Ultralow -frequency magnetic fields in the San Francisco Bay Area: Measurements, models, and signal processing

Efforts to detect magnetic precursors to earthquakes are often complicated by the presence of man-made noise. In the San Francisco Bay Area of California, the magnetic fields generated by the Bay Area Rapid Transit (BART) system exhibit power spectral amplitudes that are up to 1000 times greater than those of the natural geomagnetic background fields in the ultra-low frequency (ULF, 0.01 to 10 Hz) band. Measurements from an array of three-axis magnetometers show that the BART interference appears as a series of transients with temporal durations ranging from 4 to 30 seconds. In addition, at each observation site, the polarization vectors of the transients can be bounded by a non-isotropic subset of the three-dimensional polarization space. Electromagnetic modeling results support these experimental findings.;A framework for the identification and removal of the BART transients is proposed. The identification problem is formally posed as the detection, in the presence of 1/fgamma noise, of transients of known shapes, but unknown amplitudes, delays, and scales, where the range of unknown scales corresponds to the observed range of temporal durations. A detection method based upon pattern matching in the undecimated discrete wavelet transform (UDWT) domain is introduced. The method detects the most significant BART transients, while discriminating against non-BART-related transients with a false alarm rate of approximately 8 percent. As an additional constraint, only those transients whose polarization vectors lie within the previously described bounding subsets are considered to be BART-related.;An estimate of each detected transient is formed in the UDWT domain from those transform coefficients that are in the vicinity of the transient location, and whose amplitudes exceed one standard deviation of the transform coefficients computed for the assumed 1/fgamma background noise. The estimate is converted to the time domain with an inverse translation invariant wavelet transform, and then subtracted from the original time series. Removal of the transients significantly increases the ability to test for the presence of precursor signals.