Alan Reid

Bio: Alan Reid is an academic researcher from University of Leeds. The author has contributed to research in topics: Euler's formula & Deconvolution. The author has an hindex of 14, co-authored 31 publications receiving 2184 citations.

Magnetic interpretation in three dimensions using Euler deconvolution

Abstract: 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

Euler deconvolution of gravity tensor gradient data

Abstract: 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.

Magnetic source parameters of two-dimensional structures using extended Euler deconvolution

Abstract: 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.

Degrees of homogeneity of potential fields and structural indices of Euler deconvolution

Abstract: Homogeneity is a well-known property of the potential fields of simple point sources used infield inversion.Wefind that the analytical expressions of potential fields created by sources of complicated shape and constant or variable density or magnetization also show this property.This is true if all variables of length dimension are involved in the test of homogeneity. The coordinates of observation points and the source coordinates and sizes form an extended set of variables, in relation to which the field expression is homogeneous. In this case, the principal definition of homogeneity applied to a potential field can be treated as an operator of a space transform of similarity. The ratio between the transformed and original fields determines the value and sign of thedegreeofhomogeneityn.Thelattermaytakeonpositive, zero,ornegativevalues.Thedegreeofhomogeneitydepends onthetypeoffieldandontheassumedphysicalparameterof the field source, and can be nonunique for a given field element. We analyze the potential field of one singular point as thesimplestcaseofhomogeneity.Thus,wededuceresultsfor the structural index, N = n, in Euler deconvolution. The structural index can also be positive, zero, or negative, but it has a unique value.Analytical considerations, as well as numerical tests on the gravity contact model, confirm the proposed physical interpretation of N, and lead to an extended versionofEuler’sdifferentialequationforpotentialfields.

Magnetic interpretation using the 3-D analytic signal

Abstract: 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.

The historical development of the magnetic method in exploration

Abstract: The magnetic method, perhaps the oldest of geophysical exploration techniques, blossomed after the advent of airborne surveys in World War II. With improvements in instrumentation, navigation, and platform compensation, it is now possible to map the entire crustal section at a variety of scales, from strongly magnetic basement at regional scale to weakly magnetic sedimentary contacts at local scale. Methods of data filtering, display, and interpretation have also advanced, especially with the availability of low-cost, high-performance personal computers and color raster graphics. The magnetic method is the primary exploration tool in the search for minerals. In other arenas, the magnetic method has evolved from its sole use for mapping basement structure to include a wide range of new applications, such as locating intrasedimentary faults, defining subtle lithologic contacts, mapping salt domes in weakly magnetic sediments, and better defining targets through 3D inversion. These new applications have increased the method’s utility in all realms of exploration — in the search for minerals, oil and gas, geothermal resources, and groundwater, and for a variety of other purposes such as natural hazards assessment, mapping impact structures, and engineering and environmental studies.

Automatic conversion of magnetic data to depth, dip, and susceptibility contrast using the SPI (TM) method

Abstract: 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

High‐resolution detection of geologic boundaries from potential‐field anomalies: An enhanced analytic signal technique

Abstract: 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 technique. 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.

Detection of potential fields source boundaries by enhanced horizontal derivative method

Abstract: A high-resolution method to image the horizontal boundaries of gravity and magnetic sources is presented (the enhanced horizontal derivative (EHD) method). The EHD is formed by taking the horizontal derivative of a sum of vertical derivatives of increasing order. The location of EHD maxima is used to outline the source boundaries. While for gravity anomalies the method can be applied immediately, magnetic anomalies should be previously reduced to the pole. We found that working on reduced-to-the-pole magnetic anomalies leads to better results than those obtainable by working on magnetic anomalies in dipolar form, even when the magnetization direction parameters are not well estimated. This is confirmed also for other popular methods used to estimate the horizontal location of potential fields source boundaries. The EHD method is highly flexible, and different conditions of signal-to-noise ratios and depths-to-source can be treated by an appropriate selection of the terms of the summation. A strategy to perform high-order vertical derivatives is also suggested. This involves both frequency- and space-domain transformations and gives more stable results than the usual Fourier method. The high resolution of the EHD method is demonstrated on a number of synthetic gravity and magnetic fields due to isolated as well as to interfering deep-seated prismatic sources. The resolving power of this method was tested also by comparing the results with those obtained by another high-resolution method based on the analytic signal. The success of the EHD method in the definition of the source boundary is due to the fact that it conveys efficiently all the different boundary information contained in any single term of the sum. Application to a magnetic data set of a volcanic area in southern Italy helped to define the probable boundaries of a calderic collapse, marked by a number of magmatic intrusions. Previous interpretations of gravity and magnetic fields suggested a subcircular shape for this caldera, the boundaries of which are imaged with better detail using the EHD method.