Jeffrey D. Phillips

1. 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

2. Outline • Introduction • Matched bandpass filtering • Theory • Filter design • Example • Matched azimuthal filtering • Theory • Filter design • Example • Summary

3. Matched Bandpass Filtering

4. Matched Bandpass Filtering

5. Radial Power Spectrum of a Two-layer Model

6. 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).

7. Two-layer Model After Correction

8. 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

9. Two Layer Model After Removal of the Shallowest Layer

10. 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

11. 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.

12. 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.

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

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

15. Bandpass Filtered Results 1 2 Magnetic half-space at 2.187 km Dipole layer at 488 m

16. Bandpass Filtered Results 3 4 Dipole layer at 123 m Dipole layer at 18 m

17. Matched Azimuthal Filtering

18. Matched Azimuthal Filtering LAP of bandpass 3 Best-fit sinusoid Automatic weights

19. Matched Azimuthal Filter – Bandpass 3 Input Output

20. Azimuthally Filtered Bandpass 3 Before After

21. Final Result Observed Mag = Basement Mag

22. Final Result + Near-Surface Mag + Noise

23. 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.

24. 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: http://crustal.usgs.gov