DETERMINISTIC DECONVOLUTION OF GROUND-PENETRATING-RADAR DATA AT A LIMESTONE QUARRY
Jianghai Xia, Tom Weis, Evan Franseen, and Richard Miller
Kansas Geological Survey, The University of Kansas

Abstract
A 30 m by 30 m two-dimensional grid was designed on a flat bench behind a quarry face of predominantly limestone with thin shale layers located at a Bonner Springs, Kansas site to test the utility of ground-penetrating radar (GPR) for stratigraphic studies. GPR data were collected along seven lines parallel to the quarry face and seven lines perpendicular to the quarry face, each separated by 5 m, using 50 MHz, 100MHz, 200 MHz, and 400 MHz antennas. As a part of the project, confirmation of reflection events, ringing suppression, and velocities of electromagnetic (EM) wave propagation in the limestone were studied. GPR instrument wavelets were successfully collected in the air. With a known GPR instrument wavelet, ringing in GPR data was significantly suppressed by a deterministic deconvolution. The validity of using a wavelet acquired in air as the operator for deterministic deconvolution was shown in the real-world application of a radar system with 400 MHz antennas to a quarry site consisting of interbedded limestones and shale partings. A total of 78 horizontal holes were drilled in key locations on three exposed quarry faces where data were acquired before and after conductive steel rods, 1.5 m in length, were placed in the holes. Diagnostic GPR responses from the horizontal steel rods serve as known reflectors. The steel rods provide critical information for: 1) confirmation and nature of specific geologic reflection events in the GPR data, 2) GPR resolution limits, 3) accuracy of velocities calculated from common-midpoint data, and 4) identification of multiples. The effectiveness of suppressing ringing waveforms suggests that the deterministic deconvolution of GPR data with the GPR instrument wavelet in the air should be included as a standard GPR data processing step.

Introduction
Over the last decade ground-penetrating radar (GPR) has been widely used in environmental, engineering, and groundwater investigations (e.g., Arcone et al., 1998; Olhoeft et al., 1994; 1996b; Annan, 1996; Young et al., 1997; Powers, 1997; Cardimona et al., 1998; Asprion and Aigner, 1999; Butler et al., 2000) as well as shallow sedimentary and stratigraphic studies (Arcone, 1996; Smith and Jol, 1992; Pratt and Miall, 1993; Bridge et al., 1995; Sigurdsson and Overgaard, 1996; Liner and Liner, 1997; McMechan et al., 1997; Martinez et al., 1998; Young and Sun, 1999; Vandenberghe et al., 1999; Beres et al., 1999; Augustinus et al., 1999; Dagallier et al., 2000; Kruse et al., 2000; Bano et al., 2000; Van Dam and Schlager, 2000). Although these studies lend insight and in general demonstrate the promise and usefulness of GPR for geologic, environmental, and engineering studies, questions still remain as to all the factors responsible for the actual appearance or characteristics of GPR reflections and diffractions. By nature, GPR is very band limited. Accurate interpretation of geologic features from GPR data depends on data resolution, which requires a thorough understanding of the bandwidth and waveform. Ringing (related to narrow bandwidth and source waveform) in a GPR section needs to be identified and reduced/eliminated because it dramatically limits resolution, therefore constraining the legitimate usage of GPR and increasing the potential for misinterpretations. To increase the temporal resolution and correctly interpret GPR data in a fashion critical for shallow stratigraphic studies, deconvolution is essential. Deconvolution compresses the basic source wavelet, resulting in improved temporal resolution. There are many different deconvolution methods with application histories in seismic reflection data processing (Yilmaz, 1987). Deconvolution has also been applied to GRP data in hopes of improving resolution in a manner consistent with conventional seismic reflection. Examples include a propagation deconvolution method (Turner, 1994), a predictive deconvolution method (Todoeschuck et al., 1992), a two-sided deconvolution method (Gottsche et al., 1996), and a mixed-phase deconvolution method (Porsani and Ursin, 1996). Neves et al. (1995) presented source signature deconvolution. The source wavelet was statistically determined in their method. Unfortunately, all of these deconvolution methods require that assumptions be made about the source wavelet and/or extraction of the source wavelet from GPR data. These assumptions strongly contribute to the fact that deconvolution of GPR data in a realworld setting has never been successfully demonstrated in the literature. Deterministic deconvolution is numerically the simplest and most stable of all types of deconvolution and is equivalent to spike deconvolution when an instrument wavelet is available. An important advantage to bear in mind with this method is the fact that the instrument wavelet does not change either from place to place or as a function of antenna ground coupling. Hence, it has the potential to provide the highest possible resolution independent of data characteristics. In this paper an appropriate methodology is demonstrated for successfully acquiring the GPR instrument (source) wavelet necessary for the formulation of a convolution model, the basis of deterministic deconvolution. A realworld stratigraphic site is used to measure the success of deterministic deconvolution for improving temporal and spatial resolution of the GPR data. This paper presents results of deterministic deconvolution. Our study developed a convolution model using a GPR instrument wavelet acquired in the air, which was then verified through deterministic deconvolution of GPR data utilizing Pennsylvanian limestone and thin shale layers exposed in successive faces of a quarry in Bonner Springs, Kansas (Figure 1). This study is part of a multi-phase integrative study at the quarry site designed to address stratal, lithologic, petrophysical, and geophysical properties influencing GPR response. The objective of this study is to provide strategies and methods that allow a more accurate application of GPR to sedimentary rock studies than currently practiced. A unique aspect of the study was the utilization of conductive metal rods, 1.5 m in length, inserted into horizontal drill holes placed at key locations in exposed quarry faces. These rods provide easily identifiable signatures on GPR profiles and serve as known reflecting/ diffracting points (Butler et al., 2000). Results present here have significant implications both for improving the use (accuracy) of GPR data and to the authenticity of interpretations of GPR sections in stratigraphic studies where successful suppression of wavelet effects on GPR data is critical. Deterministic deconvolution with the true GPR instrument wavelet needs to become a standard part of GPR data processing.

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