The application of a technique from quantum dynamics to the governing equation for hydraulic head leads to a trajectory-based solution that is valid for a general porous medium. The semi-analytic expressions for propagation path and velocity of a change in hydraulic head form the basis of a travel-time tomographic imaging algorithm. An application of the imaging algorithm to synthetic arrival times reveals that a cross-well inversion based upon the extended trajectories correctly reproduces the magnitude of a reference model, improving upon an existing asymptotic approach. An inversion of hydraulic head arrival times from cross-well slug tests at the Widen field site in northern Switzerland captures a general decrease in permeability with depth, which is in agreement with previous studies, but also indicates the presence of a high-permeability feature in the upper portion of the cross-well plane.

Time-lapse geophysical monitoring has potential as a tool for reservoir characterization, that is, for determining reservoir properties such as permeability. Onset times, the calendar times at which geophysical observations begin to deviate from their initial or background values, provide a useful basis for such characterization. We found that, in contrast to time-lapse amplitude changes, onset times were not sensitive to the exact method used to related changes in fluid saturation to changes in seismic velocities. As a consequence of this, we found that an inversion for effective permeability based upon onset times was robust with respect to variations in the rock-physics model. In particular, inversions of synthetic onset times calculated using Voigt and Reuss averaging techniques, but inverted using sensitivities from Hill's averaging method, resulted in almost identical misfit reductions and similar permeability models. All solutions based on onset times recovered the large-scale, resolvable features of the reference model. Synthetic tests indicated that reliable onset times can be obtained from noisy seismic amplitudes. Testing also indicated that large-scale permeability variations can be recovered even if we used onset times from seismic surveys that were spaced as much as 300 days apart.

The center of the San Joaquin Valley is one of the most productive agricultural regions in the US. Farmers rely heavily on surface-water diversions to meet irrigation water demand. However, the 2007–2010 and 2012–2017 droughts have caused strong increases in groundwater pumping causing land subsidence with strong variability in location, magnitude (total subsidence) and rate of subsidence. In this study, we try to understand what caused these variations. We focus our analyses on three areas: (i) the Westland water district where subsidence was very small during the two drought periods, (ii) ‘El Nido’ area where the greatest subsidence rate was monitored from 2008 to 2010, and (iii) the’ Kings-Tulare counties’ area where the subsidence was small during the 2008–2010 and the largest during 2015–2017 droughts. Our main finding is that land subsidence is located in areas where the water demand for agriculture and the density of groundwater wells is the highest, whereas the rate of subsidence is strongly affected the amount of local and imported surface water and by groundwater resources. Based on these simple observations, we propose using continuous satellite-based ground deformation monitoring and geomechanical modeling to (i) localize areas most prone for future subsidence and (ii) to estimate and manage groundwater resources.

Because of its simplicity and the ability to produce a stable, slow-propagating crack, the Double-Torsion (DT) method has been used widely for investigating the critical and subcritical propagation of a slow-propagating tensile (mode-I) crack. However, to determine the complex relationship between the crack velocity vc vs. the strain energy release rate G (or the stress intensity factor K) from laboratory measurements, several corrections must be made to account for the impact of sample and crack geometry. Particularly, DT test typically produces a crack with a curved edge profile instead of a straight line, causing the local vc and G vary along the crack front. The experimentally measured vc and G data merely reflect collective, averaged behavior of the crack. This makes inversion for the intrinsic, “true” crack growth kinetics necessary, based upon the knowledge of the crack geometry. Simple and effective correction methods have been proposed and validated for the slow, chemical-reaction-controlled part (Region I) of the vc−G curve. However, reliable methods for the highly nonlinear, transport-dominated part (Region II) and its sudden transition to the dynamic propagation part (Region III) are still lacking. In this paper, we propose a method for determining the intrinsic vc−G relationship across all three Regions based upon DT test data, using a simple model function and its numerical inversion. The performance of this approach is examined and demonstrated using both synthetic and laboratory data for subcritical crack growth in soda lime glass.

Seismic characterization of flow properties is a difficult prospect, due to the indirect relationship between permeability and seismic velocity and attenuation. At best, seismic time-lapse changes can detect the effects of saturation and pressure changes in a reservoir due to fluid flow. Even in this case, the interpretation of the seismic observation in terms of the state of the reservoir depends intimately on the properties of the rock physics model, which are usually poorly known. The onset time, the calendar time of geophysical changes, provides an alternative datum for characterizing properties such as reservoir permeability. The main advantage of an onset time is that it is sensitive to the flow properties of the reservoir yet insensitive to the details of the rock physics model. Two examples of the utility of onset times are discussed: The use of travel time shifts induced by the injection of carbon dioxide between two wells, and the time-lapse time shifts for elastic waves propagating through a reservoir undergoing enhanced oil recovery. In both examples, the onset times are mapped into permeability estimates using a trajectory-based approach akin to seismic tomography.

In many subsurface industrial applications, fluids are injected into or withdrawn from a geologic formation. It is of practical interest to quantify precisely where, when, and by how much the injected fluid alters the state of the subsurface. Routine geophysical monitoring of such processes attempts to image the way that geophysical properties, such as seismic velocities or electrical conductivity, change through time and space and to then make qualitative inferences as to where the injected fluid has migrated. The more rigorous formulation of the time-lapse geophysical inverse problem forecasts how the subsurface evolves during the course of a fluid-injection application. Using time-lapse geophysical signals as the data to be matched, the model unknowns to be estimated are the multiphysics forward-modeling parameters controlling the fluid-injection process. Properly reproducing the geophysical signature of the flow process, subsequent simulations can predict the fluid migration and alteration in the subsurface. The dynamic nature of fluid-injection processes renders imaging problems more complex than conventional geophysical imaging for static targets. This work intents to clarify the related hydrogeophysical parameter estimation concepts.

The macroscopic laws controlling the advection and diffusion of solute at the scale of the porous continuum are derived in a general manner that does not place limitations on the geometry and time evolution of the pore space. Special focus is given to the definition and symmetry of the dispersion tensor that is controlling how a solute plume spreads out. We show that the dispersion tensor is not symmetric and that the asymmetry derives from the advective derivative in the pore-scale advection-diffusion equation. When flow is spatially variable across a voxel, such as in the presence of a permeability gradient, the amount of asymmetry can be large. As first shown by Auriault [J.-L. Auriault et al. Transp. Porous Med. 85, 771 (2010)TPMEEI0169-391310.1007/s11242-010-9591-y] in the limit of low Péclet number, we show that at any Péclet number, the dispersion tensor D_{ij} satisfies the flow-reversal symmetry D_{ij}(+q)=D_{ji}(-q) where q is the mean flow in the voxel under analysis; however, Reynold's number must be sufficiently small that the flow is reversible when the force driving the flow changes sign. We also demonstrate these symmetries using lattice-Boltzmann simulations and discuss some subtle aspects of how to measure the dispersion tensor numerically. In particular, the numerical experiments demonstrate that the off-diagonal components of the dispersion tensor are antisymmetric which is consistent with the analytical dependence on the average flow gradients that we propose for these off-diagonal components.

Geodetic observations, often in conjunction with other data, provide a cost-effective means for identifying and characterizing geothermal resources. A review of the various methods reveals how the technology for measuring deformation has advanced considerably in the past few decades. Currently, interferometric synthetic aperture radar is the method of choice for monitoring deformation at a geothermal field. A discussion of geodetic monitoring at The Geysers geothermal field, California, illustrates some of the progress made and the challenges that remain.