Greg Hodges

Simulated annealing for airborne EM inversion

The traditional algorithms for airborne electromagnetic (EM) inversion, e.g., the Marquardt-Levenberg method, generally run only a downhill search. Consequently, the model solutions are strongly dependent on the starting model and are easily trapped in local minima. Simulated annealing (SA) starts from the Boltzmann distribution and runs both downhill and uphill searches, rendering the searching process to easily jump out of local minima and converge to a global minimum. In the SA process, the calculation of Jacobian derivatives can be avoided because no preferred searching direction is required as in the case of the traditional algorithms. We apply SA technology for airborne EM inversion by comparing the inversion with a thermodynamic process, and we discuss specifically the SA procedure with respect to model configuration, random walk for model updates, objective function, and annealing schedule. We demonstrate the SA flexibility for starting models by allowing the model parameters to vary in a large range (far away from the true model). Further, we choose a temperature-dependent random walk for model updates and an exponential cooling schedule for the SA searching process. The initial temperature for the SA cooling scheme is chosen differently for different model parameters according to their resolvabilities. We examine the effectiveness of the algorithm for airborne EM by inverting both theoretical and survey data and by comparing the results with those from the traditional algorithms.

Predictions of bird swing from GPS coordinates

Bird attitudes, with roll, pitch, and yaw angles, are required for modeling the measured electromagnetic response of the earth. Global Positioning System (GPS) antennas can be used in airborne electromagnetic (AEM) systems to monitor airborne platform attitude and bird maneuver. We have found evidence from photographic sequences that four GPS antennas, three on the bird and one on the aircraft, generally are adequate for angular and altitude geometry control. The mounting system for the bird frame introduces vibration noise. We have developed a model that predicts bird maneuver from the use of GPS antennas already present during routine airborne surveys. The bird motion, whether inline or crossline, is modeled from the difference between the aircraft location and the mean location of the bird. This also accurately predicts the roll of the bird when an inline yoke mounting is used. The minimum number of GPS antennas required to monitor the motion of a cylindrical electromagnetic (EM) bird typical of frequency-domain systems is two, one on the aircraft and one on the bird. We have defined optimum locations of GPS antennas to enable geometric monitoring of towed-bird systems. The findings suggest that the bird be mounted with two aerodynamically efficient GPS antennas, one on the nose and one on the tail. This enables the measurement of the pitch and yaw of the bird, with roll deduced using the third GPS on the helicopter.

Wire-loop surface conductor for airborne EM system testing

The known mineral deposits used to test and compare airborne electromagnetic systems are often difficult to model because of nonideal geology, and may also be inconvenient or costly to survey. A simple wire-loop conductor has the advantage of being easily transported to the survey location and can be tuned to deliver a range of responses that will closely match the theoretical response, particularly on resistive ground. We calculated the response for such a tuned loop laid out at the surface of conductive ground and compared that response to field data. For an AEM system flown over a surface loop, when neglecting the second order of mutual induction, the receiver signal can be divided into three parts: (1) transmitter-earth-receiver (TER) signal; (2) transmitter-loop-receiver (TLR) signal; and (3) loop-earth-receiver (LER) signal. While the TER response has been extensively addressed in the literature, we modeled the more complex case of TLR and LER system responses. We first calculated the mutual inducta...

Case histories illustrating the characteristics of the HeliGEOTEM system

The HeliGEOTEM system was introduced in 2005 to provide higher resolution data than fixed-wing electromagnetic (EM) systems. The characteristics of HeliGEOTEM are illustrated by comparing the system with other airborne EM systems. A comparison with previous versions of HeliGEOTEM shows that, since 2005, the early-time information has improved allowing rapidly decaying responses to be identified. An improvement in the signal-to-noise ratio means the system is able to detect bodies at greater depth. A height attenuation test over the Nighthawk conductive body indicates that the latest system could see that target if it were buried 380 m below surface. Another target that is difficult to detect (Caber) is clearly seen on the HeliGEOTEM data. A comparison of field data at the Maimon deposit indicates that the helicopter DIGHEM frequency-domain system and the HeliGEOTEM time-domain system both acquire data with similar spatial wavelengths. Data collected away from the main ore body and along strike indicate that the HeliGEOTEM sees a less attenuated response from a deeper part of the body. Also, the HeliGEOTEM is able to estimate the conductivity, whereas the DIGHEM system cannot discriminate the conductance, it can only indicate that the body is highly conductive. The DIGHEM data, however, is better able to resolve the near-surface conductivity, and the spatial form of the DIGHEM data is simpler. The data acquired with multiple transmitter-receiver coil pairs (DIGHEM and HeliGEOTEM) provides information superior to single-component data. Tools used to display fixed-wing airborne EM data have been modified to work with HeliGEOTEM data. These tools can image the structure in cases where the ground is assumed to be comprised of a) horizontal layers or b) discrete conductors. A comparison of HeliGEOTEM with the helicopter RESOLVE and fixed-wing GEOTEM systems shows that the HeliGEOTEM is able to map most of the shallow features seen on the RESOLVE and to image the resistivity to depths comparable to the GEOTEM (in a moderately conductive environment). A traverse line from Australia over what is considered a difficult target (the Nepean Mine) demonstrates that the HeliGEOTEM system provides good signal-to-noise ratios. Using the z- and x-component data does a better job of defining the geometry of the target than using the z-component data alone.

