Lessons Learned about the Sequential versus Integrated Approach to Hydrogeophysical Inverse Problems
Using geophysical data as a quantitative constraint for hydrologic model calibration is a task of fundamental importance within the field of hydrogeophysics. There are two basic approaches that have been explored for this problem. The first is sequential in that it treats the geophysical and hydrologic inverse problems separately: a geophysical imaging step is used to map the spatiotemporal distribution of hydrologic state variables followed by a hydrologic model calibration step in which the resulting estimates are used as data constraints. In contrast, the integrated approach couples the geophysical instrument response model with a dynamic hydrologic process model to obtain a single 'hydrogeophysical' model that directly relates hydrologic parameters, such as hydraulic conductivity and dispersivity, to geophysical responses, such as GPR travel times or voltages in resistivity surveys. There are a number of studies that have now been performed comparing the sequential versus integrated approach to the inverse problem for a range of hydrologic problems and geophysical instruments. Two specific examples of these problems will be discussed in this talk: (i) monitoring water infiltration in soils with GPR and electrical resistivity, and (ii) quantifying groundwater solute transport properties in aquifers using surface-based electrical resistivity data. From these studies a number of general lessons have been learned about the hydrogeophysical inverse problem. First, the number of parameters to be estimated in the inverse problem can be drastically reduced for the integrated inverse problem relative to the sequential problem. This is because just a few hydrologic parameters, which are the target of the integrated inversion, may produce a wide range of possible subsurface states, which are the target of the sequential inversion. Second, the physical laws of hydrology govern the spatiotemporal evolution of the state of the subsurface. As a result, coupling hydrologic and geophysical models limits the physically plausible range of geophysical variability and provides an intrinsic physics-based regularization for the geophysical inverse problem. Third, the volume of data required to deliver an equivalent level of accuracy and uncertainty in estimates of hydrologic properties is much lower for the integrated versus sequential approach, making the former more suitable for transient monitoring problems. Fourth, the ability to estimate hydrologic parameters from a hydrogeophysical monitoring experiment is dependent on the design of both the hydrologic and geophysical experiment, i.e., the resolution characteristics of both problems must be considered in experimental design. Overall experience seems to indicate that the integrated inversion approach typically performs better than the sequential approach for dynamic imaging problems.
THE USE OF CPT/SMR DATA TO IDENTIFY HYDROFACIES AND ESTIMATE HYDRAULIC CONDUCTIVITY IN UNCONSOLIDATED AQUIFERS
It is well recognised that adequate aquifer characterization in support of groundwater flow modelling requires the knowledge of the spatial distribution of hydrofacies controlling hydraulic properties. The recognition of hydrofacies distribution with direct methods (i.e. hydraulic tests) is expensive and often limited to restricted areas, whereas the use of geophysical methods provides indirect information covering larger areas but with less accuracy and resolution. Even though direct-push soundings only provide vertical profiles through aquifers, they allow the rapid acquisition of high-resolution geophysical properties (mechanical and electrical), which is expected to be an efficient way to map hydrofacies and hydraulic properties in unconsolidated aquifers. In this study, we investigated the use of direct-push soundings using cone penetration tests (CPT) combined with soil moisture and resistivity (SMR) for mapping the spatial distribution of hydraulic conductivity (K). The study focuses primarily on the problem associated with the integration of non-linearly correlated data, which are also characterized by different vertical resolutions. The study site is located in an unconsolidated deltaic environment where a former landfill is located. The characterization provided geological, geophysical and hydraulic data from which hydrofacies were identified. The following hydrostratigraphic was defined: (i) aerially, grain-size is fining outward from the centre of the sub-watershed where the former landfill is located; (ii) vertically, grain-size is first coarsening upward and then gradually fining; (iii) K is controlled by hydrofacies and grain-size, resulting in gradual changes (from <10-6 to >10-4 m/s), except for a fine-medium sand hydrofacies of exceptional low-K. Data integration aims to infer K from CPT/SMR sounding responses alone, while accounting for the transitional change in hydraulic properties and the non-linear relationship between geophysical and hydraulic data. Our approach is based on Bayesian cosimulations, whose framework provides great flexibility compared to the classical cosimulation algorithms (such as Sequential Gaussian Simulations) and allows non-linear relations between variables. Results were validated with K profiles at a 0.15 m resolution obtained from borehole flowmeter at wells that were not included in the statistical analysis. However, sensitivity analysis shows a need for a systematic approach based on a priori clear understanding of the hydrogeological context.
Quantifying Vegetation Driven Moisture Dynamics Using DC Electrical Resistivity
The sensitivity of electrical conductivity to soil moisture content makes time-lapse electrical resistivity imaging (ERI) an ideal method to monitor dynamic subsurface hydrological processes. While ample data show the strengths of ERI for monitoring infiltration and solute transport processes in the vadose zone, relatively few studies have evaluated the method's viability for terrestrial ecosystem research, in particular for characterizing vegetation-driven subsurface water dynamics. The ability to derive accurate soil moisture information from ERI largely depends on the field data acquisition parameters and resistivity data inversion procedures. In addition, fluctuations in soil temperatures and pore water conductivities need to be properly considered. Here we present the results of sensitivity analysis of the relationship between soil physical properties (texture, soil temperature, fluid conductivity, and moisture content) and bulk electrical resistivity based on literature values, modeling, and experiments. To understand the implications of data acquisition settings and inversion procedures we analyzed bi-weekly multi-electrode Wenner and Dipole-dipole 2D datasets collected over a 30- month period at a field site in mid-Michigan, USA. The site has contrasting vegetation types (forest and grassland), receives ~1000 mm of precipitation a year, with a water table ~5m below the surface. During the measurement period, the average soil temperature at 80 cm depth ranged from 15 degrees celcius in summer to 4 degrees celcius in winter, measured fluid conductivity ranged from 0.04 to 0.07 S/m. Root-zone moisture observed in point sensors and estimated from ERI ranged from approximately 0.04 to 0.30 cm3/cm3. We compare unconstrained time-lapse inversion procedures with those using a-priori models for the estimation of soil moisture changes below both vegetation types. Our results show that ERI can improve the understanding of vegetation-vadose zone interactions in natural settings.
