Traveltime Inversion of Vertical Radar Profiles

Traveltimes of direct arrivals in vertical radar profiles (VRPs) are tomographically inverted to estimate the earth’s electromagnetic (EM) velocity between a surface transmitter and a downhole receiver. We determine the 1D interval velocity model that best fits the first-arrival traveltimes by using a weighted, damped, least-squares inversion scheme. We assess the accuracy of the velocity model using synthetic traveltimes from a known velocity-distribution model simulating an unconfined aquifer. The inverted velocity profile closely matched the velocity profile of the input model in the synthetic examples. Using vertical radar profile data from an unconfined aquifer near Boise, Idaho, we inverted traveltimes to obtain velocity estimates at the well location. The velocity change at a depth of 2.0 m corresponds well with the measured depth to the water table of 1.95 m, and at depths between 2 and 18 m, the velocities ranged between 0.06 and 0.1 m/ns. Our estimates approximately match the velocity distribution determined from neutron-derived porosity logs at depths greater than about 2 m. An important function of inverse methods is to assess (quantitatively and qualitatively) the uncertainty of inverted velocity estimates. We note that the velocity values in the upper and lower parts of the inverted model are not as well constrained compared to those between the depths of 4 and 13 m. From the model resolution and model covariance matrices of the real-data inversion,we determine the uncertainty in our velocity model, leading to more reliable interpretations of the subsurface

Boise Hydrogeophysical Research Site (BHRS): Objectives, Design, Initial Geostatistical Results

The Boise Hydrogeophysical Research Site (BHRS) is a wellfield developed in a shallow, coarse (cobble-and-sand), alluvial aquifer with the goal of developing cost-effective methods for quantitatively characterizing the distribution of permeability in heterogeneous aquifers using hydrologic and geophysical techniques. Responses to surface geophysical techniques (e.g., seismic, radar, transient electromagnetics) will be calibrated against a highly characterized control volume (the wellfield) with 3-D distributions of geologic, hydrologic, and geophysical properties determined from extensive field measurements. Also, these data sets will be used to investigate relationships between properties and to test petrophysical models. Well coring and construction methods, and the well arrangement in the field, are designed to provide detailed control on lithology and to support a variety of single-well, crosshole, and multiwell geophysical and hydrologic tests. Wells are screened through the cobble-and-sand aquifer to a clay that underlies the BHRS at about 20 m depth. In addition, the wellfield design optimizes well-pair distances and azimuths for determination of short-range geostatistical structure. Initial geostatistical analysis of porosity data derived from borehole geophysical logs indicates that the omnidirectional horizontal experimental variogram for porosity (possible proxy for log permeability) is best fit with a nested periodic model structure

Reflectivity Modeling of a Ground-Penetrating-Radar Profile of a Saturated Fluvial Formation

Major horizons in radar reflection profiles may correlate with contacts between stratigraphic units or with structural breaks such as fault surfaces. Minor reflections may be caused by clutter or, in some cases, may indicate material properties or structure within stratigraphic units. In this study, we examine the physical basis for major and minor reflections observed in a shallow, unconfined, fluvial aquifer near Boise, Idaho, U. S. A. We compare a 2D profile from a surface ground-penetrating-radar reflection transect with the 1D modeled reflection profiles at three wells adjacent to the surface-reflection profile. The 1D models are based on dielectric constant and electrical conductivity values from borehole logs and vertical radar profile data. Reflections at the water table/capillary fringe, at the base of a sand-filled channel, and at the base of two sand-rich lenses in a cobble-dominated unit are recognizable in the surfacereflection profile and in all 1D reflectivity models. Less prominent reflections in stratigraphic units occur in both the surface-profile model and the reflectivity model. Although such minor reflections are not correlated easily, general similarities in their presence and location indicate that sometimes the reflections may be useful for recognizing internal facies structure or character

Capacitive Conductivity Logging and Electrical Stratigraphy in a High-resistivity Aquifer, Boise Hydrogeophysical Research Site

We tested a prototype capacitive-conductivity borehole tool in a shallow, unconfined aquifer with coarse, unconsolidated sediments and very-low-conductivity water at the Boise Hydrogeophysical Research Site (BHRS). Examining such a high-resistivity system provides a good test for the capacitive- conductivity tool because the conventional induction- conductivity tool (known to have limited effectiveness in high-resistivity systems) did not generate expressive well logs at the BHRS. The capacitive-conductivity tool demonstrated highly repeatable, low-noise behavior but poor correlation with the induction tool in the lower-conductivity portions of the stratigraphy where the induction tool was relatively unresponsive. Singular spectrum analysis of capacitive- conductivity logs reveals similar vertical-length scales of structures to porosity logs at the BHRS. Also, major stratigraphic units identified with porosity logs are evident in the capacitive-conductivity logs. However, a previously unrecognized subdivision in the upper portion of one of the major stratigraphic units can be identified consistently as a relatively low-conductivity body (i.e., an electrostratigraphic unit) between the overlying stratigraphic unit and the relatively high-conductivity lower portion — despite similar porosity and lithology in adjacent units. The high repeatability and resolution and the wide dynamic range of the capacitive-conductivity tool are demonstrated here to extend to high-resistivity, unconsolidated sedimentary aquifer environments

