The traditional algorithms for airborne electromagnetic ͑EM͒ 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 ͑SA͒ 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 model͒. 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.
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.
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.
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 inductance between the transmitter and the surface loop, tak-ing the loop impedance (resistance and inductance) into account, and then we calculated the signal in the receiver by calculating the mutual inductance between the loop and the receiver. To calculate the LER response, we divided the surface loop into a series of transmitting dipoles, with the “transmitting” current in the dipoles obtained by analyzing the mutual induction between the transmitter and loop. The numerical experiments show that the free-space wire-loop response (TLR system) displays the standard exponential decay for a conductor. The loop resistance and inductance define the decay constant and initial signal value. While the TER system largely influences the receiver signal at early time channels for conductive earth, the LER system influences very late time channels. The more resistive the test ground is, the longer the time window is for the free-space wire-loop signal to dominate. For the survey over a test loop on conductive ground in the Dominican Republic, using the Fugro HeliGEOTEM system, the predicted response compares well to the collected data.
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