The Anomalous Behavior of SH‐Waves Across the Water Table

Most theoretical studies of seismic wave propagation in a porous medium do not predict a significant increase in SH-wave velocity with increasing water saturation. Although that type of behavior is commonly predicted for P-waves (and confirmed by countless observations), the expectation for SH-waves is a slight decrease in propagation velocity with increasing water saturations. While published measurements of SH-wave velocity in laboratory studies have been supportive of such a slight decrease in velocity, the data have been biased towards high pressures (typical of oil reservoirs at large depths of burial). On the other hand, the few published low pressure laboratory measurements have revealed significantly different results. The authors’ in-situ measurements of seismic wave velocities in a shallow, coarse grained, unconfined alluvial aquifer document a significant SH-wave velocity increase in the transition from the vadose zone to the water table. In one vertical seismic profile (VSP), the P-wave velocity increases by a factor of 4.2 and the SHwave velocity increases by a factor of 2.6. What is not clear at this point is the true nature of the increase. Is the velocity increase an expression of the presence of water in the pores, or does water alter the rigidity of the soil matrix? In addition to the broad-band velocity increase, we have also observed changes in the attenuation of SHwaves across the water table. After correcting for geometric spreading, the amplitude decay observed in the vadose zone has been found to be larger than that observed below the water table. However, the variation in amplitude decay as a function of frequency and the measurements of body wave dispersion were found to be larger below the water table than above. That is, the water saturated soil behavior is consistent with a Voigt solid, but the dry material appears to follow a different model. The authors will discuss these observations in the context of the current debate on Poisson’s ratio and the Vp/Vs ratio

The Effects of Sparging on P- and SH- Vertical Seismic Profiles

While the introduction of pressurized air into an unconsolidated, coarse-grained fluvial aquifer might well be expected to affect the P-wave velocity profile below the water table, we have found that S-waves are also sensitive to changes induced by air sparging. In a study spanning over a year of sparging, observations of both P- and S-waves were conducted by Vertical Seismic Profiling (VSP). While the primary objective was to characterize the aquifer, we have found that air sparging has significantly affected both P- and S-wave propagation. Below the water table we have observed as much as a 54% decrease in P-wave velocity, and as much as a 31% increase in S-wave velocity after continued sparging. Above the water table, we observe only small changes in both P- and S-wave velocities. This pattern of velocity change (decreasing P, increasing S) may be due to an increase in the amount of trapped air below the water table. Published laboratory studies in the small strain regime have shown P-wave velocities to be sensitive to void ratio, fluid content, and confining stress. On the other hand, most similar studies of S-waves have only been conducted on either dry or saturated samples. However, one recent laboratory study suggests that shear modulus and shear velocity may increase significantly at partial water saturations (due to capillary forces). Data from our in-situ survey supports this more recent lab work. We have observed that S-wave propagation may be significantly altered by fluid content when soils are partially saturated with water (where trapped air may exist, producing a 3-phase fluid-frame system). In addition, we have observed changes in the propagating wavelet. This may be an indication that viscous damping is also affected by partial water saturation. We conclude by observing that S-waves may prove to be an attractive alternative for mapping the effects of air sparging

Aquifer Heterogeneity Characterization with Oscillatory Pumping: Sensitivity Analysis and Imaging Potential

[1] Periodic pumping tests, in which a fluid is extracted during half a period, then reinjected, have been used historically to estimate effective aquifer properties. In this work, we suggest a modified approach to periodic pumping test analysis in which one uses several periodic pumping signals of different frequencies as stimulation, and responses are analyzed through inverse modeling using a “steady-periodic” model formulation. We refer to this strategy as multifrequency oscillatory hydraulic imaging. Oscillating pumping tests have several advantages that have been noted, including no net water extraction during testing and robust signal measurement through signal processing. Through numerical experiments, we demonstrate additional distinct advantages that multifrequency stimulations have, including: (1) drastically reduced computational cost through use of a steady-periodic numerical model and (2) full utilization of the aquifer heterogeneity information provided by responses at different frequencies. We first perform fully transient numerical modeling for heterogeneous aquifers and show that equivalent results are obtained using a faster steady-periodic heterogeneous numerical model of the wave phasor. The sensitivities of observed signal response to aquifer heterogeneities are derived using an adjoint state-based approach, which shows that different frequency stimulations provide complementary information. Finally, we present an example 2-D application in which sinusoidal signals at multiple frequencies are used as a data source and are inverted to obtain estimates of aquifer heterogeneity. These analyses show the different heterogeneity information that can be obtained from different stimulation frequencies, and that data from several sinusoidal pumping tests can be rapidly inverted using the steady-periodic framework

Three-Dimensional Stochastic Estimation of Porosity Distribution: Benefits of Using Ground-Penetrating Radar Velocity Tomograms in Simulated-Annealing-Based or Bayesian Sequential Simulation Approaches

Estimation of the three-dimensional (3-D) distribution of hydrologic properties and related uncertainty is a key for improved predictions of hydrologic processes in the subsurface. However it is difficult to gain high-quality and high-density hydrologic information from the subsurface. In this regard a promising strategy is to use high-resolution geophysical data (that are relatively sensitive to variations of a hydrologic parameter of interest) to supplement direct hydrologic information from measurements in wells (e.g., logs, vertical profiles) and then generate stochastic simulations of the distribution of the hydrologic property conditioned on the hydrologic and geophysical data. In this study we develop and apply this strategy for a 3-D field experiment in the heterogeneous aquifer at the Boise Hydrogeophysical Research Site and we evaluate how much benefit the geophysical data provide. We run high-resolution 3-D conditional simulations of porosity with both simulated-annealing-based and Bayesian sequential approaches using information from multiple intersecting crosshole gound-penetrating radar (GPR) velocity tomograms and neutron porosity logs. The benefit of using GPR data is assessed by investigating their ability, when included in conditional simulation, to predict porosity log data withheld from the simulation. Results show that the use of crosshole GPR data can significantly improve the estimation of porosity spatial distribution and reduce associated uncertainty compared to using only well log measurements for the estimation. The amount of benefit depends primarily on the strength of the petrophysical relation between the GPR and porosity data, the variability of this relation throughout the investigated site, and lateral structural continuity at the site

Tomography of the Darcy velocity from self-potential measurements

An algorithm is developed to interpret self-potential (SP) data in terms of distribution of Darcy velocity of the ground water. The model is based on the proportionality existing between the streaming current density and the Darcy velocity. Because the inverse problem of current density determination from SP data is underdetermined, we use Tikhonov regularization with a smoothness constraint based on the differential Laplacian operator and a prior model. The regularization parameter is determined by the L-shape method. The distribution of the Darcy velocity depends on the localization and number of non-polarizing electrodes and information relative to the distribution of the electrical resistivity of the ground. A priori hydraulic information can be introduced in the inverse problem. This approach is tested on two synthetic cases and on real SP data resulting from infiltration of water from a ditch