Carlyle R. Miller

Application of time-lapse ERT imaging to watershed characterization

Time-lapse electrical resistivity tomography ERT has many practical applications to the study of subsurface properties and processes. When inverting time-lapse ERT data, it is useful to proceed beyond straightforward inversion of data differences andtakeadvantageofthetime-lapsenatureofthedata.Weassess various approaches for inverting and interpreting time-lapse ERTdataanddeterminethattwoapproachesworkwell.Thefirst approachismodelsubtractionafterseparateinversionofthedata from two time periods, and the second approach is to use the inverted model from a base data set as the reference model or prior information for subsequent time periods. We prefer this second approach. Data inversion methodology should be considered when designing data acquisition; i.e., to utilize the second approach, it is important to collect one or more data sets for which the bulk of the subsurface is in a background or relatively unperturbed state.Athird and commonly used approach to time-lapse inversion,invertingthedifferencebetweentwodatasets,localizes the regions of the model in which change has occurred; however, varying noise levels between the two data sets can be problematic. To further assess the various time-lapse inversion approaches,weacquiredfielddatafromacatchmentwithintheDry Creek Experimental Watershed near Boise, Idaho, U.S.A. We combined the complimentary information from individual static ERTinversions,time-lapseERTimages,andavailablehydrologicdatainarobustinterpretationschemetoaidinquantifyingseasonalvariationsinsubsurfacemoisturecontent.

Image Interpretation Using Appraisal Analysis

In geophysical inversion, a significant effort is invested to obtain images of the Earth from finite data. The first step is to obtain an image i.e. solve the inverse problem. This step alone provides significant challenges that are not addressed in this paper. The next step is to interpret the image in terms of specific questions. For example, what can we say about the average value of a physical property within a certain region of the model? What scale information can we resolve from the data? These questions are problem dependent and may require that inversion be carried out several times to arrive at a satisfactory answer. Therefore the solution to an inverse problem is only a step towards answering these questions. Appraisal analysis of the solution takes the next step by providing a set of tools to judge and select from the possibly infinite suite of images that adequately fit our observations. We discuss the use of point spread functions and averaging kernels in the interpretation of images. We use a controlled source electromagnetic example to demonstrate the methodology.

Land Streamer Aided Geophysical Studies at Saqqara, Egypt

During December 2002 and January 2003, Montana Tech in collaboration with Ain Shams University, Cairo, collected Ground Penetrating Radar (GPR) and seismic data at Saqqara, Egypt. The purpose of this study was to see if GPR and seismic methods could detect manmade structures in the subsurface at Saqqara. In particular, land streamer aided, seismic diving-wave tomography was tested as a method to detect archaeological features. Saqqara was one of the principal necropolises of Memphis, an ancient capital of Egypt. The research site was near the 3rd Dynasty pharaoh Djoser’s Step Pyramid—the first monumental structure built entirely of stone. A preliminary GPR study of our site yielded numerous, possibly manmade features in the subsurface with a 4m depth of penetration using 100MHz antennas. A follow-up three-dimensional (3-D) GPR survey over one of the more interesting features showed a broad trench underneath the flat-lying sand that is seen at the surface. This feature is most likely manmade because the ho...

Watershed characterization using seasonal time‐lapse DC resistivity data

Changes in water saturation can cause significant changes in the electrical conductivity of near surface materials. Thus mapping changes in the conductivity distribution during wet and dry periods provides an indirect way to quantify changes in the saturation of the near-surface medium. This, in turn, leads to better understanding of the water mass balance in a watershed characterization problem. The conductivity imaging can also provide other information such as fracture orientations within the nearsurface medium. At Dry Creek watershed; situated at 1830m elevation near Boise, Idaho; we study seasonal changes in saturation using the time-lapse DC resistivity method. Four DC resistivity data sets were acquired between October 2005 and July 2006 to monitor the changes in conductivity. The results indicate that DC resistivity is a cost-effective tool to characterize a watershed and aids in the interpretation of other data collected in the watershed.

Resolution analysis of geophysical images: Comparison between point spread function and region of data influence measures

Practical decisions are often made based on the subsurface images obtained by inverting geophysical data. Therefore it is important to understand the resolution of the image, which is a function of several factors, including the underlying geophysical experiment, noise in the data, prior information and the ability to model the physics appropriately. An important step towards interpreting the image is to quantify how much of the solution is required to satisfy the data observations and how much exists solely due to the prior information used to stabilize the solution. A procedure to identify the regions that are not constrained by the data would help when interpreting the image. For linear inverse problems this procedure is well established, but for nonlinear problems the procedure is more complicated. In this paper we compare two different approaches to resolution analysis of geophysical images: the region of data influence index and a resolution spread computed using point spread functions. The region of data influence method is a fully non-linear approach, while the point spread function analysis is a linearized approach. An approximate relationship between the region of data influence and the resolution matrix is derived, which suggests that the region of data influence is connected with the rows of the resolution matrix. The point-spread-function spread measure is connected with the columns of the resolution matrix, and therefore the point-spread-function spread and the region of data influence are fundamentally different resolution measures. From a practical point of view, if two different approaches indicate similar interpretations on post-inversion images, the confidence in the interpretation is enhanced. We demonstrate the use of the two approaches on a linear synthetic example and a non-linear synthetic example, and apply them to a non-linear electromagnetic field data example. I N T R O D U C T I O N Geophysical inversion is inherently ill-posed and non-unique. To solve ill-posed geophysical inverse problems, we routinely incorporate prior information into our solution. This stabilizes the solution, but also complicates the appraisal process because of the bias introduced into the solution. If the end goal of our data analysis involves decisions based on our solution, it is of great importance that we take steps to quantify how ∗ E-mail: camiller@cgiss.boisestate.edu much information came from data and how much came from prior information. For different applications it is difficult to produce a unified interpretation goal; however, an important question is to determine which regions of the image are influenced by a priori information and which regions are influenced by the data. Although different ways of incorporating a priori information are sometimes considered to be subjective (Friedel 2003), regularization an essential step in obtaining a stable solution that is physically meaningful. Therefore, we usually cannot neglect imposing a priori information through the regularization procedure in the inverse problem. However, if we can C

Site Characterization For Groundwater Using Controlled-Source Electromagnetics

Controlled source electromagnetic data were acquired at two sites in Southern California in order to characterize the subsurface and identify structures that would influence water flow and distribution. The electromagnetic data were inverted to ascertain the subsurface electrical conductivity structure of the sites. Due to higher data quality and validity of layered Earth assumption, 1D inversion was sufficient for characterizing the Anza, California field site. The Joshua Tree, California site presented a greater challenge due to more subsurface heterogeneities and variable electrode coupling conditions. 1D inversion was attempted for these data, but fitting the data with the 1D inversion proved to be nearly impossible. These data were inverted in 3D at lower frequencies in order to characterize the deep structure of the site. The 3D inversion results are relatively consistent with what is known about the subsurface geology for the site.

Electrical conductivity imaging using controlled source electromagnetics for subsurface fluid flow characterization

In this paper we present a case history for mapping electrical conductivity using Controlled Source Audio Magnetotellurics (CSAMT). We have completed a first pass 1D inversion of a 3D CSAMT data set collected over a geothermal reservoir located in western Idaho. We compare the inversion results of data combinations including apparent resistivity, phase, and direct inversion of the electric field component. The 1D profiles from the first pass inversion are combined to generate 2D subsurface conductivity images. We include our interpretation of the subsurface conductivity structure to determine the pathways of the fluid conduits in the geothermal reservoir. Our eventual goal is to obtain a 3D conductivity model by inverting these data using 3D CSAMT inversion.