H. Maurer

GPR Full-Waveform Sensitivity and Resolution Analysis Using an FDTD Adjoint Method

GPR tomography is a useful tool for mapping the conductivity and permittivity distributions in the shallow subsurface. By exploiting the full GPR waveforms it is possible to image sub-wavelength features and improve resolution relative to what is possible using ray-based approaches. Usually, mere convergence in the data space is the only criterion used to appraise the goodness of the final result, therefore limiting the reliability of the inversion. A better indication of the correctness of an inverted model and its various parts could be obtained by means of a formal resolution and information content analysis. We present here a novel method for computing the sensitivity kernels (Jacobian matrix) based on an FDTD adjoint method. We show that the column sum of absolute values of the Jacobian, often used as a proxy for model resolution, is inadequate, such that a formal resolution analysis should be performed. The eigenvalue spectrum of the pseudo-Hessian matrix provides a measure of the information content of the experiment and shows the extent of the unresolved model space.

Full-waveform inversion of crosshole ground penetrating radar data to characterize a gravel aquifer close to the Thur River, Switzerland

Imaging results of crosshole GPR can be significantly improved by using full-waveform inversion compared to conventional ray-based inversion schemes. A recently developed 2D finite difference time domain (FDTD) vectorial full-waveform crosshole radar inversion method was made more flexible to allow using an optimized acquisition setup that reduces the measurement speed and the computational cost. This improved algorithm was used to invert crosshole GPR data acquired within a gravel aquifer in northern Switzerland. Compared to the ray-based inversion, the results from the full-waveform inversion show significantly higher resolution images in the depth range of 6m - 10m. Comparison of the inversion results with borehole logs shows that porosity estimates obtained from Neutron-Neutron data correspond well with the GPR porosities derived from the permittivity distribution in the depth range 6 m - 10 m and that the trends are in good qualitative agreement. Furthermore, there is a good correspondence between the conductivity tomograms and natural Gamma logs at the boundary between the gravel layer and the underlying lacustrine clay sediments.

High resolution imaging of the unsaturated and saturated zones of a gravel aquifer using full-waveform inversion

Full-waveform inversion can significantly improve imaging results of cross-hole GPR data compared to conventional ray-based inversion schemes. Recently, a 2D full-waveform finite difference time domain (FDTD) approach was used to invert cross-hole GPR data measured in the saturated zone of a gravel aquifer. Due to water table refractions and reflections, the upper part of the aquifer was not reliably imaged. Here, we reconstruct the upper part of the aquifer by imaging both the saturated and unsaturated zones. Estimating one effective wavelet, as was done for the saturated zone inversion alone, is insufficient because the effective wavelet strongly depends on the location of both the transmitter and receiver antennas. Therefore, four different source wavelets were estimated for the different combinations of antennas placement in the two zones, and the full-waveform inversion algorithm adapted accordingly. This resulted in improved images of the aquifer. In general, the observed and the synthetic traces show a good correspondence in both shape and amplitude. For the transmitters in the unsaturated domain, the amplitude fit was not optimum and can probably be improved by adjusting the conductivity starting model.

GPR full waveform sensitivity and resolution analysis using an FDTD adjoint method

Radar tomography is a useful technique for mapping the permittivity and conductivity distributions in the shallow subsurface. By exploiting the full radar waveforms, it is possible to improve resolution and, thus, image subwavelength features not resolvable using ray-based approaches. Usually, mere convergence in the data space is the only criterion used to appraise the goodness of a final result, possibly limiting the reliability of the inversion. A better indication of the correctness of an inverted model and its various parts could be obtained by means of a formal model resolution and information content analysis. We present a novel method for computing the sensitivity functions (Jacobian matrix) based on a time-domain adjoint method. Because the new scheme only computes the sensitivity values for the transmitter and receiver combinations that are used, it reduces the number of forward runs with respect to standard brute-force or other virtual-source schemes. The procedure has been implemented by using a standard finite-difference time-domain modeling method. A comparison between cumulative sensitivity (column sum of absolute values of the Jacobian) images, which is sometimes used in geoelectrical studies as a proxy for resolution in practical cases, and formal model resolution images is also presented. We show that the cumulative sensitivity supplies some valuable information about the image, but when possible, formal resolution analyses should be performed. The eigenvalue spectrum of the pseudo-Hessian matrix provides a measure of the information content of an experiment and shows the extent of the unresolved model space.

Seismic Velocity Structure of a Fossilized Icelandic Geothermal System - A Combined Laboratory and Field Study

Magmatic geothermal systems, such as in Iceland are complex geological structures. They comprise quasi-horizontally layered basaltic lava flows of variable rock-texture and -morphology, repeatedly intruded magma chambers, and numerous intersecting sub-vertical dykes and sub-horizontal sheets. In order to estimate whether seismic techniques can detect signatures of geothermal activity and image reservoirs embedded in such a heterogeneous background medium, this study examined the seismic velocity structure of the fossil geothermal system of Geitafell, southeast Iceland. We combined seismic tomography field experiments with ultrasonic measurements in the laboratory to obtain a comprehensive picture of the velocity systematics. We recorded six shallow seismic profiles (to depths of 30-50 m) over outcrops of different parts of the exposed magmatic system and we investigated 10 specimens of basalt, diorite, and gabbro in the laboratory. Our results demonstrate that even in the fossilized, and hence cold, geothermal system of Geitafell, seismic velocities can vary over a wide range of around 1500 m/s. Moreover, we discovered ultrasonic velocities measured in the laboratory under comparable pressure (depth) conditions to be up to 15 % higher than seismic velocities inverted from the field data. Such factors are important to consider when interpreting seismic profiles recorded over geothermal exploration areas.

Full-waveform inversion of cross-hole GPR data measured at the boise gravel aquifer

Cross-hole radar tomography is a useful tool for mapping shallow subsurface dielectric permittivity (ε) and electrical conductivity (σ) parameters. Conventional ray-based tomography suffers from some shortcomings: it provides relatively low resolution images and it cannot supply reliable information on certain types of low velocity structure. Higher resolution images can be provided by full-waveform inversion that uses significantly more information of the data. Since the first application of full-waveform inversion on experimental GPR data, the algorithm has been significantly improved. An overview is given of all developments by applying different versions of the full-waveform inversion to the experimental data set acquired at the Boise Hydrogeophysics Research Site in Idaho. Almost all improvements resulted in a reducing final misfit between the measured and synthetic data and a reducing gradient at the final iteration.