Spectral Analysis

Spectral analysis is a technique used to analyse characteristics of potential field data (magnetic and gravity) in the frequency domain by using Fourier Transformation. The expressions for the potential field in the frequency domain have simple and direct forms with separated factors including physical properties, horizontal dimensional geometry, top depth, bottom depth, earth field vector, etc. The parameters of a body can be estimated by analysing the energy spectrum of the anomaly. This technique is widely used in interpreting potential field data. Since 1937, many geoscientists have developed and improved the technology. The most impressive work was carried out by Spector (1968) and Spector and Grant (1970).  They considered an ensemble of bodies with varied depth, width, thickness and magnetisation as a statistical model and made the assumption that the observed magnetic anomaly were caused by several ensemble blocks. The basic model used in their method is the tabular prism model. They carried out spectral analysis on total magnetic field data and demonstrated how the average depths of deep-seated anomalies and near-surface anomalies and the thickness of shallow bodies could be determined.

The technique has been further developed by many geophysicists and applied widely in the potential field. Dr Zhiqun Shi has used and developed the depth estimation and anomaly separation technique in both gravity and magnetic field data since 1978.

The advantages of the technique are that it is easy use, it allows fast computation and may also provide depth estimations for the bulk of unclear shaped magnetic or gravity sources, which do not produce distinctive anomalies.

The disadvantages of the technique are:

• The solutions are not accurate.
• The estimated solutions are not easily related to the individual anomalies.
• The shapes of estimated sources are unknown.

This technique can be used as a tool to assist in obtaining regional magnetic or gravity basement depths quickly but cannot be used to generate a depth-to-basement map.Redial energy spectra distributionThe data example above is well distributed in the frequency domain. A portion of the radial energy spectrum of the grid is shown in the top graph. Five (5) sections can be identified with boundaries relating to different anomaly wavelengths. Anomaly wavelength (not to be confused with source depth) is determined from the wave number on the x-axis (Wavelength = 1/wavenumber x 1000). Between these boundaries, each section has a straight slope; the break points are marked by a red line and the relative wavelengths of the break points are marked beside each line. In this example, the data can be roughly separated by wavelengths greater than 500km, 500km, 200km, 100km and 20km. An approximate depth corresponding to a particular wavelength can be found in the lower diagram. Wavelength-depth relationship is dataset-specific and must be determined for each dataset. In the last segment, wavelengths less than 20km are made up of anomalies derived from data noise or near surface geology.

Based on the average wavelengths derived from the radial spectra, a set of Low-pass, High-pass & Band-pass filters are produced for the purpose of achieving a set of rough anomaly separation images. These are used to isolate certain features and assist in a comprehensive geological interpretation of the complete dataset.