A random‐walk algorithm for modeling lithospheric density and the role of body forces in the evolution of the M idcontinent R ift

This paper develops a Monte Carlo algorithm for extracting three‐dimensional lithospheric density models from geophysical data. Empirical scaling relationships between velocity and density create a 3‐D starting density model, which is then iteratively refined until it reproduces observed gravity and topography. This approach permits deviations from uniform crustal velocity‐density scaling, which provide insight into crustal lithology and prevent spurious mapping of crustal anomalies into the mantle. We test this algorithm on the Proterozoic Midcontinent Rift (MCR), north‐central United States. The MCR provides a challenge because it hosts a gravity high overlying low shear‐wave velocity crust in a generally flat region. Our initial density estimates are derived from a seismic velocity/crustal thickness model based on joint inversion of surface‐wave dispersion and receiver functions. By adjusting these estimates to reproduce gravity and topography, we generate a lithospheric‐scale model that reveals dense middle crust and eclogitized lowermost crust within the rift. Mantle lithospheric density beneath the MCR is not anomalous, consistent with geochemical evidence that lithospheric mantle was not the primary source of rift‐related magmas and suggesting that extension occurred in response to far‐field stress rather than a hot mantle plume. Similarly, the subsequent inversion of normal faults resulted from changing far‐field stress that exploited not only warm, recently faulted crust but also a gravitational potential energy low in the MCR. The success of this density modeling algorithm in the face of such apparently contradictory geophysical properties suggests that it may be applicable to a variety of tectonic and geodynamic problems.