Limitations of determining density or magnetic boundaries from the horizontal gradient of gravity or pseudogravity data

Abstract

The horizontal‐gradient method has been used since 1982 to locate density or magnetic boundaries from gravity data (Cordell, 1979) or pseudogravity data (Cordell and Grauch, 1985). The method is based on the principle that a near‐vertical, fault‐like boundary produces a gravity anomaly whose horizontal gradient is largest directly over the top edge of the boundary. Magnetic data can be transformed to pseudogravity data using Fourier techniques (e.g., Hildenbrand, 1983) so that they behave like gravity data; thus the horizontal gradient of pseudogravity also has maximum magnitude directly over the boundary. The method normally is applied to gridded data rather than to profiles. The horizontal‐gradient magnitude is contoured and lines are drawn or calculated (Blakely and Simpson, 1986) along the contour ridges. These lines presumably mark the top edges of magnetic or density boundaries. However, horizontal‐gradient magnitude maxima (gradient maxima) can be offset from a position directly over the boundary for several reasons. Offsets occur when boundaries are not near‐vertical, or when several boundaries are close together. This note predicts these offsets. Many other factors also cause offsets, but they are less straightforward and usually are only significant in local studies; we discuss these factors only briefly.

Aeromagnetic data, processing, and maps of Fort Irwin and vicinity, California

“…This method assumes that magnetic bodies have vertical sides; for nonvertical sides, calculated points will shift in the direction of dip. For sides with moderate to steep (45° to vertical) dip, however, the horizontal displacement of a gradient maximum from the top edge of an offset horizontal layer is always less than or equal to the depth to the top of the source (Grauch and Cordell, 1987). Because of the altitude at which the data were collected, the resulting aeromagnetic anomaly may be wider than the magnetic source, even if the magnetic source is exposed at the surface.…”

Geologic and geophysical maps of the El Casco 7.5′ quadrangle, Riverside County, southern California, with accompanying geologic-map database

“…Gradient maxima occur approximately over steeply dipping contacts that separate rocks of contrasting densities. For moderate to steep dips (45 0 to vertical), the horizontal displacement of a gradient maximum from the top edge of an offset horizontal layer is always less than, or equal to, the depth to the top of the source (Grauch and Cordell, 1987). Table 4.…”

Evidence of basement controlled faulting of cretaceous strata in the Middle Benue Trough, Nigeria from lineament analysis of gravity data

“…Horizontal derivative maps highlight anomaly pattern discontinuities (which might occur at faulted boundaries) and can provide higher resolution and greater accuracy at wider line spacing (Hogg, 2004). The amplitude of the horizontal gradient magnitude as given by Grauch and Cordell (1987) is expressed as equation (1).…”