> Home > Documentation > Fortran 95 > Gravity and Magnetics

SHMagPowerSpectrum

Compute the power spectrum of the magnetic field given the Schmidt seminormalized magnetic potential spherical harmonic coefficients.

Usage

call SHMagPowerSpectrum (c, a, r, lmax, spectrum, exitstatus)

Parameters

c : input, real*8, dimension (2, lmax+1, lmax+1): The Schmidt seminormalized spherical harmonic coefficients of the magnetic potential.
a : input, real*8: The reference radius of the magnetic potential spherical harmonic coefficients.
r : input, real*8: The radius to evaluate the magnetic field.
lmax : input, integer: The maximum spherical harmonic degree to calculate the power spectrum.
spectrum : output, real*8, dimension (lmax+1): The power spectrum of the magnetic field.
exitstatus : output, optional, integer: 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.

Description

SHMagPowerSpectrum will calculate the power spectrum of the magnetic field at radius r given the magnetic potential Schmidt seminormalized spherical harmonic coefficients c evaluated at radius a. For a given degree l, this is explicitly calculated as (Lowes 1966):

S(l) = (l+1) (a/r)**(2l+4) Sum_{m=0}^l [ c(1, l+1, m+1)**2 + c(2, l+1, m+1)**2 ].

Reference

Lowes, F. J., Mean-square values on sphere of spherical harmonic fields, J. Geophys. Res., 71(8), 2179, 1966.

SHMagPowerSpectrum

Usage

Parameters

Description

Reference

See also