Continuous Spectrum of the Total‐magnetic‐field Anomaly Due to a Rectangular Prismatic Body

Abstract

The Fourier transform of the total‐magnetic‐field anomaly due to a rectangular prismatic body with arbitrary magnetization yields the two‐dimensional spectrum of the anomaly. In the expression for the spectrum the individual effects of the horizontal and vertical dimensions of the body appear as separate factors. Another factor in the expression takes into account the combined influence of the orientation of the magnetization vector and the dip and declination of the earth’s magnetic field. The expression for the two‐dimensional spectrum is used to obtain analytical formulas of the spectra for magnetic‐field values along profiles parallel to the two horizontal axes of the body. This theoretical study provides a quantitative picture of the shift of the spectrum to the low‐frequency end with increase in either depth or horizontal dimension, or in both, of the magnetized body. It has thus been possible to realize the feasibility of a method for separating the effects of near‐surface high‐amplitude components from those of deep crustal sources in total‐field aeromagnetic maps. Separation of these effects is, however, not unique because of spectral overlap between anomalies due to “shallow” and “deep” sources. A detailed discussion has been made about the characteristics of amplitude and phase spectra of anomalies due to prismatic bodies of differing dimensions. The spectra of anomalies seem to be useful in rapid estimation of the dimensions of a body under suitable conditions. The effect of demagnetization on the fields due to prismatic bodies has been ignored in this paper.

Rapid 3‐D forward model of potential fields with application to the Palinuro Seamount magnetic anomaly (southern Tyrrhenian Sea, Italy)

“…In this sense, Bhattacharyya [1966] evaluated the spectrum of the magnetic anomaly of a rightrectangular prism. Pedersen [1985] calculated the spectral expressions for magnetic and gravity anomalies of ellipsoidal bodies.…”

An iterative approach to optimising depth to magnetic source using the spectral method

“…The original work in estimating the depth to a single rectangular prismatic body using Fourier analysis was by Bhattacharyya (1966). Spector and Grant (1970) expanded this approach to incorporate an ensemble of rectangular vertical sided prismatic bodies of various geometries.…”

Comparison of Magnetic Basement Depth Values from Spectral Technique, SPITH and Slope Techniques using HRAM

“…The application of the power spectrum method to potential field data has been well establised, and the determination of the anomalous body depth has also been given [20,21]. This method has been used extensively by many researchers like [22,23].…”

“…The residual data obtained was contoured into 2-D and 3-D maps in Figure 3a,b giving us the first impression of the study area. In its complex form, the two dimensional Fourier transform pair may be written as in eqn 3.0 and 4.0 [20,24]:…”