shadmitcorr.1

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.TH "shadmitcorr" "1" "2021-02-15" "Fortran 95" "SHTOOLS 4.10"
.hy
.SH SHAdmitCorr
.PP
Calculate the admittance and correlation spectra of two real functions.
.SH Usage
.PP
call SHAdmitCorr (\f[V]gilm\f[R], \f[V]tilm\f[R], \f[V]lmax\f[R],
\f[V]admit\f[R], \f[V]corr\f[R], \f[V]admit_error\f[R],
\f[V]exitstatus\f[R])
.SH Parameters
.TP
\f[V]gilm\f[R] : input, real(dp), dimension (2, \f[V]lmaxg\f[R]+1, \f[V]lmaxg\f[R]+1)
The real spherical harmonic coefficients of the function \f[V]G\f[R].
.TP
\f[V]tilm\f[R] : input, real(dp), dimension (2, \f[V]lmaxt\f[R]+1, \f[V]lmaxt\f[R]+1)
The real spherical harmonic coefficients of the function \f[V]T\f[R].
.TP
\f[V]lmax\f[R] : input, integer(int32)
The maximum spherical harmonic degree that will be calculated for the
admittance and correlation spectra.
This must be less than or equal to the minimum of \f[V]lmaxg\f[R] and
\f[V]lmaxt\f[R].
.TP
\f[V]admit\f[R] : output, real(dp), dimension (\f[V]lmax\f[R]+1)
The admittance function, which is equal to \f[V]Sgt/Stt\f[R].
.TP
\f[V]corr\f[R] : output, real(dp), dimension (\f[V]lmax\f[R]+1)
The degree correlation function, which is equal to
\f[V]Sgt/sqrt(Sgg Stt)\f[R].
.TP
\f[V]admit_error\f[R] : output, optional, real(dp), dimension (\f[V]lmax\f[R]+1)
The uncertainty of the admittance function, assuming that \f[V]gilm\f[R]
and \f[V]tilm\f[R] are related by a linear isotropic transfer function,
and that the lack of correlation is a result of uncorrelated noise.
.TP
\f[V]exitstatus\f[R] : output, optional, integer(int32)
If present, instead of executing a STOP when an error is encountered,
the variable exitstatus will be returned describing the error.
0 = No errors; 1 = Improper dimensions of input array; 2 = Improper
bounds for input variable; 3 = Error allocating memory; 4 = File IO
error.
.SH Description
.PP
\f[V]SHAdmitCorr\f[R] will calculate the admittance and correlation
spectra associated with two real functions expressed in real spherical
harmonics.
The admittance is defined as \f[V]Sgt/Stt\f[R], where \f[V]Sgt\f[R] is
the cross-power spectrum of two functions \f[V]G\f[R] and \f[V]T\f[R].
The degree-correlation spectrum is defined as
\f[V]Sgt/sqrt(Sgg Stt)\f[R], which can possess values between -1 and 1.
.PP
If the optional argument \f[V]admit_error\f[R] is specified, then the
error of the admittance will be calculated by assuming that \f[V]G\f[R]
and \f[V]T\f[R] are related by a linear isotropic transfer
function:\f[V]Gilm = Ql Tilm + Nilm\f[R], where \f[V]N\f[R] is noise
that is uncorrelated with the topography.
It is important to note that the relationship between two fields is
often not described by such an isotropic expression.
.SH See also
.PP
shpowerspectrum, shcrosspowerspectrum