We present a new automatic method of interpretation of magnetic data, called AN‐EUL (pronounced “an oil”). The derivation is based on a combination of the analytic signal and the Euler deconvolution methods. With AN‐EUL, both the location and the approximate geometry of a magnetic source can be deduced. The method is tested using theoretical simulations with different magnetic models placed at different depths with respect to the observation height. In all cases, the method estimated the locations and the approximate geometries of the sources. The method is tested further using ground magnetic data acquired above a shallow geological dike whose source parameters are known from drill logs, and also from airborne magnetic data measured over a known ferrometallic object. In both these cases, the method correctly estimated the locations and the nature of these sources.

In this paper, we describe a system for the collection and interpretation of aeromagnetic data. The great interdependence of the detection instrumentation, the navigation instrumentation, the compilation procedures, and the interpretation techniques is defined. Doppler radar is the basis for aircraft navigation; it drives the recording devices to produce spatial‐domain data. A digital system provides a means for rapid computer interpretation. A distinction is made between data‐processing techniques that aid in interpretation and those that are involved in the actual definition of magnetic anomalies in terms of the horizontal and vertical position of the causative bodies. The computerized interpretation technique described herein is an extension of a technique first described by S. Werner of the Geological Survey of Sweden. Depths are calculated for all geologic events with some elongation, regardless of the events’ strike, dip, and remanent magnetization; and the calculations are valid at any magnetic inclination. Our system is illustrated with model studies and actual examples.

A reformulation of the Werner deconvolution algorithm using the analytic signal is extended to multiple source bodies. The extended algorithm involves solving a linear least‐squares problem; the coefficients so obtained determine a complex polynomial whose roots define the locations and depths of the body contacts. The extended algorithm has been used to map the structure of the Cobb offset zone of the Juan de Fuca Ridge from aeromagnetic data; both the top and bottom of the spreading center basalts can be delineated. Connections between the multiple‐source Werner technique and CompuDepth™ are discussed.

This paper presents a procedure to resolve magnetic anomalies due to two‐dimensional structures. The method assumes that all causative bodies have uniform magnetization and a cross‐section which can be represented by a polygon of either finite or infinite depth extent. The horizontal derivative of the field profile transforms the magnetization effect of these bodies of polygonal cross‐section into the equivalent of thin magnetized sheets situated along the perimeter of the causative bodies. A simple transformation in the frequency domain yields an analytic function whose real part is the horizontal derivative of the field profile and whose imaginary part is the vertical derivative of the field profile. The latter can also be recognized as the Hilbert transform of the former. The procedure yields a fast and accurate way of computing the vertical derivative from a, given profile. For the case of a single sheet, the amplitude of the analytic function can be represented by a symmetrical function maximizing exactly over the top of the sheet. For the case of bodies with polygonal cross‐section, such symmetrical amplitude functions can be recognized over each corner of each polygon. Reduction to the pole, if desired, can be accomplished by a simple integration of the analytic function, without any cumbersome transformations. Narrow dikes and thin flat sheets, of thickness less than depth, where the equivalent magnetic sheets are close together, are treated in the same fashion using the field intensity as input data, rather than the horizontal derivative. The method can be adapted straightforwardly for computer treatment.It is also shown that the analytic signal can be interpreted to represent a complex “field intensity,” derivable by differentiation from a complex “potential.” This function has simple poles at each polygon corner. Finally, the Fourier spectrum due to finite or infinite thin sheets and steps is given in the Appendix.

A new method for magnetic interpretation has been developed based on the generalization of the analytic signal concept to three dimensions. The absolute value of the analytic signal is defined as the square root of the squared sum of the vertical and the two horizontal derivatives of the magnetic field. This signal exhibits maxima over magnetization contrasts, independent of the ambient magnetic field and source magnetization directions. Locations of these maxima thus determine the outlines of magnetic sources. Under the assumption that the anomalies are caused by vertical contacts, the analytic signal is used to estimate depth using a simple amplitude half‐width rule. Two examples are shown of the application of the method. In the first example, the analytic signal highlights a circular feature beneath Lake Huron that has been identified as a possible impact crater. The second example illustrates the continuation of terranes across the Cabot Strait between Cape Breton and Newfoundland in eastern Canada.

