A study is made of magnetic anomalies due to prism‐shaped bodies with arbitrary polarization. Expressions of the total field and its first and second derivatives are derived on the assumption of uniform magnetization through out the body. Formulas for all possible cases in connection with a rectangular prism with vertical sides can be obtained either directly from this paper or by simple extension of the formulas given here. Using the exact expressions given in this paper, the total field and its derivatives are evaluated conveniently and rapidly with the aid of a digital computer. The effect of the dip angle anti declination of the polarization vector on the size and shape of the magnetic anomaly is then studied for the case when the earth’s normal total field vector has a dip angle of 60° and declination of 0°. With an increase in the dip angle of the polarization vector, the negative anomaly occurring on the north of the causative body diminishes in magnitude, whereas the positive and second derivative anomalies increase to maximum values and then decrease. With an increase in declination, this latter trend is repeated with the positive anomaly but the negative and second‐derivative anomalies decrease systematically. Both the positive and second‐derivative anomalies become more and more symmetrical with respect to the prismatic body with increase in either the inclination or declination of the polarization vector.

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.

The bottom of the magnetized crust determined from the spectral analysis of residual magnetic anomalies is generally interpreted as the level of the Curie point isotherm. This paper studies the spatial variation of the Curie point isotherm level in Yellowstone National Park with the help of aeromagnetic data. A very shallow isothermal surface at a depth of only 5-6 km below sea level is associated with the central part of the Yellowstone caldera. It seems to extend along a narrow corridor toward the southwestern and eastern edges of the map. Except in a few localized spots, the isotherm deepens considerably in the areas outside the caldera. Because the caldera encloses most of the areas of hydrothermal alteration, fumaroles, and boiling springs in the park, this study indicates a strong correlation between the spatial variation of the Curie isotherm level and the concentration of subsurface geothermal energy.

The expressions for the spectra of both gravity and magnetic anomalies due to a two‐dimensional structure consist of (except for a factor) sums of exponentials. The exponents of these exponentials are functions of frequency and the locations of the corners of the polygonal cross‐section of the structure. Two computationally feasible methods for determining the exponents from a given spectrum are described in this paper; they are essentially based on the generation of a system of linear equations. The unknown coefficients in this system of equations are functions of the corner locations. The first method requires expansion of the exponentials in the expressions for the spectra in the form of a series and works reliably when the amplitudes of low frequencies are analyzed. The unknown parameters are determined fairly accurately with this method by suitable combinations of the spectra of the observed anomaly and its moments. The second method utilizes an exponential approximation technique for producing the system of linear equations. If only the spectrum of the anomaly is used, the system of equations becomes ill‐conditioned in most cases resulting in grossly inaccurate solutions. However, particular combinations of the spectra of the anomaly and its first and second order moments are found to improve significantly the behavior of the system of equations and thus the quality of results. It has also been found that the mean values of corner locations can be calculated fairly accurately by taking the ratios of the spectra of the anomaly and its moments. Once the corner locations are found, computation of the density contrast in the case of a gravity anomaly and the magnetization contrast for a magnetic anomaly is straightforward.

The total magnetic field values over an area can be represented exactly by a double Fourier series expansion. In this analysis, such an expansion is used to evaluate very accurately the fields continued downward and upward from the plane of observation and the vertical derivatives of the total field. This harmonic expansion of the anomalous total field makes it possible to calculate, with exceptional accuracy, the field reduced to the magnetic pole and its second derivative. The results of the calculations are free from the effect of the inclination of the earth’s main geomagnetic field and that of the polarization vector, at all magnetic latitudes and for all possible directions of polarization. In order to determine the influence of remanence on the above field, a number of anomalies caused by rectangular block‐type bodies with known polarization are reduced to the magnetic pole, correcting only for the obliquity of the earth’s normal field. It is concluded from a study of these anomalies that the interpretation of magnetic data based on the assumption of rock magnetization due solely to induction in the earth’s field may yield erroneous results, particularly when remanence is important.