Mathematics – Logic
Scientific paper
Feb 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011geoji.184..689m&link_type=abstract
Geophysical Journal International, Volume 184, Issue 2, pp. 689-698.
Mathematics
Logic
Time-Series Analysis, Fourier Analysis, Marine Electromagnetics
Scientific paper
In the marine controlled-source electromagnetic method, the Earth response varies in frequency; therefore, using a wide range of frequencies may better constrain geological structure than using a single frequency or only a few closely spaced frequencies. Binary waveforms, such as the square wave, provide a number of frequencies, though many are limited in usefulness because of the rapid decline of amplitude with frequency. Binary waveform design can be improved by recognizing that the class of doubly symmetric waveforms has special properties: they are compact, have controlled phase, are never polarizing and can be described by a simple closed-form mathematical solution. Using this solution, we discovered a compact waveform in which the amplitudes of the third and seventh harmonics are maximized and which has a signal-to-noise advantage at higher frequencies over several other common waveforms.
Compact waveforms make possible improved methods for time-series processing. Using short time windows and a first-difference pre-whitener lessens spectral contamination from magnetotelluric signal and oceanographic noise; robust stacking reduces bias from time-series noise transients; and accurate variance estimates may be derived from averages of waveform-length Fourier transform windows of the time-series.
Constable Steven
Key Kerry
Myer David
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