David V. Fitterman

Transient Electromagnetic Sounding for Groundwater

The feasibility of using the transient electromagnetic sounding (TS or TDEM) method for groundwater exploration can be studied by means of numerical models. As examples of its applicability to groundwater exploration, we study four groundwater exploration problems: (1) mapping of alluvial fill and gravel zones over bedrock; (2) mapping of sand and gravel lenses in till; (3) detection of salt or brackish water interfaces in freshwater aquifers; and (4) determination of hydrostratigraphy. These groundwater problems require determination of the depth to bedrock; location of resistive, high‐porosity zones associated with fresh water; determination of formation resistivity to assess water quality; and determination of lithology and geometry, respectively. The TS method is best suited for locating conductive targets, and has very good vertical resolution. Unlike other sounding techniques where the receiver‐transmitter array must be expanded to sound more deeply, the depth of investigation for the TS method is a...

Calculations of self‐potential anomalies near vertical contacts

The self‐potential anomalies due to streaming potential effects in the vicinity of a vertical contact are analyzed. This approach is different from most previous studies in that the source is tied to a specific physical mechanism instead of arbitrarily selected charge distributions or current sources. The analysis is valid for any source mechanism that can be thought of in terms of crosscoupled flows, e.g., the thermoelectric effect or chemical potential gradients. The anomalies tend to be antisymmetric across the contact with the magnitude of the anomaly being larger on the more resistive side of the contact. An analytic expression for the case of a constant intensity, rectangular source is derived from the general solution. The anomalies for this simple case are computable with a handheld calculator and can be used to estimate the location, extent, and magnitude of the anomaly source region. With this information it is possible to determine the most probable crosscoupling source mechanism.

Inversion of self-potential data from the Cerro Prieto geothermal field, Mexico

Self‐potential (SP) data from the Cerro Prieto geothermal field in Baja California, Mexico have been inverted using a model consisting of a vertical contact separating regions of different electrical properties. A temperature source is assumed to coincide with the vertical contact between materials with different thermoelectric coupling coefficients. A derivative‐free Levenberg‐Marquardt algorithm is used to estimate values for the depth, vertical extent, length, and intensity of the source region. The depth to the top of the source is estimated to be about 1.3 ± 0.2 km, which agrees quite well with the depth to the top of the production zone determined from drilling. The vertical extent and length of the source region are estimated to be 11 ± 3 km and 9.9 ± 0.4 km, respectively. There appears to be geologic evidence for the presence of a fault or fault zone within the geothermal field that roughly coincides in location with the self‐potential source region. The conductivity on the east side of the produc...

Effect of transmitter turn-off time on transient soundings

Abstract A general procedure for computing the effect of non-zero turn-off time on the transient electromagnetic response is presented which can be applied to forward and inverse calculation methods for any transmitter-receiver configuration. We consider in detail the case of a large transmitter loop which has a receiver coil located at the center of the loop (central induction or in-loop array). For a linear turn-off ramp of width t 0 , the voltage response is shown to be the voltage due to an ideal step turn-off averaged over windows of width t 0 . Thus the effect is similar to that obtained by using averaging windows in the receiver. In general when time zero is taken to be the end of the ramp, the apparent resistivity increases for a homogeneous half-space over a limited time range. For time zero taken to be the start of the ramp the apparent resistivity is affected in the opposite direction. The effect of the ramp increases with increasing t 0 and first-layer resistivity, is largest during the intermediate stage, and decreases with increasing time. It is shown that for a ramp turn-off, there is no effect in the early and late stages. For two-layered models with a resistive first layer ( ρ 1 > ρ 2 ), the apparent resistivity is increased in the intermediate stage. When the first layer is more conductive than the second layer ( ρ 1 ρ 2 ) and the layer thickness is comparable or greater than the loop radius, similar results are obtained; however, when the layer is thin compared to the loop radius the apparent resistivity is initially decreased and then increases as time increases. Examples are presented which illustrate the strong influence of the geoelectrical section on the turn-off effect. Neglecting the turn-off ramp will affect data interpretation as shown by field examples; the influence is the greatest on near-surface layer parameters.

