Overcoming Practical Pitfalls in DC Resistivity Inversion
Most DC resistivity inversion algorithms are solved by minimizing an objective function comprised of a misfit norm, a model norm and a regularization parameter that is used to balance the relative contribution of these two entities. The regularization parameter is adjusted so that the final misfit is "about right" and also that the model does not have "too much", or "too little", structure. To accommodate the end user, inversion codes often come prewired with default parameters so that an inversion result is quickly obtained. Unfortunately, most users are content to stop at this first stage and not query the validity of the recovered model or attempt to explore existence of other, and better, solutions. Worse still, are circumstances in which users have accepted the output model without questioning if it satisfactorily fits the data. The results from the inversion depend upon the precise definitions of the misfit and model norms and on how the regularization parameter is estimated. In this talk I elaborate upon these items and their impact upon the final outcome. Some difficulties can be overcome by having a more regimented workflow which makes the processor focus upon crucial items and answer specific questions before proceeding to the next step. Irrespective of the methodological fix however, it is imperative that the user have a through understanding about the basics of inversion, the details of the DC survey and the data, knowledge about the conductivity of the rocks relevant to the local geology, and a clear understanding about what geologic, geophysical, or engineering questions are to be answered.
Inversion of Electrical Resistivity Data: Some Pitfalls and Remedies
Electrical resistivity surveys are now widely used in many areas of Earth and Environmental Science. In
subsurface hydrology the technique is the most widely used geophysical imaging method due to: the sensitivity
of electrical resistivity to key hydrogeological properties and states; the ease of conducting surface deployed
surveys and the relative low cost of instrumentation. The availability of relatively easy to use and robust
processing software has, no doubt, contributed to the popularity of this geophysical method. It is now relatively
easy to carry out multi-electrode DC resistivity (and even induced polarisation) surveys and produce images of
resistivity (and polarisability) variation in the shallow subsurface. It is also, unfortunately, relatively easy to
generate inappropriate models of the subsurface, particularly if inadequate attention is placed on a number of
factors, including: errors in the data and errors in the modelling, including three-dimensionality of the
subsurface. Using data from laboratory, field and synthetic modelling studies we examine the role of these
effects on the inversion of electrical resistivity data and suggest guidelines for successful use of this powerful
technique. We also offer some suggestions for improved characterisation of the subsurface through resistivity
Field Data Sets Made Available for a Community Discussion of the Inversion of Electrical Resistivity Imaging Data
Electrical resistivity imaging (ERI) can be used to obtain information about subsurface structure, properties, and processes for a wide range of near-surface applications. A critical step in the use of ERI is the inversion of the acquired data to obtain an image that displays the magnitude of the electrical resistivity throughout the subsurface region of interest. In order to obtain this image, a number of critical choices need to be made - a choice is made of an inversion algorithm, and further choices are made in terms of its implementation and the incorporation of prior geologic knowledge and constraints. These choices can significantly affect the obtained resistivity image in ways that are not often documented or well understood. It is important that the near-surface geophysics community, and other users of ERI data, engage in an ongoing discussion of how we develop, use, and share inversion algorithms. Two 2D surface electrical resistivity field data sets have been made available to the community to be used as the starting point for this discussion; they are available through the NS website. One data set was acquired in Mack Creek in the H. J. Andrews Experimental Forest to map out the interface between the alluvial sediments and the underlying bedrock. Information about the thickness of the sediments is needed to constrain hydrogeological models and has been difficult to obtain due to the remote location of the site and the inability to install boreholes. An important issue is the need to quantify the uncertainty in the ERI-derived location of the sediment-bedrock interface; a measure of uncertainty in the location of this interface could be included in the hydrogeologic modeling. The second data set was acquired during the monitoring of an infiltration test in the Mojave Desert. Measurements of the dynamically changing distribution of infiltrated water by standard means, using single-point probes installed in the subsurface, cannot adequately characterize the soil-moisture properties or fluxes because natural soils have great spatial variability and high sensitivity to mechanical disturbance. In this field study ERI provided high-resolution spatial and temporal sampling of the region below and nearby the infiltration pond.
