparently significant radially variable viscosity structure in the shallow mantle (e.g., the upper 200 km), but the resolution of such variations is not clear. We use a geophysical inverse procedure to address the resolving power of inferred shallow mantle viscosity structure using postearthquake relaxation data. We apply this methodology to 9 years of GPS‐constrained crustal motions after the 16 October 1999 M = 7.1 Hector Mine earthquake. After application of a differencing method to isolate the postearthquake signal from the “background” crustal velocity field, we find that surface velocities diminish from ∼20 mm/yr in the first few months to ⪅2 mm/yr after 2 years. Viscoelastic relaxation of the mantle, with a time‐dependent effective viscosity prescribed by a Burgers body, provides a good explanation for the postseismic crustal deformation, capturing both the spatial and temporal pattern. In the context of the Burgers body model (which involves a transient viscosity and steady state viscosity), a resolution analysis based on the singular value decomposition reveals that at most, two constraints on depth‐dependent steady state mantle viscosity are provided by the present data set. Uppermost mantle viscosity (depth ⪅ 60 km) is moderately resolved, but deeper viscosity structure is poorly resolved. The simplest model that explains the data better than that of uniform steady state mantle viscosity involves a linear gradient in logarithmic viscosity with depth, with a small increase from the Moho to 220 km depth. However, the viscosity increase is not statistically significant. This suggests that the depth‐dependent steady state viscosity is not resolvably different from uniformity in the uppermost mantle.

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