On the numerical interpretation of gravity and other potential field anomalies caused by layers of varying thickness Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/7p88cj649

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  • This thesis involves the interpretation of gravity and other potential field anomalies caused by layers of varying thickness. The partial differential equations of potential field theory are reviewed for gravitational and magnetic force fields. A similar review is carried out for steady-state heat transport and diffusion processes. For the gravitational force fields, solutions of the partial differential equations are listed in integral form for the following cases: single body with given constant density, infinitely thin sheet with variable mass density, two homogeneous layers with a slowly undulating interface and two layers with a vertically-constant-density lower layer. The solutions give the gravity anomaly in terms of the parameters of the source body. Heat transport phenomena of a similar nature are also discussed. The general expression obtained for the two homogeneous layers with a slowly undulating interface is used as an integral equation and applied to the derivation of crustal thickness variation in Oregon on the basis of two different computational methods. The first method, called the digitized algebraic method, solves the quasi-linearized form of the general integral equation by an iterative technique for three reference va1ues of the mean depth of the crust-mantle interface, viz., 25 km, 30 km, and 35 km. The second approach, called the second derivative approximation method, gives a solution by the Fourier transform technique to the linearized form of the general integral equation for the same three reference values of the mean depth of the crust-mantle interface. The above results as to the depth of the crust-mantle interface are compared with recent results with seismic refraction and dispersion data obtained along a profile in eastern Oregon. The value of the reference depth d which best reconciles with the above results and the seismic results turns out to be 30.25 km for the depth data on the basis of the algebraic method and 28.90 km for the depth data obtained with the second derivative approximation method.
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