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Hi, Aaron
Balasch, You can
have two ways to do the grid vertical derivatives in Oasis montaj: 2D FFT or convolution
filter. In FFT
method, the grid data are Fourier transformed to frequency domain, then applied
the filter function of r to n-th power (r is wavenumber, n is order of differentiation),
finally inverse Fourier transformed back to the space domain to obtain the
vertical derivative results. (Refer magmap menu in details). Alternatively,
in convolution method, the integral for analytic continuation above the grid plane
is used with a Lagrange extrapolation polynomial to derive a general determinant
expression from which the field at depth and the various derivatives on the
surface and at depth can be obtained. The vertical derivative results are calculated
in space domain using center (calculation) point and 10 circles (radii from 1 to
25 grid cell units) averaged value of the grid with the 11 filter coefficients
(not 3x3 filter). The first (not 3rd)
degree trend is removed from the grid before the convolution calculation. For the
more details, please refer the paper “A comprehensive system of automatic
computation in magnetic and gravity interpretation: Roland G. Henderson,
Geophsics, vol. 25, no. 3, pp. 569-585, 1960.” Please contact
me if there are more queries. Cheers, Ting. Geosoft. -----Original
Message----- Hi
everyone, I'm
just too curious. This morning, I was playing around with vertical derivatives.
This is where the curious part came in; I wanted to know exactly what the
vertical derivative was doing, like a lot of other things in the math world,
there are more than one way of doing things. The vertical derivative is pretty
straight forward but I still wanted to see for myself. I was kind of
dissapointed that it the drevative process is hidden within a wrapper;
GridVD_IMU(). Does anyone out there know the actual 3x3 convolution
filter that is used. Also, to my surprise, I found that it appears that a 3rd
degree trend is taken away from the grid. Is ths a common practice in
magnetics or gravity processing? I also
remember experimenting with gridshad awhile ago which from what I would expect
is similar, but not quite the same, as a horizontal gradient. From what I
understand, the declination of the sun in gridshad is equivalent to the
direction of the horizontal gradient, but what I can't figure out is where the
inclination in to the horizontal gradient and how the result of the gridshad
operation gives results between -1 and 1. Can
anyone offer any answers to these questions? Thanks. Aaron
Balasch |
- [gxnet]: Questions about grid derivatives. Aaron Balasch
- Ting Dai
