Cross-correlation estimates of telluric and magnetotelluric parameters
Procedures using cross-correlation functions to analyze telluric and magnetotelluric field data can be designed which, in certain applications, are more efficient than conventional techniques using fast Fourier transforms. One such application, involving the processing ofband-limited data, is presented here. The linear coupling relations between fields in a limited frequency band are estimated from transient time series by minimizing, in a least squares sense, the residuals between observed and predicted values of the frequency coefficients. The resulting normal equations contain integral averages over the continuous auto- and cross-energy spectra which are efficiently evaluated as Fourier transforms of windowed auto- and cross-correlation functions in the time domain.
The method is outlined in general terms, then illustrated with a specific example involving the analysis of 30–80 second pulsation data.
Stage I: Data sections approximately 2000 seconds long are digitally sampled at 1 second intervals, filtered at 50 seconds and decimated to 500 point series with 4 second sampling intervals.
Stage II: The correlation functions are formed for 16 lags (of 4 secs. each) on either side of zero and multiplied by a Gaussian window.
Stage III: These modified correlation functions are Fourier transformed at the single period, 50 seconds; the band-averaged energy spectra which result are used to solve the desired field relations for either the telluric or the magnetotelluric coupling coefficients.
Several built-in advantages are demonstrated. Since the window is concentrated around the origin, the correlation functions only need to be calculated out to relatively small lags. Decimation of the data during filtering further improves efficiency by dramatically reducing the number of points summed over. Visual display of intermediate results throughout the analysis not only provides added insight, but improves reliability by pinpointing problems early.
For the examples considered here, linear coupling coefficients are shown to be stable within about 5 percent over several data sets. The method gives results within 1 percent of those determined by fast Fourier transform techniques while using half the computer time.
Key wordsMagnetotelluries Cross-correlation
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