Phase‐compensating filtering to reduce distortion caused by in‐aircraft reactive integrators

Abstract

Low‐pass filters based on reactive integrators necessarily introduce temporal phase delays into data. The use of such filters in airborne geophysical surveys, therefore, produces equivalent spatial phase delays which displace the high‐wavenumber Fourier components of anomalies downstream along the flight line, causing distortion of the anomaly shapes. A linear filter is described which eliminates this distortion by introducing a compensating, frequency‐dependent phase advance. The restored data provide anomalies as would be seen from an aircraft moving with zero speed. Exact phase compensation for each stage of reactive low‐pass filtering requires an acausal filter whose coefficients are a weighted sum of zeroth‐ and first‐order modified Hankel functions, the weighting being determined by the integrator’s time constant. A very short and useful approximation to the ideal phase‐compensating filter is also described and subsequently applied in the restoration of data obtained from an airborne electromagnetic (EM) survey flown near Hawksbury, Ontario. The example clearly demonstrates the usefulness of applying phase compensation to geophysical data obtained in high‐resolution airborne surveys.