Crustal strain rates, upper mantle seismic wave speeds, and implications for lower crustal strength in southern California

In southern California the dilatational strain rate field of the crust imaged using GPS geodesy is strongly correlated with upper mantle wave speeds imaged using Rayleigh wave tomography. This correlation suggests that small-scale upper mantle convection may be actively contributing to upper crustal deformation. Understanding this correlation is important for determining whether geodesy has a role to play in advancing our understanding of upper mantle dynamics, and for improving tectonic interpretations of crustal motion data, particularly with regard to hazards assessment. To study this issue further, we developed an analytical model in which a viscoelastic crust is driven by tractions induced by negatively buoyant cylinders sinking in a viscous mantle halfspace. This model may serve as a numerical analog for delaminated crustal roots or lithospheric mantle drips. For models in which the crust is composed of a single viscoelastic layer with viscosity that is higher than that of the upper mantle, we found that tractions on the base of the crust associated with Stokes-like flow may result in horizontal motions of the crustal surface of order 1 mm/yr or more over distances of as small as 50 km (strain rates of order 20 nanostrain/yr), depending on crustal thickness, cylinder size and density contrast, and crust and mantle viscosities. These strain rates are comparable to the dilatational strain rates observed in southern California. For models in which the lower crust behaves as a weak, low viscosity layer sandwiched between stronger upper crust and mantle, the horizontal components of upper crust are decoupled from mantle flow. Thus, the geodetic strain rate and seismic tomography data for southern California may suggest that the lower crust of southern California is relatively strong. This inference is consistent with long-time scale rheologic properties recently inferred by other researchers from short-time scale postseismic deformation data for the southern California region.