Direct seismic energy modeling and application to the 1979 Imperial Valley earthquake

[1] The seismic energy associated with an earthquake has two representations: the work of the seismic waves done against a distant surface or a fault representation. For a fault subject to slip-weakening friction, the energy density is the difference between an elastostatic work and a work density spent in fracture and relaxation. We apply this to a dynamic simulation of the 1979 Imperial Valley earthquake, whose initial conditions are inspired by previous kinematic studies. A large area of the fault has a negative energy density, and the emission of energy is roughly confined to small parts of the fault with large positive energy density. We compute the work of the seismic waves against the surface of a sphere enclosing the source, and we find the same amount of energy. We produce a map of energy directivity that shows that 40% of the energy passes through only 6.5% of the sphere.