| Forward modeling of potential field anomalies is a fundamental tool for quantitative inter-pretation and has received consistent research attention. An initial model for the source body is constructed based on geologic and geophysical intuition. The model’s anomaly is calculated and compared with the observed anomaly, then model parameters are adjusted in order to improve the fit between the two anomalies. The three-step process of body adjustment, anomaly calculation, and anomaly comparison is effectively inversion by trial-and-error.Forward methods for potential fields can be roughly divided into to categories:space-domain methods and Fourier-domain methods. Space-domain methods provide directly closed-form e-quations to calculate the anomaly. It is more straightforward, field points in the whole space can be calculated uniformly by closed-form equations and the results obtained can be considered as precise. However, the expressions of space-domain solutions usually are rather complex and the derivation process can be cumbersome; and when large number of field points are to be modeled, space-domain solutions are considerably slow. Fourier-domain forward methods first calculate an-alytically the1-D,2-D or3-D Fourier transform (spectrum) of the anomalies of a profile, a plane or the whole3-D space caused by the source body, then calculate numerically the inverse Fourier transform by the Fast Fourier Transform (FFT) algorithm. Compare to space-domain expressions, Fourier-domain expressions (spectra) for potential field anomalies are usually simpler and more compact, many geometric characteristics of the source are expressed as simple multiplicative fac-tors within the anomaly spectrum, and by applying the Fast Fourier Transform (FFT) algorithm, forward modeling in the Fourier domain can be computationally more efficient.However, when the continuous Fourier transform is evaluated numerically by the FFT algorithm (the trapezoidal rule), the oscillatory nature of the continuous Fourier integral give rise to several problems, including im-posed periodicity and edge effect, that become major limitations on the wide use of Fourier-domain forward methods.Existing methods to improve the accuracy of Fourier-domain forward modeling are standard FFT method with grid expansion and the shift-sampling technique. We analyze the Fourier-domain forward problem of potential fields as a numerical quadrature problem, and demonstrated that grid expansion method is equivalent to the numerical evaluation of the oscillatory Fourier integral using the trapezoidal rule with smaller steps; and the reason why shift-sampling technique reduces errors to several tenth of standard FFT method is that the shift Fourier transform expression constitute a piecewise two-nodes Gaussian quadrature rule of the continuous Fourier integral. Based on this proof, we developed a new method:Gauss-FFT method for high-precision Fourier forward mod-eling of potential fields. The convergence behavior of standard FFT method with grid expansion and the Gauss-FFT method are compared by both theoretical deduction and numerical tests. The Gauss-FFT method converges to the space domain solution much faster than the standard FFT method with grid expansion.In this thesis, the fundamental theory and algorithm details of Gauss-FFT method is first p-resented. Comparison of precision between standard FFT method with grid expansion and Gauss-FFT method is carried out based on forward modeling of basic2D and3D source bodies:the infinitely long cylinder and the sphere. After that, the gravity and magnetic anomalies of more complex models, like arbitrary2D bodies, arbitrary3D bodies and the prism-stacked terrain mod-. el(Parker model) are tested using2D Gauss-FFT method to show its reliability and adaptivity. Finally, the3D whole-space gravity anomalies due to some simple sources (sphere and prism) are tested using the3D Gauss-FFT method, the origin and distribution property of forward errors are analysed. |
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