Magnetic-survey data in grid form may be interpreted rapidly for source positions and depths by deconvolution using Euler' s homogeneity relation. The method employs gradients, either measured or calculated. Data need not be pole-reduced, so that remanence is not an interfering factor. Geologic constraints are imposed by use of a structural index. Model studies show that the method can locate or outline confined sources, vertical pipes, dikes, and contacts with remarkable accuracy. A field example using data from an intensively studied area of onshore Britain shows that the method works well on real data from structurally complex areas and provides a series of depth-labeled Euler trends which mark magnetic edges, notably faults, with good precision.

The analysis of palaeomagnetic data where only inclinations are available is considered. Maximum likelihood estimates for the mean inclination lo and Fisher's precision parameter K are derived. It is shown that they are in all cases biased although the bias is small for low inclinations. The case of steep inclinations and small values of K is examined and it is shown that in this region I. and K are not separable as distinct variables, because the lack of declination information in this region leads to fundamental ambiguities. Unbiased estimates for lo and ( 1 /~) are derived for the case where the portion of the distribution folded about the vertical is insubstantial. A worked example of the method, with calculation of confidence limits, is appended.

The Euler homogeneity relation expresses how a homogeneous function transforms under scaling. When implemented, it helps to determine source location for particular potential field anomalies. In this paper, we introduce an additional relation that expresses the transformation of homogeneous functions under rotation. The combined implementation of the two equations, called here extended Euler deconvolution for 2-D structures, gives a more complete source parameter estimation that allows the determination of susceptibility contrast and dip in the cases of contact and thin-sheet sources. This allows for the structural index to be correctly chosen on the basis of a priori knowledge about susceptibility and dip. The pattern of spray solutions emanating from a single source anomaly can be attributed to interfering sources, which have their greatest effect on the flanks of the anomaly. These sprays follow different paths when using either conventional Euler deconvolution or extended Euler deconvolution. The paths of these spray solutions cross and cluster close to the true source location. This intersection of spray paths is used as a discriminant between poor and well-constrained solutions, allowing poor solutions to be eliminated. Extended Euler deconvolution has been tested successfully on 2-D model and real magnetic profile data over contacts and thin dikes.

Tensor Euler deconvolution has been developed to help interpret gravity tensor gradient data in terms of 3-D subsurface geological structure. Two forms of Euler deconvolution have been used in this study: conventional Euler deconvolution using three gradients of the vertical component of the gravity vector and tensor Euler deconvolution using all tensor gradients. These methods have been tested on point, prism, and cylindrical mass models using line and gridded data forms. The methods were then applied to measured gravity tensor gradient data for the Eugene Island area of the Gulf of Mexico using gridded and ungridded data forms. The results from the model and measured data show significantly improved performance of the tensor Euler deconvolution method, which exploits all measured tensor gradients and hence provides additional constraints on the Euler solutions.

Aeromagnetic surveys are flown with a wide variety of terrain clearances, sampling rates, and line spacings. The results are generally presented as contour maps, implying that the survey grid defines the continuous magnetic field sufficiently well to justify interpolation.