Trajectory-based modelling of broad-band electromagnetic wavefields

Astronomy and Astrophysics – Astronomy

Scientific paper

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Asymptotic Methods, Electromagnetic Waves, Tomography

Scientific paper

A trajectory-based solution of Maxwell's equations is derived using the method of multiple scales. This time-domain technique utilizes an asymptotic expansion in terms of the ratio of the wave front length-scale to the length-scale of the heterogeneity. The approach provides an alternative to an expansion in terms of frequency and allows one to model electromagnetic wave propagation over a wide frequency band. At the lower end of the frequency band, the trajectory-based solution reduces to a previously derived diffusive solution. Similarly, at higher frequencies one obtains the `delta-like' solution associated with hyperbolic wave propagation. However, the solution is also valid at intermediate frequencies which cannot be characterized as either diffusive or hyperbolic. A numerical illustration demonstrates the importance of both conduction and displacement currents at frequencies between 10 and 100 MHz. The amplitudes computed using the trajectory-based approach compare well with analytic results for a homogeneous whole-space. Using the technique I am able to model observations from a broad-band (3-300 kHz) experiment at the Richmond Field Station in California. In addition, ground penetrating radar waveforms in the 5-200 MHz range, gathered at the Boise Hydrogeophysical Research Site, are matched using the results of a radar velocity tomogram.

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