Several noniterative, imaging methods for potential field data have been proposed that provide an estimate of the 3D magnetization/density distribution within the subsurface or that produce images of quantities related or proportional to such distributions. They have been derived in various ways, using generalized linear inversion, Wiener filtering, wavelet and depth from extreme points (DEXP) transformations, crosscorrelation, and migration. We demonstrated that the resulting images from each of these approaches are equivalent to an upward continuation of the data, weighted by a (possibly) depth-dependent function. Source distributions or related quantities imaged by all of these methods are smeared, diffuse versions of the true distributions; but owing to the stability of upward continuation, resolution may be substantially increased by coupling derivative and upward continuation operators. These imaging techniques appeared most effective in the case of isolated, compact, and depth-limited sources. Because all the approaches were noniterative, computationally fast, and in some cases, produced a fit to the data, they did provide a quick, but approximate picture of physical property distributions. We have found that inherent or explicit depth-weighting is necessary to image sources at their correct depths, and that the best scaling law or weighting function has to be physically based, for instance, using the theory of homogeneous fields. A major advantage of these techniques was their speed, efficiently providing a basis for further detailed, follow-up modelling.
Total magnetic‐field data, from the Athabasca basin of northern Saskatchewan and Alberta, Canada, have been inverted to produce a magnetization map of the sub‐Athabasca crystalline basement. Since the basement topography is variable, the problem is nonlinear and an extra degree of freedom in the solution is caused by the existence of a distribution of magnetization (the annihilator) that produces no external magnetic field. I outline an iterative frequency‐domain inversion scheme, which is based on an approximation to the true partial derivative matrix for the linearized problem. This approximation causes each iteration to be equivalent to a simple frequency‐domain deconvolution. Modeling of selected anomalies allows determination of the magnetization at a number of points in the study area. These values are then used to determine the amount of annihilator to be added to the general solution found from the inversion. The procedure automatically corrects for the effects of variable attenuation of anomalies due to changes in basement depth. Thus, magnetization units and geology that are correlated in areas of outcrop can be extended beneath the sedimentary cover to provide improved geologic mapping control.
Although few magnetization measurements are available for the structural elements of the Chicxulub impact crater, the magnetization intensities of the melt sheet, upper breccia unit, and central uplift are 3–4 orders of magnitude greater than the 3‐ to 4‐km‐thick carbonate and evaporite stratigraphy covering the Yucatan block. This allows three‐dimensional modeling of the crater's structure by inversion using a two‐layer model. Two layers are separately inverted by dividing the crater's magnetic field expression into <40‐ and >40‐km wavelength components. The upper layer (average depth 2 km) models the distribution of highly‐magnetized zones in the crater's melt sheet. The lower layer (average depth 5 km) represents relief on the Yucatan block's basement surface and effectively maps the crater's ∼50‐km‐diameter central uplift and possibly the expression of the surrounding collapsed disruption cavity fill. The shallower magnetized zones consist of two generally concentric distributions, at radii of ∼20 and ∼45 km. These highly magnetized zones are thought to result from hydrothermal systems, localized at the edge of the central uplift and the collapsed disruption cavity, having produced magnetic phases during alteration of the melt sheet.
We present a method to reconstruct crustal deformation in a continental regime using digital potential field data. The technique requires a continuous strain map estimated from available geological and geophysical data. Using this strain pattern, paleo-latitudes and paleo-longitudes are mapped as a function of their present-day geographic coordinates. These data, in turn, may be used to transform any digital data from the same region to an undeformed state. The method can incorporate non-uniformly distributed strain and is demonstrated by reconstructing a simple lineament map of the Matachewan dyke swarm as well as a gridded aeromagnetic data set. Data are from the central Superior Province of the Canadian Shield and reveal deformation associated with the Kapuskasing structural zone. Reconstructed field data display the three subswarms of linear Matachewan dykes radiating from a broad focal region. Once restored, data sets such as these may be used to examine the continuity of other geologic features, refine estimates of deformation, and identify other possible tectonic events.
Recently, a number of automated methods for source location from 2D (profile) magnetic data have been developed, based on either the local wavenumber (Thurston and Smith, 1997; Smith et al., 1998; Thurston et al., 2002; Salem et al., 2005; Smith and Salem, 2005) or the amplitude of the analytic signal (Hsu et al., 1996; Bastani and Pedersen, 2001; Salem and Ravat, 2003; Salem et al., 2004; Salem, 2005). The main advantage of using derived quantities such as the local wavenumber (LW) and amplitude of the analytic signal (AS) is that they are generally independent of source magnetization and dip effects, therefore allowing positional parameters such as depth and horizontal location to be determined more directly than from the magnetic field.