Shallow Seismic Imaging to Characterize Shallow Groundwater Conditions at Ancient Hierakonpolis in Egypt and Unexpected Discoveries of New Artifacts
Nearby agricultural irrigation from the Nile River has progressively raised the local groundwater levels at the Hierakonpolis Temple-Town site near Edfu, Egypt from 4.5 m in 1897 to between 1.0 and 1.5 m presently. Our multidisciplinary geological, geophysical, hydrogeological and archaeological investigations have been focused on characterizing the present shallow groundwater conditions, identifying specific water sources and the associated flow regime, and devising mitigation strategies to dewater either locally or over the site to enable further archaeological excavations to depths of 4 to 5 m. Shallow seismic imaging from over 150 seismic lines on and around the archaeological site has defined the water table, a shallow reflector (aquifer?) at a depth of approximately 30 m, an old Nile channel at a depth of approximately 100 m, and a deeper, higher velocity layer at approximately 150 m depth. From comparisons with a large number of piezometers it was found that seismic refraction depths to the water table agree with the directly measured depths to within approximately 2.5 cm enabling accurate profiles of the water table surface to be quickly and efficiently determined. Additionally the development of the 3-D cone of depression from a dewatering experiment was determined using repeated refraction lines across the pumping well. Additionally, in the course of carrying out shallow seismic imaging of the subsurface prominent high-velocity, high-frequency signals from very shallow depths were observed along some of the numerous seismic refraction profiles run within the perimeter wall of the ancient Hierakonpolis Temple-Town. These anomalies are characterized by laterally continuous high- frequency (200-300 Hz) arrivals with velocities comparable to or exceeding the deeper water table refraction velocities. These anomalous zones are imbedded in the 1 to1.5 m-thick upper layer of unconsolidated, air- filled sediments that have extremely low velocities and very high Q. The considerable spatial extent of these shallow anomalous zones was mapped from sets of crossing refraction profiles. Subsequent excavations at several locations in the anomalous zone have discovered the presence of a zone of closely spaced artifacts (dense in potsherds and stone fragments) that revealed new evidence of occupation in the ancient town as early as Dynasty I, c. 3200 BCE. In the first northwest excavation an 'in situ' deposit of special pottery lay next to a bench, a large block of dressed limestone. Additional excavation at this site in January 2009 has found a leg from an ebony statue, a very rare type of artifact from anywhere in Egypt, another leg, a jawbone, and a statue's eyes. Further to the north, layered occupation was found suggesting a secular context with pottery of Dynasty II, 2900 BCE and a new early date, terminus ante quem, for the accompanying figurines, thus far exclusive to only two temple sites in southern Egypt. Further excavations of these mapped anomalous areas are planned and they are expected to provide many additional new artifacts not previously found at the site.
Application of Surface Time-Lapse Seismic Refraction Tomography (TLSRT) to Quantifying Changes in Saturation Within the Vadose Zone
Seismic p-wave propagation velocity of a medium is a function of the effective elastic constants of the material, and has been previously demonstrated to be related to hydrologic parameters according to the Gassmann equation. Above the water table (i.e., in the vadose zone), seismic p-wave velocity is expected to vary linearly as a function of density. Similarly, bulk density is expected to vary linearly as a function of the porosity and the pore-fluid density, where the pore-fluid density is described as the weighted mean of the pore-fluid density and density of air, dependent upon the saturation. Thus, the equations for calculating a change in saturation given two successive seismic p-wave propagation velocity measurements at a coincident point in the vadose zone are straightforward, given a priori values for bulk density or porosity for the medium. In the absence of in situ information for a given medium, subsurface variations in density can be derived using the multi-channel analysis of shear waves (MASW) technique that yields estimates of s-wave propagation velocity (Vs). As Vs is a function of the shear modulus and density, and shear modulus is invariant due to saturation according the Gassmann equation, a direct estimate of density can be derived via MASW. Thus, using MASW to establish initial conditions, a direct measure of changes in vadose zone saturation can be estimated using time-lapse seismic refraction tomography (TLSRT). In order to validate the above approach to quantifying saturation in the vadose zone, an ephemeral perched water table at the Oak Ridge Field Research Center (ORFRC) located at the Oak Ridge National Laboratory in Tennessee was monitored using TLSRT and correlated with traditional point hydrologic measurements. From October 2007 through February 2009, 35 coincident datasets were acquired along a 100-m profile. The hydrologic measurements provide a binary measure of the existence of an elevated water table, and the TLSRT data characterize the spatial extent (i.e., vertical and horizontal limits) of the ephemeral perched water table. Percent change in saturation is calculated for the various time-steps, and additional information regarding porosity can be inferred if boundary conditions are assumed. The increased spatial extent of TLSRT measurements compared to traditional point hydrologic measurements demonstrably provides a better estimate of saturation in heterogeneous media, and can be used to indicate preferential flowpaths, which may be important in many environmental remediation projects.