Analysis of far‐field vibroseis signals

Abstract

Summarv Vibroseis data contain nonminimum-phase components, notably the Klauder wavelet; it is zero-phase. A largely unrecognized nonminimum-phase component is a time derivative arising from wave propagation. We recorded the far-field signal from a vibrator with a VSP sonde at a depth of 1006 m along with both ground-force and baseplate-velocity signals. Using these data, we tested whether wavelet processing based on standard theory of vibrator radiation produced a properly phased wavelet, and whether the use of ground-force correlation rather than baseplate-velocity correlation made a significant difference in the result. We applied spiking deconvolution to both the correlated data and to the model of the data containing the autocorrelation of the reference signal (either ground force or baseplate velocity), a Q-filter, one or two time derivatives, additive noise, and the geopone response. This deconvolution will hompensate for minimum-phase filters arising from transmission of the far-field signal, but the actual phase of the result depends critically on the the assumption that only minimum-phase effects are present, a condition violated by both additive noise and time derivatives. A phase correcting filter designed to correct the deconvolved model to zero phase was applied to the data. It corrected the data to within 20 degrees of zero phase at all frequencies in the source bandwidth, indicating that the model properly accounts for all significant elements of the signal propagation. Model-based phase correction of the wavelet was equally effective when applied to ground-force correlated data or to baseplate-velocity correlated data. For the earth conditions encountered in this experiment, we conclude that modelbased wavelet processing can produce a stable wavelet when using either signal for correlation.