Effects of Signal Processing and Antenna Frequency on the Geostatistical Structure of Ground-Penetrating Radar Data

Recent research has suggested that the geostatistical structure of ground-penetrating radar data may be representative of the spatial structure of hydraulic properties. However, radar images of the subsurface can change drastically with application of signal processing or by changing the signal frequency. We perform geostatistical analyses of surface radar reflection profiles in order to investigate the effects of data processing and antenna frequency on the semivariogram structure of radar reflection amplitudes. Surface radar reflection data collected at the Boise Hydrogeophysical Research Site illustrate the processing- and antenna-dependence of radar semivariograms for a fluvial, cobble-and-sand aquifer. Compensating for signal attenuation and spreading using a gain function removes a nonstationary trend from the data and a trace-specific gain function reduces fluctuation of semivariogram values at large lags. Otherwise, geostatistical structures of surface reflection data are quite robust to the effects of data gains. Migration is observed to reduce the strength of diffraction features in the semivariogram fields and to increase the principal exponential range. Principal exponential range increases only slightly after application of migration with a realistic velocity but over-migration results in a significant artificial increase of exponential range. The geostatistical structures of radar reflection data exhibit marked dependence on antenna frequency, thus highlighting the critical importance of the scale of measurement. Specifically, the exponential ranges of radar reflection amplitudes decrease in proportion to the increased signal frequency for the 50 MHz, 100 MHz and 200 MHz range of antennas. Results demonstrate that processing and antenna frequency must be considered before the application of radar reflection data in a geostatistical context

Multivariate Analysis of Cross-Hole Georadar Velocity and Attenuation Tomograms for Aquifer Zonation

We have investigated the potential of combining cross-hole georadar velocity and attenuation tomography as a method for characterizing heterogeneous alluvial aquifers. A multivariate statistical technique, known as k-means cluster analysis, is used to correlate and integrate information contained in velocity and attenuation tomograms. Cluster analysis allows us to identify objectively the major common trends in the tomographic data and thus to ‘‘reduce’’ the information to a limited number of characteristic parameter combinations. The application of this procedure to two synthetic data sets indicates that it is a powerful tool for converting the complex relationships between the tomographically derived velocity and attenuation structures into a lithologically and hydrologically meaningful zonation of the probed region. In addition, these synthetic examples allow us to evaluate the reliability of further petrophysical parameter estimates. We find that although absolute values of the tomographically inferred petrophysical parameters often differ significantly from the actual parameters, the clustering approach enables us to reliably identify the major trends in the petrophysical properties. Finally, we have applied the approach to a cross-hole georadar data set collected in a well-studied alluvial aquifer. A comparison of the clustered tomographic section with well-log data demonstrates that our approach delineates the hydrostratigraphic zonation

VSP Traveltime Inversion: Near-Surface Issues

P-wave velocity information obtained from vertical seismic profiles (VSPs) can be useful in imaging subsurface structure, either by directly detecting changes in the subsurface or as an aid to the interpretation of seismic reflection data. In the shallow subsurface, P-wave velocity can change by nearly an order of magnitude over a short distance, so curved rays are needed to accurately model VSP traveltimes. We used a curved-ray inversion to estimate the velocity profile and the discrepancy principle to estimate the data noise level and to choose the optimum regularization parameter. The curved-ray routine performed better than a straight-ray inversion for synthetic models containing high-velocity contrasts. The application of the inversion to field data produced a velocity model that agreed well with prior information. These results show that curved-ray inversion should be used to obtain velocity information from VSPs in the shallow subsurface

A Field Comparison of Fresnel Zone and Ray-Based GPR Attenuation-Difference Tomography for Time-Lapse Imaging of Electrically Anomalous Tracer or Contaminant Plumes

Ground-penetrating radar (GPR) attenuation-difference tomography is a useful tool for imaging the migration of electrically anomalous tracer or contaminant plumes. Attenuation-difference tomography uses the difference in the trace amplitudes of tomographic data sets collected at different times to image the distribution of bulk-conductivity changes within the medium. The most common approach for computing the tomographic sensitivities uses ray theory, which is well understood and leads to efficient computations. However, ray theory requires the assumption that waves propagate at infinite frequency, and thus sensitivities are distributed along a line between the source and receiver. The infinite-frequency assumption in ray theory leads to a significant loss of resolution (both spatially and in terms of amplitude) of the recovered image. We use scattering theory to approximate the sensitivity of electromagnetic (EM) wave amplitude to changes in bulk conductivity within the medium. These sensitivities occupy the first Fresnel zone, account for the finite frequency nature of propagating EM waves, and are valid when velocity variations within the medium do not cause significant ray bending. We evaluate the scattering theory sensitivities by imaging a bromide tracer plume as it migrates through a coarse alluvial aquifer over two successive days. The scattering theory tomograms display a significant improvement in resolution over the ray-based counterparts, as shown by a direct comparison of the tomograms and also by a comparison of the vertical fluid conductivity distribution measured in a monitoring well, located within the tomographic plane. By improving resolution, the scattering theory sensitivities increase the utility of GPR attenuation- difference tomography for monitoring the movement of electrically anomalous plumes. In addition, the improved accuracy of information gathered through attenuation-difference tomography using scattering theory is a positive step toward future developments in using GPR data to help characterize the distribution of hydrogeologic propertie