The increased use of computer simulation methods in geomechanics (e.g. finite element), allows for complex heterogeneous structures to be modeled. It is relatively trivial, using these approaches, to create layered or block type linear elastic models with moduli that vary from formation to formation. Such models are frequently used to understand and predict the displacements and stress perturbations induced by industrial processes such as reservoir depletion or fluid injection over periods of many years. Because inertial terms are negligible for deformations on these time scales it is often assumed that static moduli are the appropriate parameters to apply, and a simplistic comparison to laboratory data would appear to confirm this view. Indeed, there are a number of studies in the literature that describe methods for deriving static properties to populate such numerical models. However, it is reasonable to assume that the majority of the difference between static and dynamic moduli can be ascribed to simple poroelasticity and that the appropriate time scales that define the static and dynamic end member cases are governed by pressure diffusion. A straightforward analysis that simply considers the most basic drained and undrained cases, and rudimentary diffusion, makes it apparent that in most cases the use of static moduli is only really appropriate for formations that are being actively depleted. Other formations will generally exhibit undrained or dynamic behavior on time scales of years or millennia.
This paper is concerned with geomechanical models of contracting or expanding subsurface reservoir formations (water, oil or gas, either extraction or injection), used to determine surface deformation and stress/strain perturbations. Hence, there are implicit assumptions about length, time and stress scales, of the order of kilometers, decades and tens of MPa, that influence this study but the general approach should be more broadly applicable.