Effect of bird maneuver on frequency-domain helicopter EM response

Bird maneuver, the rotation of the coil-carrying instrument pod used for frequency-domain helicopter electromagnetic surveys, changes the nominal geometric relationship between the bird-coil system and the ground. These changes affect electromagnetic coupling and can introduce errors in helicopter electromagnetic (HEM) data. We analyze these effects for a layered half-space for three coil configurations: vertical coaxial, vertical coplanar, and horizontal coplanar. Maneuver effect is shown to have two components: one that is purely geometric and another that is inductive in nature. The geometric component is significantly larger. A correction procedure is developed using an iterative approach that uses standard HEM inversion routines. The maneuver effect correction reduces inversion misfit error and produces laterally smoother cross sections than obtained from uncorrected data.

Electromagnetic mapping of buried paleochannels in eastern Abu Dhabi Emirate, U.A.E.

Abstract Transient electromagnetic soundings and terrain conductivity meter measurements were used to map paleochannel geometry in the Al Jaww Plain of eastern Abu Dhabi Emirate, U.A.E. as part of an integrated hydrogeologic study of the Quaternary alluvial aquifer system. Initial interpretation of the data without benefit of well log information was able to map the depth to a conductive clay layer of Tertiary age that forms the base of the aquifer. Comparison of the results with induction logs reveals that a resistive zone exists that was incorporated into the interpretation and its lateral extent mapped with the transient electromagnetic sounding data.

Direct time‐domain calculation of the transient response for a rectangular loop over a two‐layer medium

The time derivative of the vertical magnetic field due to an electric dipole on the surface of a two‐layer half‐space is computed directly in the time domain by applying the residue theorem to the analytic field expressions. The second layer must be either insulating (σ2=0) or perfectly conducting (σ2=∞). The first case can be used to estimate the response of a conductive overburden for mining exploration problems. The second case is useful in explaining the overshoot seen in transient sounding voltage apparent‐resistivity curves when a conductive basement underlies a resistive first layer. In the late stage, the time derivative of the vertical magnetic field decays as t-4 and the late‐stage apparent resistivity increases as t for σ2=0, while for σ2=∞, these quantities behave as t-4e-αt and te2αt/3, respectively, where α=π2/4μ0σ1h12, σ1, is the first‐layer conductivity, h1 is the first‐layer thickness, and μ0=4π10-7H/m. The electric dipole expressions are integrated to obtain solutions for rectangular loo...

Modeling of self‐potential anomalies near vertical dikes

The self‐potential (SP) Green’s function for an outcropping vertical dike is derived from solutions for the dc resistivity problem for the same geometry. The Green’s functions are numerically integrated over rectangular source regions on the contacts between the dike and the surrounding material to obtain the SP anomaly. The analysis is valid for thermoelectrical source mechanisms. Two types of anomalies can be produced by this geometry. When the two source planes are polarized in opposite directions, a monopolar anomaly is produced. This corresponds to the thermoelectrical properties of the dike being in contrast with the surrounding material. When the thermoelectric coefficients change monotonically across the dike, a dipolar anomaly is produced. In either case positive and negative anomalies are possible, and the greatest variation in potential will occur in the most resistive regions. Examples of the effect of changing different model parameters are given for sources that have constant intensity throu...

Thermoelectrical self‐potential anomalies and their relationship to the solid angle subtended by the source region

The calculation of self‐potential (SP) anomalies produced by thermoelectric sources is shown to be equivalent to calculating the weighted solid angle subtended at the observation point by the source region and its images where the weighting function is the source intensity. This interpretation provides an easy way of visualizing the effect of different source geometries, and describes the nonuniqueness associated with SP sources. For example, changes in a model which keep the product of source intensity and area constant do not appreciably change the produced anomaly. Similarly, deepening a source requires an increase of source intensity or size to produce the same anomaly. When conductivity contrasts become small or nonexistent, the number of image sources becomes finite or zero, respectively, further simplifying the calculation. As an example, the SP anomaly of a dipping rectangular source of constant intensity is computed using the method. This model is applied to SP data from the East Mesa geothermal ...

Detectability levels for central induction transient soundings

A question usually asked during the planning of a transient sounding survey is, “Can information useful to solving the geologic problem at hand be obtained from the measurements?” This question is usually answered by constructing a geologic model for the survey area based upon the best available information to determine which model parameters can be resolved. Specifically, this determination can be accomplished by computing a forward model, varying a parameter of interest, and observing whether the responses of the original and perturbed models are different. Alternatively, inversion‐based methods can be used to estimate parameter resolution (Inman, 1975; Glenn and Ward, 1976).