Linking Surface Evolution with Mantle Dynamic Processes Using Adjoint Models with Data Assimilation

Quantifying the relationship between subsolidus mantle convection and surface evolution is a fundamental goal of geophysics. Toward this goal progress has been slow due to incomplete knowledge of the earth’s internal structure and properties. While seismic tomography reveals details on internal 3D structure of the present mantle, evolution of the subsolidus mantle during the geological past remains elusive. This thesis attempts to solve the time inversion of mantle convection using the adjoint method based on present-day seismic images and geological and geophysical observations dictating the past evolution of solid earth. The adjoint method, widely used in meteorological and oceanographic predictions, can be applied to mantle convection for the recovery of unknown initial conditions through the assimilation of present-day mantle seismic structure. We propose that an optimal first guess to the initial condition can be obtained through a simple backward integration (SBI) of the governing equations thus lessening the computational expense. By incorporating time-dependent surface dynamic topography in addition to present-day mantle structure, the adjoint method is improved so as to constrain uncertain mantle dynamic properties and initial condition simultaneously. The theory is derived from the governing equations of mantle convection and validated by synthetic experiments for a single- and two-layer viscosity mantle within regionally bounded spherical shells. For both cases, we show that the theory can constrain mantle properties with errors arising through the adjoint recovery of the initial condition. For the two-layer model, there is a trade-off between the temperature scaling and lower mantle viscosity. By assimilating seismic structure and plate motions in the inverse mantle convection model, we reconstruct Farallon plate subduction back to 100 Ma. We put constraints on basic mantle properties, including both the depth dependence of mantle viscosity and slab buoyancy, by predicting proxies of dynamic topography evident in the stratigraphy of the North American Cretaceous western interior seaway. Models that fit stratigraphy well require the Farallon slab to have been flat lying in the Late Cretaceous, consistent with geological reconstructions. The models predict an extensive zone of shallow-dipping subduction extending beyond the flat-lying slab farther east and north, while the limited region of subducting flat slab resembles an oceanic plateau. In order to test the hypothesis of oceanic plateau subduction and its relationship to the Laramide orogeny, we compare the inverse convection model with plate reconstructions. Two prominent seismic anomalies on the Farallon plate recovered from inverse models coincide with paleogeographically-restored positions of conjugates to the Shatsky and Hess plateaus when they subducted beneath North America. The distributed shortening of the Laramide orogeny closely tracked the passage of the Shatsky conjugate beneath North America, while the effects of Hess conjugate subduction were restricted to the northern Mexico foreland belt. We find that Laramide uplifts were consequences of the removal, rather than the emplacement, of the Shatsky conjugate, and we predict that these subducted plateaus should be detectable by the USArray seismic experiment. The inverse convection models predict a continuous vertical motion history of western U.S., which is further validated by constraints on the vertical motion of the Colorado Plateau since the Cretaceous. With the arrival of the flat-lying Farallon slab, dynamic subsidence swept from west to east over the western U.S., peaking at 86 Ma within the Colorado Plateau. This eastward migrating dynamic subsidence is consistent with a recently compiled backstripping study that shows a long-wavelength residual subsidence shifting to the east, coincident with the passage of the flat slab beneath North America in our inverse model. Two stages of uplift followed the removal of the Farallon slab below the Colorado Plateau: one in the latest Cretaceous, and the other in the Eocene, with a cumulative uplift of ~1.2 km; the former represents the Laramide uplift which also marks the initial uplift of the entire western U.S. Both the descent of the slab and buoyant upwellings raised the Colorado Plateau to its current elevation during the Oligocene. A locally thick lithosphere enhances coupling to the upper mantle so that the Colorado Plateau has a higher topography with sharp edges. Our models also predict that the plateau tilted downward to the northeast before the Oligocene, caused by northeast-trending subduction of the Farallon slab, and that this northeast tilting diminished and reversed to the southwest during the Miocene in response to buoyant upwellings. Overall, this thesis shows that the adjoint models with data assimilation are useful in linking surface evolution to deep mantle processes both over North America and areas beyond. While more research is clearly needed to construct a more earth-like model, this thesis presents an important advance in data-oriented geodynamic models.