One of the most challenging problems in geophysics is the quantification of stresses and rheology of the Earth's plates and plate boundary zones. We address this problem through a comprehensive global treatment of the lithosphere/mantle convection system. We first solve the depth-integrated 3-D force-balance equations (using thin sheet approximation) for the lithosphere, where the effective body force inputs are: (1) the horizontal variations in depth integrated vertical stress (gravity potential energy differences - GPE) and (2) the horizontal and radial tractions applied to the base of the lithosphere, associated with large-scale mantle circulation. GPE estimates rely on accurate (seismically-defined) crustal and upper mantle structure. Mantle circulation models satisfy plate motions, geoid, and dynamic topography. Plate motions are self-generated, and not imposed. Convection models have both radial and lateral viscosity variations, and are driven by deeper density buoyancies, inferred from tomography and history of subduction. Modeling performed to date has provided an unprecedented quality of fit between model deviatoric stress fields and stress indicators; the GPE differences calibrate the magnitudes of deviatoric stress, and the observationally - constrained modeling has placed limits on the magnitude and distribution of tractions that exist at the base of the lithosphere. This modeling of the lithosphere system, therefore, plays an important role in constraining convection models as well. We are also calculating forward dynamic models of the lithosphere that predict the full horizontal velocity gradient tensor field (which can be compared with GPS measurements), along with the deviatoric stress field. The forward modeling, which incorporates anisotropic treatment within transform fault zones, enables us to refine our estimates of depth integrated effective viscosity within the plates and plate boundary zones and further refine coupling models. A final and important part of this project is to investigate full 3-D lithosphere models that are coupled to full 3-D convection models. We will build the global infrastructure, incorporating subduction in 3-D, continental orogeny in 3-D, the role of anisotropic zones (e.g., strike-slip faults), layered elastic and viscous systems, viscoelastic and power law mantle rheology, and full 3-D flexure. This global-scale 3-D treatment of the lithosphere is necessary in order to make further progress on the problem of understanding lithosphere interaction with mantle circulation. This observationally-based treatment will have a significant impact on the understanding of the lithosphere/convection system. Because this work places constraints on the absolute magnitudes of deviatoric stress and the lateral variations in strength of the lithosphere, it has implications for understanding fault mechanics, and even the earthquake rupture energy budget and earthquake cycle. The 3-D spherical treatment is precise and the codes and method are being made available to researchers.
We have investigated self-consistent global dynamic models that include the effects of topography and lithosphere structure along with coupling with 3-D whole mantle flow. The 3-D convections models, which provide traction boundary conditions on a high resolution lithosphere model, are constrained by tomography and history of subduction models. We have delineated the range of radial and lateral viscosity variations within the mantle and lithosphere that enable an acceptable fit between model and observed plate motions, as well as strains and stresses within the plate interiors and plate boundary zones. We have also determined where tractions from mantle flow resist plate motions and where they play a role in driving plate motions. On average, about 70% of the magnitude of deviatoric stresses are associated with lithosphere coupling with mantle flow. The remainder is associated with topography and lithosphere structure (gravity potential energy per unit area - GPE). The relative contribution of GPE and tractions from mantle flow varies spatially, however. Within subduction zones the GPE influence dominates. On the other hand, near mid-ocean ridges, and within some plate interiors, the contribution from tractions dominates over the contribution from GPE. This work provided support and training for a femaile post-doctoral scientist. The work also provided support for 2 undergraduate students as well as 3 high school students who were Intel Semi-finalists. This work has implications for refining our understanding of the state of stress within the lithosphere, the driving mechaisms for plate motions, mountain building, and continental rifting. This work provides a foundation for understanding the forces that lead to earthquake deformation.