Electrical Resistance Imaging for Evaluation of Soil-Water Behavior in Desert Ecosystems
As part of an effort to evaluate habitat types in the Mojave National Preserve, we conducted infiltration/redistribution experiments to investigate unsaturated hydraulic properties and soil-water dynamics. Two investigated locations contrasted sharply in degree of pedogenic development: (1) recently deposited sediments in an active wash and (2) a highly developed soil of late Pleistocene age. Water flow through these materials may be strongly influenced by such features as biotic crusts, vesicular horizons, textural variations, calcic horizons, preferential flow paths, and other forms of vertical and lateral spatial variability. In each location we ponded water in a 1-m-diameter infiltration ring for 2.3 h, generating 1.93 m of infiltration in the active wash and 0.52 m in the Pleistocene soil. Combining input flux data with quantitative knowledge of water content and soil water pressure over space and time provides a basis for estimating soil hydraulic properties. TDR probes and tensiometers, placed outside but within a few m of the infiltration pond at depths to 1.5 m, provided subsurface hydraulic data. In addition to probe measurements, we conducted electrical resistance imaging (ERI) measurements during the infiltration period and for six days of redistribution. Electrodes were in two crossed lines at the surface, 24 in each, at 0.5 m spacing. On each line data were collected over an eight- minute period using a hybrid geometry, with 0 to 6 electrodes skipped between those used for the measurement. Relative change in the inverted resistivities relates to relative change in soil water content. Spatially exhaustive and minimally invasive characterization is valuable because of the extreme difficulty of quantifying soil-moisture distribution over a broad heterogeneous area using a set of individual probes. Soil moisture data directly under the ponded area are especially important, and ERI was our only means for such measurements because probe installation would have required either power drilling machinery (not permitted at this wilderness location), or the punching of holes in surficial layers whose flow-impeding effects are crucial to the system under investigation. ERI results show that the relatively coarse and homogeneous active wash sediments have minimal small-scale variation in water content and comparatively little ability to retain water over time. In the older soil, infiltrated water does not go nearly as deep, but spreads to a slightly greater lateral extent; both effects are consistent with the development of horizons that contrast sharply in texture, structure, or calcification. Water content in this developed soil shows pronounced spatial variability, especially in the direction across rather than down the alluvial fan. Certain small (<1 m3) parcels of the Pleistocene soil at depths less than 0.5 m have especially great ability to retain water. The juxtaposition of these with parcels of soil that strongly transmit but weakly retain water creates a net enhancing effect on the root-accessible soil's ability to hold water over extended time, as is vital in a climate of infrequent infiltration. Present ERI results indicate the basic spatial distribution of resistivity and its evolution over time. The rate of spreading of subsurface water, as well as the shape, character, and heterogeneity of its distribution, can be inferred from these, so the results already have substantial ecohydrologic value. Advances in ERI data inversion and water- content calibration would lead toward greatly enhanced value for quantifying unsaturated hydraulic properties and water fluxes.
Synthetic resistivity calculations for the canonical depth-to-bedrock problem: A critical examination of the thin interbed problem and electrical equivalence theories
One of the key factors in the sensible inference of subsurface geologic properties from both field and laboratory experiments is the ability to quantify the linkages between the inherently fine-scale structures, such as bedding planes and fracture sets, and their macroscopic expression through geophysical interrogation. Central to this idea is the concept of a "minimal sampling volume" over which a given geophysical method responds to an effective medium property whose value is dictated by the geometry and distribution of sub- volume heterogeneities as well as the experiment design. In this contribution we explore the concept of effective resistivity volumes for the canonical depth-to-bedrock problem subject to industry-standard DC resistivity survey designs. Four models representing a sedimentary overburden and flat bedrock interface were analyzed through numerical experiments of six different resistivity arrays. In each of the four models, the sedimentary overburden consists of a thinly interbedded resistive and conductive laminations, with equivalent volume-averaged resistivity but differing lamination thickness, geometry, and layering sequence. The numerical experiments show striking differences in the apparent resistivity pseudo-sections which belie the volume-averaged equivalence of the models. These models constitute the synthetic data set offered for inversion in this Back to Basics Resistivity Modeling session and offer the promise to further our understanding of how the sampling volume, as affected by survey design, can be constrained by joint-array inversion of resistivity data.