envelopes of 2d and 3d magnetic data and analytical signal Haney Johnston Li Nabighian SEG2003英文电子书.pdf

Envelopes of 2D and 3D magnetic data and their relationship to the analytic signal: Preliminary results † † † Matthew Haney , Cambrey Johnston , Yaoguo Li , and Misac Nabighian Center for Wave Phenomena and † Gravity and Magnetics Research Consortium Department of Geophysics, Colorado School of Mines, Golden, CO 80401 Summary The 2D Envelope Unlike the 2D case, the total gradient (magnitude of We first explore what is already known - that the ampli- the gradient vector) in 3D is not the envelope of either tude of the analytic signal in 2D, or the total gradient, the vertical or horizontal derivatives of the total-field is indeed the envelope over all inclination directions. To anomaly over all possible directions of the earth’s field begin, we examine a function of x and θ defined as: and source magnetization. Instead, the total gradient of the reduced-to-pole data defines the envelope for f = a(x) cos θ + b(x) sin θ (1) the vertical derivative while the total gradient of the reduced-to-equator data defines the envelope for the which is chosen since the total-field anomaly has the form horizontal derivative. of f in 2D with θ representing the earth’s inclination plus the source’s inclination minus the dip (Nabighian, 1972). The parameter x is the horizontal coordinate. From Zaud- Introduction erer (1989), the envelope of the function f over all values of θ can be obt