An equation is derived for the vertical gravity field due to a homogeneous body with polygonal cross-section and finite strike-length. The equation can be separated into the two-dimensional (2-D) terms of Talwani et al (1959) and exact terms for the contributions of the ends of the prism. Equations for the magnetic field due to a similar body were derived by Shuey and Pasquale (1973), who coined the term "two-and-a-half dimensional" (2%-D) to describe the geometry. Magnetic intensities are expressed as a vector sum, from which the common dot product formulation can be obtained by binomial expansion. INTRODUCTIONIn the quantitative interpretation of gravity and magnetic surveys, two-dimensional (2-D) calculations along profiles perpendicular to the axis of an infinitely long prismatic body have been popular (Talwani et al, 1959; Talwani and Heirtzler, 1964). Reasons for this popularity are that structures which approach two-dimensionality are common in geology, and data are often collected in profiles perpendicular to strike; polygonal cross-sections ti 2-D hodies are conveniently represented on paper and input to the computer. Shuey and Pasquale ( 1973) derived equations for the magnetic field of a compromise 2%-D body, invariant in cross-section but terminated a finite distance along strike. I have derived the equations for the gravity field of a 2%-D body. The 2%-D approach has the convenience and speed of the 2-D approach with much of the generality of the three dimensional (3-D) approach.The equations have been incorporated into a general purpose 2%-D gravity and magnetic modeling computer program. The program permits both gravity and magnetic calculations for multiple bodies, along profiles with variable field point elevation. If observed gravity and magnetic values are provided, a simple linear inversion permits calculation of density and magnetic susceptibility or components of magnetization. The derivation and an early version of the program, including test cases, were released by Cady (1977). A listing of this inversion program, accompanied by a users manual including test cases, is available from the SEC office upon request and payment of reproduction costs. DERIVATION OF 2%-D GRAVITY EQUATIONSThe gravitational field at a point P external to a continuous mass distribution p uO) contained within a volume V (Figure 1) is given by Z FIG. I. Density distribution p(fo) within volume V as seen from field point i. Downloaded 03/15/15 to 142.58.129.109. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/ 1508 Cady P(P) = -VU(P), where the gravitational potential is (1) L'(P) = -G (2) (Grant and West, 1965, p. 211). G is the universal gravitational constant. Figure 2 defines the right-handed coordinate system and shows the body over which we integrate. The y-axis is parallel to the strike of the body, and observations lie along a profile contained within the x-z plane. The z-axis is positive downward, in the derivation, for consistency with Shuey and Pasquale (i973' )...
Magnetic and gravity anomalies, with typical amplitudes of 1,000 7 and 50 mgal, respectively, occur over the Great Valley of California. Aeromagnetic data were combined to make a composite aeromagnetic map of most of the Great Valley and adjoining areas. Good correlation between local details of the gravity and magnetic anomalies suggests that dense, magnetic rock is the source of the anomalies. A nearly continuous magnetic high and weak gravity highs occur where serpentinite is exposed along the Coast Range thrust fault. Magnetic highs, but no associated gravity highs, occur where serpentinite crops out in the western Sierra Nevada metamorphic belt. The metavolcanic rocks are relatively nonmagnetic. Major magnetic highs with strong associated gravity highs are caused by gabbro at three places in the western Sierra Nevada. Two of these gabbro occurrences are probably part of ophiolite complexes.Gravity, magnetic, and drill-hole data were used to construct a map of basement rock types. Gabbro and similar mafic rocks are abundant beneath the crest of the Great Valley anomalies. Ultramafic rocks are very rare in drill holes that reach basement. A major break in the anomaly patterns suggests a possible east-trending fault in the basement rocks near Fresno.A two-dimensional crustal model was made across central California through the use of seismic refraction data and gravity and magnetic modeling. Magnetic rock comes to within 2.5 km of the surface just east of the center of the Great Valley and dips steeply to the west beneath the western side of the valley. If gabbro is the source of the anomalies, then sialic crust must be virtually nonexistent beneath the Great Valley. Analogy with the ophiolite complexes of the Sierra Nevada foothills suggests that the source of the Great Valley anomalies is a tectonically emplaced fragment of oceanic crust.In Late Jurassic time, an eastward-dipping subduction zone in the western Sierra Nevada foothills became detached and stepped westward to the present position of the Coast Range thrust fault, leaving behind a fragment of oceanic crust. I propose that this fragment, covered by Tithonian and younger strata, causes the Great Valley magnetic and gravity anomalies.
The northern Yukon‐Koyukuk province is characterized by low elevation and high Bouguer gravity and aeromagnetic anomalies in contrast to the adjacent Brooks Range and Ruby geanticline. Using newly compiled digital topographic, gravity, and aeromagnetic maps, I have divided the province into three geophysical domains. The Koyukuk domain, which is nearly equivalent to the Koyukuk lithotectonic terrane, is a horseshoe‐shaped area, open to the south, of low topography, high gravity, and high‐amplitude magnetic anomalies caused by an intraoceanic magmatic arc. The Angayucham and Kanuti domains are geophysical subdivisions of the Angayucham lithotectonic terrane that occur along the northern and southeastern margins of the Yukon‐Koyukuk province, where oceanic rocks have been thrust over continental rocks of the Brooks Range and Ruby geanticline. Basalt of the Angayucham domain causes strong gravity highs and weak magnetic highs. The Kanuti domain is distinguished from the Angayucham domain by intense magnetic highs caused by cumulus mafic and ultramafic plutonic rocks, abundant ultramafic mantle tectonites, and magnetic syenite and monzonite. Long‐wavelength, low‐intensity magnetic highs and undulating gravity anomalies indicate an undulating basement surface of varied lithology beneath the Kobuk‐Koyukuk and Lower Yukon basins. Modeling of gravity and magnetic anomalies shows that oceanic rocks of the Angayucham and Kanuti domains dip inward beneath the Kobuk‐Koyukuk basin. The modeling supports, but does not prove, the hypothesis that the crust of the Kobuk‐Koyukuk basin is 32–35 km thick, consisting of a tectonically thickened section of Cretaceous volcanic and sedimentary rocks and older oceanic crust. Plutons of the Brooks Range and the southern Ruby geanticline are nonmagnetic, ilmenite series, S‐type granites that cause magnetic lows. Plutons of the northern Ruby geanticline are variable in their magnetic properties and cause both highs and lows. Plutons of both the eastern and western Yukon‐Koyukuk province are variable in their magnetic expression but commonly cause magnetic lows in contrast to andesite.
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