A high‐resolution technique is developed to image geologic boundaries such as contacts and faults. The outlines of the geologic boundaries can be determined by tracing the maximum amplitudes of an enhanced analytic signal composed of the nth‐order vertical derivative values of two horizontal gradients and one vertical gradient. The locations of the maximum amplitudes are independent of the ambient potential field. This technique is particularly suitable when interference effects are considerable and/or when both induced and remanent magnetizations are not negligible. The corresponding depth to each geologic boundary can be estimated from the amplitude ratio of the enhanced and the simple analytic signals, which provides a simple estimation Such a method has been applied to magnetic data acquired in the Ilan Plain of Taiwan located at the southwestern end of the Okinawa Trough. The quantitative analysis shows that the underlying geologic boundaries deepen southward and slightly eastward. The enlargement of the Ilan Plain in the direction of the Okinawa Trough and the existence of north‐northwest and west‐northwest trending faults near the city of Ilan reveal a discontinuity between the Okinawa Trough backarc extension and the compressional process in Taiwan.

A new method has been developed for the automatic and general interpretation of gravity and magnetic data. This technique, based on the analysis of 3-D analytic signal derivatives, involves as few assumptions as possible on the magnetization or density properties and on the geometry of the structures. It is therefore particularly well suited to preliminary interpretation and model initialization. Processing the derivatives of the analytic signal amplitude, instead of the original analytic signal amplitude, gives a more efficient separation of anomalies caused by close structures. Moreover, gravity and magnetic data can be taken into account by the same procedure merely through using the gravity vertical gradient. The main advantage of derivatives, however, is that any source geometry can be considered as the sum of only two types of model: contact and thin‐dike models. In a first step, depths are estimated using a double interpretation of the analytic signal amplitude function for these two basic models. Second, the most suitable solution is defined at each estimation location through analysis of the vertical and horizontal gradients. Practical implementation of the method involves accurate frequency‐domain algorithms for computing derivatives with an automatic control of noise effects by appropriate filtering and upward continuation operations. Tests on theoretical magnetic fields give good depth evaluations for derivative orders ranging from 0 to 3. For actual magnetic data with borehole controls, the first and second derivatives seem to provide the most satisfactory depth estimations.

The analytical signal of the magnetic field is used to automatically determine the source parameters of dikelike structures. The method is particularly useful for interpreting large amounts of data collected during airborne surveys because it makes full use of the high density of data along the flight lines while simultaneously checking for two‐dimensionality and strike directions by searching for coherent signals in neighboring profiles. The maximum horizontal curvature of the amplitude of the analytical signal is used to locate the dikes along a given profile. Tests with synthetic data show that the dike’s horizontal position is resolved accurately. Magnetic data from the Siljan impact structure in Sweden show that the estimated strikes are reliable and that dip, depth, and width estimates are coherent, especially for well‐isolated dikelike structures.

The Source Parameter Imaging (SPI™) method computes source parameters from gridded magnetic data. The method assumes either a 2-D sloping contact or a 2-D dipping thin‐sheet model and is based on the complex analytic signal. Solution grids show the edge locations, depths, dips, and susceptibility contrasts. The estimate of the depth is independent of the magnetic inclination, declination, dip, strike and any remanent magnetization; however, the dip and the susceptibility estimates do assume that there is no remanent magnetization. Image processing of the source‐parameter grids enhances detail and provides maps that facilitate interpretation by nonspecialists. The SPI method tests successfully on synthetic profile and gridded data. SPI maps derived from aeromagnetic data acquired over the Peace River Arch area of northwestern Canada correlate well with known basement structure and furthermore show that the Ksituan Magmatic Arc can be divided into several susceptibility subdomains.

A method for rapidly making depth estimates from large amounts of magnetic data is described. The technique is based upon Euler’s homogeneity relationship (hence, the acronym EULDPH) and differs from similar techniques which are currently available in that no basic geologic model is assumed. Therefore, EULDPH can be applied in a wider variety of geologic situations than can model‐dependent techniques. The price paid for this increased flexibility is a heavier burden on the interpreter. Successful interpretation of EULDPH results is partially dependent upon the interpreter’s intuitive understanding of the concept of the equivalent stratum and also partially dependent upon experience with model studies. The theoretical basis, the computational algorithm, and applications of EULDPH to model and real data are presented.

