Understanding Complications in Near-Surface Geophysical Inverse Problems I
Presiding: P S Routh, Boise State University; G A Oldenborger, Boise State University
NS12A-01 INVITED 10:30h
Challenges to Near-Real-Time Classification of Buried Conductive Targets Based on the Spatiotemporal EMI Response
Classification of conductive targets using controlled-source electromagnetic induction (EMI) is an important task in near-surface applied geophysics. Target classification is sometimes required in near real-time, requiring efficient and fast data processing algorithms. We select empirical physics-based target parameters that are invariant under transmitter-receiver geometry. We used a modifed EM63 metal detector to construct a response database. The target collection consists of hollow and solid spheres, cylinders, plates and inert ordnance. The inversion method is based on non-linear least-squares combined with numerical continuation. The spatiotemporal forward response is that of a body whose induced magnetization tensor undergoes a stretched-exponential transient decay. The early-time background response and late-time system noise produce a rough objective function. In such cases, gradient descent methods can stop at sub-optimal solutions. Nevertheless, we observe model-space clustering of recovered target parameters that can be used a basis for classification, which is achieved here simply by association of an unknown target response with the category assigned to the nearest cluster. We discuss how noise and non-uniqueness of the inverse problem sometimes result in misclassification.
NS12A-02 INVITED 10:45h
A Multi-Object Inversion Approach for Efficient Magnetic Discrimination of Unexploded Ordnance
Magnetometery is one of the primary methods used for detecting buried unexploded ordnances, either in a standalone mode, or in conjunction with electromagnetic induction. UXO's and other metallic debris generally appear as dipolar anomalies overprinting larger scale magnetic features due to near-surface magnetite variations and the regional geology. Non-linear high-pass filters are usually used to remove the larger scale effects and the remaining dipolar anomalies are inverted one at a time by an efficient bound-constrained optimization algorithm. This process works well when the individual anomalies are well separated and the geological variations are at larger scales than the UXO anomalies. When these conditions don't apply the inversion results are unreliable and the process of inverting each anomaly becomes time-consuming and unwieldy. We have developed an efficient multi-object inversion routine that allows simultaneous inversion of an arbitrary number of dipolar anomalies. Providing a good initial guess as to the number, location, magnitude and orientation of each dipole is critical to the success of the algorithm. We have found that an Automated Wavelet Detection algorithm we developed in a previous paper is ideal for this purpose. The multi-object inversion approach is very effective in most situations, but, like the original single-object approach, has trouble dealing with datasets with significant geological contamination. In an effort to overcome this problem we outline a framework for coupling our multi-object inversion scheme with an equivalent layer technique that attempts to model the background geology.
NS12A-03 INVITED 11:00h
Reconciling Electrical Resistivity Tomography Images and Hydrological Models
Electrical resistivity tomography (ERT) holds the promise of providing information on the parameters controlling flow and potentially monitoring flow itself. The resolution of electrical resistivity tomography surveys is limited by the data quantity, data quality, and the survey configuration (electrode count, spacing, and borehole separation). Inevitably, we must interpret data from regions containing substantial variability at a scale much finer than the resolution of the method. This study used earlier field experiments performed at the Sandia-Tech Vadose Zone facility near Socorro, NM as a template to study the effects of fine-scale structure on geophysical images. A series of hydrological models were created that ranged from homogeneous half-space models to models with layers of random but spatially correlated hydrological parameters. A 12 x 12 x 12 m was modeled using grid sizes as small as 6.25 cm. Moisture content was converted to electrical conductivity using Archie's equation and forward modeled using a mesh at the same scale as the hydrological models. Normally-distributed, pseudo-random noise was added to create synthetic data. These data were then inverted with the same coarse mesh used to interpret field results from the original project. Modeling of ERT data for very large meshes was somewhat more difficult than anticipated and required determining optimal choices for mesh size particularly in the background and boundary regions. Initial results showed that ERT produces images that are smoother than the correct model, but preserves large-scale features. In fact, strongly layered, non-stochastic models appeared to be more difficult to image than the complex stochastic ones. However, the nature of the images of synthetic model data and the original field data were far more different than anticipated. The models had higher infiltration rates, higher moisture contents, sharper boundaries around the infiltration region, and larger contrasts between the pre- and post-infiltration saturations. The initial inversion parameters had to be adjusted to accommodate the larger contrasts present in the synthetic models. This also brought into question whether the hydrological models were representative of realistic field conditions. Work is underway to revise both the pre-infiltration and post-infiltration hydrological models to more closely approximate field conditions.
