1. A computer-implemented method for earth modeling of a geologic volume of interest, the method being implemented in a computer system that includes one or more physical computer processors and a user interface, the method comprising: a. receiving, at the one or more physical computer processors, a rock model that describes properties of the geologic volume of interest as a function of position within a rectangular grid through the geologic volume of interest; b. obtaining, at the one or more physical computer processors, boundary conditions; c. initiating, using the one or more physical computer processors, a stress field in at least part of the rock model; d. modeling, via the one or more physical computer processors, resultant displacements using a finite difference method which allows for leaking kinetic energy out of the rock model as a function of time while decreasing potential energy in lockstep using a Virial theorem; e. calculating, via the one or more physical computer processors, at least one of resultant strains, stresses, elastic energies, and/or elastic stiffnesses based on the resultant displacements; f. predicting, via the one or more physical computer processors, physical changes in the rock model using the at least one of resultant strains, stresses, elastic energies, and/or elastic stiffnesses; and g. outputting visual information depicting predictions of physical changes in the rock model via the user interface.