Influence of displacement currents on the response of helicopter electromagnetic systems

For the purpose of shallow-earth geophysical mapping, progressively higher frequencies have been developed for helicopter electromagnetic (HEM) systems. However, concern has been expressed about the vulnerability of high-frequency EM signals to the influence of the displacement current, especially the phase shift of the HEM signal resulting from the finite speed of light that describes the propagation of the EM wave in free space. In this paper we investigate the influence of the displacement current and the finite speed of light on HEM responses, based on a full solution of the EM field for a conductive, magnetically, and dielectrically polarizable earth half-space and an overlying half-space of air with free-space dielectric permittivity. We calculate the amplitude change and the phase shift of the HEM signal and the change in the apparent resistivity. We find that the displacement current, when both the air and the earth half-space assume the free-space dielectric permittivity, has a small influence on the HEM signal, while substantial influence may occur when the earth is dielectrically polarizable. The finite speed of the EM propagation in free space does not result in significant phase changes in the HEM signal.

3D animated visualization of EM diffusion for a frequency-domain helicopter EM system

The electromagnetic fields inside the earth are calculated by continuation downward of the electromagnetic (EM) solutions at the location of a frequency-domain helicopter electromagnetic (HEM) sensor. Models examined using the continuation approach include a layered isotropic and anisotropic earth. The finite-element approach is used to model 2D structures of a dipping contact or a dipping dike. By incorporating a time factor, we display the EM diffusion in the earth (change in direction and amplitude of the EM field through time) as 3D animated vectors or contours. The propagation of the EM smoke ring, influenced by the resistivity and structure of the earth, is apparent from the dynamic presentations. The current propagates downward and outward with time, becoming wider and more diffuse, and the phase varies with time, depth, and outward distance. The downward propagation of EM fields is slower in more conductive geology. In a layered isotropic earth, the current ring is symmetric with no vertical current flow for both vertical and horizontal dipole transmitters. In anisotropic or 2D structures; however, the current flow is significantly distorted resulting in vertical current flow and nonsymmetric smoke rings.

Induction-response functions for frequency-domain electromagnetic mapping system for airborne and ground configurations

A helicopter-towed electromagnetic (EM) sensor of the type typically flown in frequency-domain surveys may be towed over the ground on a trailer. The in-phase and quadrature components measured by a trailer-towed sensor will be dramatically different from those determined when the sensor is flown. For the airborne case, the in-phase and quadrature curves of the induction-response function are governed by the superposed-dipole behavior, in which flying height substantially exceeds the transmitting-receiving coil separation. In contrast, for a ground-based sensor, the coil separation substantially exceeds the sensor height, yielding the infinitely separated dipole case in which the sensor height is negligible compared to the coil separation. These two end cases — the superposed dipole and the infinitely separated dipole —yield EM amplitudes and phase angles that are very different from each other. For the superposed-dipole case of the airborne sensor, the in-phase component reaches a high positive value as ...

Modeling Results of On- and Off-time B and dB/dt for Time-domain Airborne EM Systems

Airborne time-domain EM modeling generally uses the convolution of the transmitting current with the system responses. However, if no special attention is paid to the singularity of the system responses, serious stability problem may occur in the modeling of on-time and off-time magnetic induction B and time-derivative of magnetic induction dB/dt. In this paper, after a through investigation of different convolution modes, we choose a stable algorithm for modeling the responses of time-domain airborne EM systems, where the step response of the airborne EM system is calculated and convolved with the transmitting current by Gaussian quadratures. While the algorithm can be used for any arbitrary transmitting waveforms, we choose a half-sine and trapezoid wave as an example. The preliminary results for a half-space model show a clearly consistent integral-derivative relationship between the B and dB/dt responses.

Levee Evaluation Studies in Sacramento, California: Correlating helicopter-borne EM data, borings and geology.

On-going studies of the flood-control levees in the Sacramento Valley in California have included airborne EM and magnetic surveys, geomorphologic studies, DC resistivity surveys, cone penetrometer testing and reverse-circulation borings. This paper reports on how airborne EM is being used in conjunction with these methods to provide a regional overview of the levee foundations, tie-together and extend the ground information, as well as provide mapping of the horizontal extent of sand channels. Examples from several levee study areas show how the regional, relatively low-resolution but continuous coverage of the airborne EM compliments the detailed local results of the boring explorations and geological information to build a comprehensive picture of the sub-surface which identifies high risk areas of the levee that will require mitigation.