NS12A-04 11:15h
Sensitivity of electrical resistivity tomography data to electrode position
The electrical resistivity tomography (ERT) method has proven to be a valuable geophysical tool for a variety of shallow subsurface imaging tasks. Limitations of tomographic imaging arise due to the difficulty of quantifying the reliability of tomographic images. A major source of uncertainty in tomographic inversion is data error. Near surface environmental and engineering geophysical surveys are often such that target size may be of the same order of scale as the experiment dimensions. It is at these overlapping scales that errors in electrode positions can significantly contaminate the ERT data. Electrode mislocation can result from borehole deviation, poor electrode emplacement or surveying mistakes. Position errors are particularly problematic as they do not show up in either reciprocal or repeatability tests but rather, propagate via forward modeling of the data. The dependence of the data on electrode mislocations is characterized by the sensitivity of electrical potential to both source and receiver positions. In the homogeneous case, the sensitivity of potential with respect to source/receiver position is purely geometrical and dependent on the electrode-electrode separation. The homogeneous sensitivity distributions illustrate the susceptibility to position errors for hypothetical survey geometries (cross-hole vs. common-hole) and data types (pole vs. dipole). In the heterogeneous case, the sensitivity of potential with respect to source/receiver electrode position is described by a scattering-type equation and, therefore, the sensitivity depends not only on electrode-electrode separation but also on the location and magnitude of contrasts in electrical conductivity. Accordingly, for surveys in which electrodes may be close to the target, sensitivity to source/receiver position can be high. Using synthetic experiments, we demonstrate that variations in the data due to errors in electrode position are comparable in magnitude to typical experimental noise levels and, in some cases, may overwhelm variations in the data due to changes in material properties. Furthermore, the statistical distribution of electrode position errors can be complicated and multi-modal such that bias may be introduced into the ERT data.
NS12A-05 11:30h
A Pitfall in the Design of 3D Surface Resistivity Arrays
Multielectrode arrays, computer-controlled data acquisition, and commercially available resistivity inversion software have increased interest in 3D resistivity imaging. Recent research has demonstrated the advantages of using 3D inversion in areas where off-line heterogeneities would otherwise distort 2D results. For convenience in the field, multielectrode arrays used to collect 3D resistivity data are typically laid out on a Cartesian grid with potential measurements acquired using electrode pairs oriented along the X and Y axes. The current flow away from a given injection electrode, however, has radial symmetry in the case of a homogeneous, isotropic half-space, and near-radial symmetry otherwise, unless the ground is extremely heterogeneous or anisotropic. Consequently, many of the voltage measurements made using standard electrode combinations are tangential or nearly-tangential to the voltage equipotentials, resulting in the worst possible signal to noise ratio. Using data collected in karst terrain near Easton, PA, we compare results from a standard pole-dipole measurement sequence with measurements made using the same pattern of electrodes, but choosing potential electrode pairs oriented along lines radiating from the injection electrode. The remarkable improvement in data quality illustrates the importance of considering the potential gradient when designing resistivity data collection schemes.
NS12A-06 11:45h
Improved Inversion of High-Angle Ray Data in Crosshole GPR Tomography
Over the past decade, crosshole ground-penetrating radar (GPR) tomography has become an important tool for the estimation of subsurface moisture content. In order to produce the highest resolution images possible with this technique, raypaths covering a wide range of angles between the boreholes are required. In practice, however, including high-angle ray data in crosshole GPR inversions often results in poor data fitting and tomographic images with obvious artifacts. As a result, high-angle ray data are usually discarded prior to inverting. This produces stable tomographic images, but with limited horizontal resolution that impacts the use of such images for estimating hydrologic properties. We have found that the incompatibility of high-angle ray data in crosshole GPR tomography can be largely explained by the finite length of the borehole radar antennas. Whereas tomographic inversions treat the antennas as point sources and receivers, in reality the antenna length is often a significant fraction of the borehole separation. At high angles, we have found that first arrival energy can often represent coupling between the tips of the antennas, and not between their centers as is presently assumed. This results in significant geometrical errors in the inversion of high-angle data. The effect is most significant for small borehole separations. We present a means of dealing with high-angle rays in crosshole GPR tomography so that all available data can be incorporated into the inversion process. First, we obtain a starting velocity model from an aperture-limited subset of the available travel time picks. Next, we construct nine different tomographic kernel matrices that represent coupling between all primary radiation points along the antennas (i.e., the antenna centers and tips). Using these kernels, we then determine which coupling path arrives first for each transmitter/receiver configuration in the entire data set. From this information, we construct a new tomographic kernel matrix and solve the system for the velocity distribution between the boreholes. Tests on synthetic data show that this procedure allows for the successful incorporation of all recorded data into crosshole GPR tomography, and produces results with noticeably improved horizontal resolution over aperture-limited data subsets.