Designing Matched Bandpass and Azimuthal Filters for the Separation of Potential-Field Anomalies by Source Region and Source Type Jeffrey D. Phillips U.S. Department of the Interior U.S. Geological Survey

Outline Introduction Matched bandpass filtering Theory Filter design Example Matched azimuthal filtering Theory Filter design Example Summary

Matched Bandpass Filtering

Radial Power Spectrum of a Two- layer Model

Power Spectrum of a Two-layer Model The observed power spectrum (in white) is the superposition of the individual layer spectra (yellow and magenta) plus cross terms (cyan). At high wavenumbers, cross terms and interference are minimized, so parameters of the shallowest equivalent layer can be estimated accurately (Spector, 1968).

Two-layer Model After Correction

Estimated Layer Parameters Layer geometry (thin sheet or half-space) must be specified a priori, and the log power spectrum must be corrected for the geometry by: Subtracting 2 log k if n = 1 (thin magnetic dipole layer) Adding 2 log k if n = -1 (density half-space) No correction if n = 0 (magnetic half-space or density layer) After correction: Slope of the log power = 2*depth Y-intercept = 2 log B

Two Layer Model After Removal of the Shallowest Layer

Estimated Layer Parameters Layer geometry (thin sheet or half-space) must be specified a priori, and the log power spectrum must be corrected for the geometry by: Subtracting 2 log k if n = 1 (thin magnetic dipole layer) Adding 2 log k if n = -1 (density half-space) No correction if n = 0 (magnetic half-space or density layer) After correction: Slope of the log power = 2*depth Y-intercept = 2 log B

Filter Design Strategy - I Prepare the input grid for Fourier transform. Compute the Fourier transform and power spectrum. Average the power around all azimuths to generate the radial-average power spectrum. Correct the radial-average power spectrum (if necessary) for the assumed geometry of the shallowest equivalent layer. Estimate the parameters of the shallowest layer by fitting a line to the high-wavenumber end of the corrected spectrum.

Filter Design Strategy - II Remove the effects of this layer from the power spectrum. Repeat the process for the next shallowest equivalent layer. Continue with deeper equivalent layers until no power is left. Use non-linear least-squares adjustment of layer parameters to improve the fit.

Aeromagnetic Data NW Albuquerque Basin, New Mexico Broad basement anomaly N-S sedimentary faults NW-SE pipeline E-W flight line noise

Matched Bandpass Filters Power Spectra data 4-layer model Bandpass Filters

Bandpass Filtered Results Magnetic half-space at km Dipole layer at 488 m 12

Bandpass Filtered Results Dipole layer at 123 mDipole layer at 18 m 34

Matched Azimuthal Filtering

LAP of bandpass 3 Best-fit sinusoid Automatic weights

Matched Azimuthal Filter – Bandpass 3 Input Output

Azimuthally Filtered Bandpass 3 Before After

Final Result Observed Mag = Basement Mag

Final Result + Near-Surface Mag + Noise

Summary Matched bandpass filtering of potential-field data, based on a multi-layer equivalent source model, provides a useful way to separate short-wavelength anomalies that originate at shallow depths from long- wavelength anomalies that generally originate at deeper depths.

Summary Matched azimuthal filtering can be used in conjunction with the bandpass filtering to suppress directional noise or enhance directional signal. A public-domain implementation of this algorithm is available in the USGS potential- field software package for the PC: