The Use of Linear Filtering in Gravity Problems

Abstract

The technique of Fourier analysis is reviewed and the equivalence and relative advantages of convolution filtering in the space domain and multiplication filtering in the frequency domain are demonstrated with actual field examples. We discuss the design of ideal filters in terms of the relationships between the main lobe and the side lobes. Cut‐and‐try methods appear to favor the hanning window or the hamming window, since these windows minimize the Gibbs phenomenon associated with the downward continuation or high‐pass filtering operation. New sets of coefficients for convolution filtering, based upon Fourier transform theory and the sampling theory, are derived.

Normalized downward continuation of potential fields within the quasi‐harmonic region

“…It was noted (e.g., Roy 1967) that this level marks the limit of the convergence of the continuation process by using the Fourier transform operator. However, Ku, Telford and Lim (1971) pointed out that, for discrete data, a prior filtering is performed by the choice of the sampling step. This observation implies that the oscillatory character of a downward continued field is determined not only by the depth of the continuation level but also by the sampling step, in the sense that the smaller the sampling step, the nearer the continuation level will be at which the transformation becomes unstable.…”

A stable downward continuation by using the ISVD method

“…Consistently, the recognition of an oscillatory character of the continued field was used to indicate the depth to the source. Ku et al (1971) pointed out that, for discrete data, a prior filtering is performed by the choice of sampling step. This observation implies that the oscillatory character of a downward continued field is determined not only by the depth of the continuation level, but also by the sampling step, in the sense that the smaller the sampling step the nearer will be the continuation level at which the transformation becomes unstable.…”

Γεωφυσικη Διασκοπησης Της Περιοχης "Λουτρακιου-Σουσακιου"

“…0 Griffin (1949) Όλες σχεδόν OL μέθοδοι διαχωρισμού γενικού-υπολειματικού πεδίου, που ήδη αναφέρθηκαν, περιλαμβάνουν εξομάλυνση των μαγνητικών τιμών στην περιοχή του χώρου (Mesko 1965.Ful ler 1967, Zurflueh 1967, Darby and Davies 1967. Με την ανά πτυξη , όμως, του προγραμματισμού και των ηλεκτρονικών υπολο γιστών μεγάλης ταχύτητας, καθώς επίσης με την επινόηση του γρήγορου μετασχηματισμού Fourier (FFT, Cooley and Tukey 1965) άρχισε η χρήση μαθηματικών τελεστών οι οποίοι ορίζονται στο χώρο των συχνοτήτων (Glarke 1969, Spector and Grant 1970, Ku et al 1971, Meyer 1974 Ackerman and Dix (1955)δόθηκε από τους Pe ters (194 9) και Constantinescu and Eldaim (1963).…”