James Irving

Numerical modeling of ground-penetrating radar in 2-D using MATLAB

We present MATLAB codes for finite-difference time-domain (FDTD) modeling of ground-penetrating radar (GPR) in two dimensions. Surface-based reflection GPR is modeled using a transverse magnetic (TM-) mode formulation. Crosshole and vertical radar profiling (VRP) geometries are modeled using a transverse electric (TE-) mode formulation. Matrix notation is used in the codes wherever possible to optimize them for speed in the MATLAB environment. To absorb waves at the edges of the modeling grid, we implement perfectly matched layer (PML) absorbing boundaries. Although our codes are two-dimensional and do not incorporate features such as dispersion in electrical properties, they capture many of the important elements of GPR surveying and run at a fraction of the computational cost of more elaborate algorithms. In addition, the codes are well commented, relatively easy to understand, and can be easily modified for the users specific purpose.

Removal of wavelet dispersion from ground‐penetrating radar data

Wavelet dispersion caused by frequency‐dependent attenuation is a common occurrence in ground‐penetrating radar (GPR) data, and is displayed in the radar image as a characteristic “blurriness” that increases with depth. Correcting for wavelet dispersion is an important step that should be performed before GPR data are used for either qualitative interpretation or the quantitative determination of subsurface electrical properties. Over the bandwidth of a GPR wavelet, the attenuation of electromagnetic waves in many geological materials is approximately linear with frequency. As a result, the change in shape of a radar pulse as it propagates through these materials can be well described using one parameter, Q*, related to the slope of the linear region. Assuming that all subsurface materials can be characterized by some Q* value, the problem of estimating and correcting for wavelet dispersion becomes one of determining Q* in the subsurface and deconvolving its effects using an inverse‐Q filter. We present a...

Improving crosshole radar velocity tomograms: A new approach to incorporating high-angle traveltime data

To obtain the highest-resolution ray-based tomographic images from crosshole ground-penetrating radar (GPR) data, wide angular ray coverage of the region between the two boreholes is required. Unfortunately, at borehole spacings on the order of a few meters, high-angle traveltime data (i.e., traveltime data corresponding to transmitter-receiver angles greater than approximately 50° from the horizontal) are notoriously difficult to incorporate into crosshole GPR inversions. This is because (1) low signal-to-noise ratios make the accurate picking of first-arrival times at high angles extremely difficult, and (2) significant tomographic artifacts commonly appear when high- and low-angle ray data are inverted together. We address and overcome thesetwo issues for a crosshole GPR data example collected at the Boise Hydrogeophysical Research Site (BHRS). To estimate first-arrival times on noisy, high-angle gathers, we develop a robust and automatic picking strategy based on crosscorrelations, where reference wav...

Effect of antennas on velocity estimates obtained from crosshole GPR data

To obtain tomographic images with the highest possible resolution from crosshole ground-penetrating radar (GPR) data, raypaths covering a wide range of angles between the boreholes are required. In practice, however, the inclusion of high-angle ray data in crosshole GPR inversions often leads to tomograms so dominated by inversion artifacts that they contain little reliable subsurface information. Here, we investigate the problems that arise from the standard assumption that all first-arriving energy travels directly between the centers of the antennas. Through numerical modeling, we show that this assumption is often incorrect at high transmitter-receiver angles and can lead to significant errors in tomographic velocity estimates when the antenna length is a significant fraction of the borehole spacing.

Numerical simulation of antenna transmission and reception for crosshole ground-penetrating radar

Numerical models that account for realistic transmitter and receiver antenna behavior are necessary to develop waveform-based inversion methods for crosshole ground-penetrating radar (GPR) data. A challenge in developing such models is simulating the antennae in a computationally efficient manner so that inversions can be performed in a reasonable amount of time. We present an approach to efficiently simulate crosshole GPR transmission and reception in heterogeneous media. The core of our approach is a finite-difference timedomain (FDTD) solution of Maxwell’s equations in 2D cylindrical coordinates. First, we determine the behavior of the current on a realistic GPR antenna in a borehole through detailed FDTD modeling of the antenna and its immediate surroundings. To model transmission and reception, we then replicate this antenna current behavior on a much-coarser grid using a superposition of point-electric-dipole source and receiver responses. Results obtained with our technique agree with analytical results, with numerical modeling results where the transmitter antenna and borehole are explicitly accounted for using a fine discretization, and with crosshole GPR field data.

Discrete-dual-porosity model for electric current flow in fractured rock

The identification of fractures and the characterization of their properties are of critical importance in a wide variety of research fields and applications. To this end, geophysical methods are of significant interest as they can provide information regarding the spatial distribution of a number of subsurface physical properties in a rapid and noninvasive manner. Electrical resistivity surveying, in particular, has been shown in several previous investigations to exhibit sensitivity to the presence of fractures, suggesting that geoelectrical experiments may contain important information regarding how fractures are distributed and connected in the subsurface. However, a lack of suitable numerical modeling tools for electric current flow in fractured media has prevented a detailed and systematic exploration of this concept. To address this issue, we present a novel discrete-dual-porosity modeling approach that is specifically tailored to the electrical resistivity problem. With our approach, an analytical formulation for fracture-matrix current flow exchange at the fracture scale is integrated into a discrete-fracture-network model, which is then combined with a block-scale finite-volume representation of the rock matrix. Our methodology allows for low-cost and accurate simulation of electric current flow through both the fractures and matrix, and is readily applicable to complex fracture networks at relatively large scales. Although formulated here in two dimensions, this work represents an important first step toward investigating the effect of fracture-network characteristics on bulk electrical properties, as well as toward the simulation of geoelectrical survey data in realistic fractured-rock environments.

