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downcontfiltermc.3
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downcontfiltermc.3
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.\" Automatically generated by Pandoc 3.1.3
.\"
.\" Define V font for inline verbatim, using C font in formats
.\" that render this, and otherwise B font.
.ie "\f[CB]x\f[]"x" \{\
. ftr V B
. ftr VI BI
. ftr VB B
. ftr VBI BI
.\}
.el \{\
. ftr V CR
. ftr VI CI
. ftr VB CB
. ftr VBI CBI
.\}
.TH "downcontfiltermc" "1" "2021-02-15" "Fortran 95" "SHTOOLS 4.11"
.hy
.SH DownContFilterMC
.PP
Calculate a minimum-curvature downward continuation filter for a given
spherical harmonic degree.
.SH Usage
.PP
\f[V]wl\f[R] = DownContFilterMC (\f[V]l\f[R], \f[V]half\f[R],
\f[V]r\f[R], \f[V]d\f[R])
.SH Parameters
.TP
\f[V]wl\f[R] : output, real(dp)
The amplitude of the downward continuation filter.
.TP
\f[V]l\f[R] : input, integer(int32)
The spherical harmonic degree.
.TP
\f[V]half\f[R] : input, integer(int32)
The spherical harmonic degree where the filter is equal to 0.5.
.TP
\f[V]r\f[R] : input, real(dp)
The reference radius of the gravitational field.
.TP
\f[V]d\f[R] : input, real(dp)
The radius of the surface to downward continue to.
.SH Description
.PP
\f[V]DownContFilterMC\f[R] will calculate a minimum-curvature downward
continuation filter for a given spherical harmonic degree \f[V]l\f[R].
The input parameters include \f[V]half\f[R], which is the degree where
the filter is equal to 0.5, and \f[V]r\f[R] and \f[V]d\f[R], which are
the reference radius of the gravitational field and the radius of the
surface to downward continue to, respectively.
.PP
A simple analytic expression exists for the downward continuation
filter, following the methodology of Wieczorek and Phillips (1998), only
when taking the first, third, fifth, and so on, derivatives of their
equation 17.
For this minimum-curvature filter, which corresponds to the second
derivative, the form has simply been generalized using the solutions of
the odd derivatives.
This may or may not turn out to be exact.
In any case, the form of this filter is numerically very similar to the
Cartesian minimum-curvature filter of Phipps Morgan and Blackman (1993).
.SH References
.PP
Phipps Morgan, J., and D.
K.
Blackman, Inversion of combined gravity and bathymetry data for crustal
structure: A prescription for downward continuation, Earth Planet.
Sci.
Lett., 119, 167-179, 1993.
.PP
Wieczorek, M.
A.
and R.
J.
Phillips, Potential anomalies on a sphere: applications to the thickness
of the lunar crust, J.
Geophys.
Res., 103, 1715-1724, 1998.
.SH See also
.PP
downcontfilterma, batohilm batohilmrhoh