D8 Geological Numerical Modeling

Topic

Numerical geological modeling solves the differential equations governing the physical processes of the solid Earth on a mesh that divides the spatial domain into a large number of discrete elements, employing the finite element method, finite difference method, or boundary element method, depending on the specific problem. Numerical geological modeling is the only method capable of integrating the Earth's actual geometric complexity with the nonlinear physics of its internal processes; it allows for the exploration of a full range of possible parameters and the testing of hypotheses that could not otherwise be directly verified.

A mantle flow model solves the same equations that govern the flow of an incompressible viscous fluid, where viscosity is not constant but depends exponentially on temperature and pressure at each point within the mantle. In this type of model, the pressure gradient at any given point is balanced by the viscous resistance the mantle itself exerts against motion, while the conservation of mass requires that the mantle flow neither compresses nor expands the material at any point along its path.

The viscous timescale of the Earth's mantle is enormously long—on the order of one billion to one hundred billion years—so long that the mantle's inertia is completely negligible compared to its viscous resistance; consequently, the mantle flows in what is known as a creeping regime, the same regime in which cold honey moves when poured very slowly.

Dynamic seismic rupture modeling solves elastic wave equations within the rock medium alongside a constitutive friction law applied to the fault plane itself—a law that makes fault friction dependent on slip velocity and the fault's internal state, or alternatively, a law in which friction decreases as slip progresses; either law determines how fault friction evolves as the fault slips during an earthquake. Sediment transport modeling employs a law relating fluvial erosion to water discharge and channel slope—combined with diffusion processes that smooth hillslopes over time and models describing sediment deposition within a basin—to simulate the evolution of entire landscapes over millions of years.

Machine learning, utilizing convolutional neural networks and transformer-based architectures, is currently applied to tasks ranging from the detection of seismic phases in continuous seismograms (with accuracy surpassing that of humans) to the automated lithological classification of rock core images; these methods complement the previously described models of mantle flow, seismic rupture, and sediment transport to complete the toolkit used in geological numerical modeling to explore hypotheses that would otherwise be impossible to verify.

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