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.

Gravity gradiometric data or gravity data transformed into vertical gradient can be efficiently processed in three dimensions for delineating density discontinuities. Model studies, performed with the combined use of maxima of analytic signal and of horizontal gradient and the Euler deconvolution techniques on the gravity field and its vertical gradient, demonstrate the superiority of the latter in locating density contrasts. Particularly in the case of interfering anomalies, where the use of gravity alone fails, the gravity gradient is able to provide useful information with satisfactory accuracy.

Euler deconvolution is used for rapid interpretation of magnetic and gravity data. It is particularly good at delineating contacts and rapid depth estimation. The quality of the depth estimation depends mostly on the choice of the proper structural index and adequate sampling of the data. The structural index is a function of the geometry of the causative bodies. For gravity surveys, station distribution is in general irregular, and the gravity field is aliased. This results in erroneous depth estimates. By weighting the Euler equations by an error function proportional to station accuracies and the interstation distance, it is possible to reject solutions resulting from aliasing of the field and less accurate measurements. The technique is demonstrated on Bouguer anomaly data from the Charlevoix region in eastern Canada.

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.

Standard Euler deconvolution is applied to potential-field functions that are homogeneous and harmonic. Homogeneity is necessary to satisfy the Euler deconvolution equation itself, whereas harmonicity is required to compute the vertical derivative from data collected on a horizontal plane, according to potential-field theory. The analytic signal modulus of a potential field is a homogeneous function but is not a harmonic function. Hence, the vertical derivative of the analytic signal is incorrect when computed by the usual techniques for harmonic functions and so also is the consequent Euler deconvolution. We show that the resulting errors primarily affect the structural index and that the estimated values are always notably lower than the correct ones. The consequences of this error in the structural index are equally important whether the structural index is given as input (as in standard Euler deconvolution) or represents an unknown to be solved for. The analysis of a case history confirms serious errors in the estimation of structural index if the vertical derivative of the analytic signal is computed as for harmonic functions. We suggest computing the first vertical derivative of the analytic signal modulus, taking into account its nonharmonicity, by using a simple finite-difference algorithm. When the vertical derivative of the analytic signal is computed by finite differences, the depth to source and the structural index consistent with known source parameters are, in fact, obtained.

This paper presents a new approach to detecting and two approaches to displaying lineaments associated with high-angle magnetic contacts, based on analysis of the curvature of the total horizontal gradient of the total magnetic field reduced to the pole. The first display is a contour or color plot of minus the principal curvature of largest absolute value. The second is a point plot of the local maxima of minus the largest principal curvature in regions where this curvature is negative. The paper also develops a depth-estimation technique for magnetic contacts based on the ratio of the curvature of the total gradient to the total gradient itself. Tests on synthetic data yield excellent results in detecting and delineating magnetic contact edges, and reasonable performance in producing depth estimates for the magnetic contacts. Results obtained using aeromagnetic data from the Finger Lakes region of New York State show good correlation with known structural features.

Gravity and magnetic data have unique advantages for studying the lateral extents of geologic bodies. There is a class of methods for edge recognition called maximum-edge-recognition methods (MERMs) that use their extreme values to locate the edges of geologic bodies. These methods include the total horizontal derivative (THDR), the analytic signal amplitude, the theta map, and the normalized standard deviation. These are all first-order derivative-based techniques. There are also higher-order derivative-based methods that are derived from the first-order filters, for example, the THDR of the tilt angle. We have developed an edge-recognition filter that is based on the idea of the normalized vertical derivatives (VDRs) of existing methods. For each MERM, we first calculate its nth-order VDR and then use thresholding to locate its peaks. The peak values are subsequently normalized by the values of the original MERM. Testing on synthetic and real data indicates that the normalized VDRs of the MERMs have higher accuracy and better lateral resolution and they are more interpretable than existing techniques; thus, they are a worthwhile addition to the set of edge-detection tools for potential-field data.