SCEC Award Number 12053 View PDF
Proposal Category Individual Proposal (Integration and Theory)
Proposal Title Stress field models from Maxwell stress functions
Investigator(s)
Name Organization
Peter Bird University of California, Los Angeles
Other Participants
SCEC Priorities 2d, 1b, 1e SCEC Groups SDOT, Geodesy, CS
Report Due Date 03/15/2014 Date Report Submitted N/A
Project Abstract
 The lithospheric stress field is divided into 3 components: a standardized pressure curve, a topographic stress anomaly, and a tectonic stress anomaly. The topographic stress anomaly is computed by numerical convolution of 3 tensor Green’s functions provided by Boussinesq, Cerruti, and Mindlin. By assuming either a seismically-estimated or isostatic Moho depth, and by using Poisson ratio of either 0.25 or 0.5, I obtain 4 alternative topographic stress models. The tectonic stress field, which satisfies the homogeneous quasi-static momentum equation, is obtained from particular second-derivatives of Maxwell vector potential fields which are weighted sums of basis functions representing constant stress components, linearly-varying stress components, and harmonically-varying stress components. Boundary conditions include zero traction due to tectonic stress at sea level, and zero traction due to total stress anomaly on model boundaries at asthenospheric depths. The total stress anomaly is fit by least-squares to both World Stress Map data and a previous faulted-lithosphere, realistic-rheology dynamic model of the region computed with Shells. Constraints of computer memory, execution time, and ill-conditioning of the linear system (which requires damping) limit spatially-oscillating stress to no more than 5 cycles per axis of the model. No conflict is seen between the two target datasets, and the best-fitting model (using an isostatic Moho and Poisson ratio 0.5) gives minimum directional misfits relative to both targets. Peak shear stresses in this preferred model are 130 MPa, and peak vertically-integrated shear stresses are 3.4×1012 N/m. Channeling of deviatoric stress along the strong Peninsular Ranges and Great Valley is evident.
Intellectual Merit The FlatMaxwell algorithm and program represent important advances in stress modeling, in 3 ways:
1. It is now possible to merge stress data (which are usually just stress directions, and come primarily from the upper crust) with output from dynamic models (based on laboratory flow laws, plate-velocity boundary conditions, and computed geotherms) which constrain the likely magnitudes of deviatoric stresses and also the likely form of the mantle stress field.
2. FlatMaxwell is free of assumptions about which flow laws (and flow-law constants) regulate the level of deviatoric stress. Admittedly, such assumptions are made in program Shells, which contributed an important input dataset to this modeling effort. However, replacing this Shells dataset with that from a competing dynamic model would be very easy, and would not require any reprogramming.
3. Stress fields in FlatMaxwell obey the quasi-static equilibrium equation exactly, at all points. This is superior to stress fields obtained from finite-element models which solve a weak form of equilibrium (sometimes weakened further by vertical integration) on a coarse grid.
One immediate scientific result from this exploratory model is that, at least in southern California, deviatoric stress is anti-correlated with long-term deformation rate. Regions of low heat-flow and no active faults are strong, and collect deviatoric stress (by geometric amplification) into “stress guides.” However, zones of many active faults are regulated to modest levels of deviatoric stress even though their long-term strain-rates are orders of magnitude higher. This anti-correlation makes the true tectonic situation in southern California fundamentally different from that in any model that lacks spatial heterogeneity inherited from prior geologic and tectonic history.
Broader Impacts The ability to visualize a candidate stress field for southern California with any desired map or section plane, using any desired measure of the stress tensor, is an important advance in education. Even if the current model is later found to wrong in important ways, it will have advanced understanding of the kinds of stress field that are permissible (and impermissible) under quasi-static equilibrium.
To the extent that the deviatoric stress magnitudes in the model are (approximately) correct, they may inform studies of the effective rheology of the lithosphere of southern California, and thus its composition and thermal state, and perhaps even its pore-pressure distribution.
Investigators who need an estimate of the long-term-average stress directions in the southern California lithosphere (e.g., for Coulomb-triggering studies) can use these models as one possible resource.
Investigators who monitor stress changes through time could consider the possibility of using a FlatMaxwell model as an initial (or final) condition, yielding models of tensor stress in 4 dimensions.
Exemplary Figure Figure 2. Vertically-integrated shear stresses (colored map) from preferred model Final032, which was based on topographic stress model Isostasy0.50. Overlain line segments show trend of most-compressive principal axis of the vertically-integrated stresses; shorter line segments imply steeper plunges. Color of the overlaid line segment indicates tectonic regime (normal, strike-slip, or thrust).