Geophone rotation analysis by polarity inversion
Robert James Ferguson
A technique is presented by which multicomponent geophone data are rotated such that the preferred geophone component is aligned with the direction of the incident wave form. Wave forms of interest are restricted to first-arrival P- waves, and S-waves polarized normal to the plane that contains both the source and the geophone. Rotation is based on that fact that the geophone orientation, and the apparent rotation that it imparts to the incident waveform, is equivalent to the application of a 3x3 unitary matrix, and that the inverse of the operator is also unitary.
Given a 3C recording, the inverse operator is deduced from a processed version of the recording through inversion by least-squares. This inverse operator is then applied to the raw recording to achieve the desired orientation. Decomposition of the inverse operator yields the dip and azimuth of the geophone orientation.
Synthetic examples are presented that demonstrate the performance of this inversion in the presence of noise. Inverted waveforms are compared to the idealized input waveforms, and dip and azimuth estimates are made. It is found that waveform comparisons compare very well qualitatively in the presence of noise, and that dip and azimuth estimates degrade with increased noise. Dip and azimuth estimates are found to improve to acceptable accuracy with judicious application of band-pass filters to the input.