Facies discrimination with electrical resistivity tomography using a probabilistic methodology: Effect of sensitivity and regularization

Electrical resistivity tomography has become a standard geophysical method in the field of hydrogeology, as it has the potential to provide important information regarding the spatial distribution of facies. However, inverted electrical resistivity tomography images tend to be grossly smoothed versions of reality because of the regularisation of the inverse problem. In this study, we use a probabilistic methodology based upon co-located measurements to assess the utility of electrical resistivity tomography to identify hydrofacies in alluvial aquifers. With this methodology, electrical resistivity tomography images are interpreted in terms of the probability of belonging to pre-defined hydrofacies. We first analyse through a synthetic study the ability of electrical resistivity tomography to discriminate between different facies. As electrical resistivity tomography data suffer from a loss of sensitivity with depth, we find that low-sensitivity regions are more affected by misclassification. To counteract this effect, we adapt the probabilistic framework to include the spatially varying data sensitivity. We then apply our learning to a field case. For the latter, we consider two different regularisation procedures. In contrast to the data sensitivity that affects the facies probability to a limited amount, the regularisation can affect the probability maps more considerably because it has a strong influence on the spatial distribution of inverted resistivity. We find that a regularisation strategy based on the most realistic prior information tends to offer the most reliable discrimination of facies. Our results confirm the ability of electrical resistivity tomography surveys, when properly designed, to detect facies variations in alluvial aquifers. The method can be easily extended to other contexts.

Streaming potential modeling in fractured rock: Insights into the identification of hydraulically active fractures

Numerous field experiments suggest that the self-potential (SP) geophysical method may allow for the detection of hydraulically active fractures and provide information about fracture properties. However, a lack of suitable numerical tools for modeling streaming potentials in fractured media prevents quantitative interpretation and limits our understanding of how the SP method can be used in this regard. To address this issue, we present a highly efficient two-dimensional discrete-dual-porosity approach for solving the fluid flow and associated self-potential problems in fractured rock. Our approach is specifically designed for complex fracture networks that cannot be investigated using standard numerical methods. We then simulate SP signals associated with pumping conditions for a number of examples to show that (i) accounting for matrix fluid flow is essential for accurate SP modeling and (ii) the sensitivity of SP to hydraulically active fractures is intimately linked with fracture-matrix fluid interactions. This implies that fractures associated with strong SP amplitudes are likely to be hydraulically conductive, attracting fluid flow from the surrounding matrix.

Waveform Inversion of Crosshole Georadar Data: Influence of Source Wavelet Variability and the Suitability of a Single Wavelet Assumption

Waveform-based tomographic imaging of crosshole georadar data is a powerful method to investigate the shallow subsurface because of its ability to provide images of electrical properties in near-surface environments with unprecedented spatial resolution. A critical issue with waveform inversion is the a priori unknown source signal. Indeed, the estimation of the source pulse is notoriously difficult but essential for the effective application of this method. Here, we explore the viability and robustness of a recently proposed deconvolution-based procedure to estimate the source pulse during waveform inversion of crosshole georadar data, where changes in wavelet shape with location as a result of varying near-field conditions and differences in antenna coupling may be significant. Specifically, we examine whether a single, average estimated source current function can adequately represent the pulses radiated at all transmitter locations during a crosshole georadar survey, or whether a separate source wavelet estimation should be performed for each transmitter gather. Tests with synthetic and field data indicate that remarkably good tomographic reconstructions can be obtained using a single estimated source pulse when moderate to strong variability exists in the true source signal with antenna location. Only in the case of very strong variability in the true source pulse are tomographic reconstructions clearly improved by estimating a different source wavelet for each transmitter location.

Evaluation of the viability and robustness of an iterative deconvolution approach for estimating the source wavelet during waveform inversion of crosshole ground-penetrating radar data

Summary A major issue in the application of waveform inversion methods to crosshole ground-penetrating radar (GPR) data is the accurate estimation of the source wavelet. Here, we explore the viability and robustness of incorporating this step into a recently published time-domain inversion procedure through an iterative deconvolution approach. Our results indicate that, at least in non-dispersive electrical environments, such an approach provides remarkably accurate and robust estimates of the source wavelet even in the presence of strong heterogeneity of both the dielectric permittivity and electrical conductivity. Our results also indicate that the proposed source wavelet estimation approach is relatively insensitive to ambient noise and to the phase characteristics of the starting wavelet. Finally, there appears to be little to no trade-off between the wavelet estimation and the tomographic imaging