FilterMatrixWindowedPotentialCoefficients
Create a spherical harmonic window matrix. The window matrix $\mathbf{W}$ is generated in space domain through spherical harmonic synthesis and analysis matrices. The resulting linear operator can be written as \[ \mathbf{W} = \mathbf{K} \mathbf{A} \mathbf{\Omega} \mathbf{S} \mathbf{K}^{-1}. \]Here, $\mathbf{K}$ is a diagonal matrix with the kernel coefficients on the main diagonal, $\mathbf{S}$ is the spherical harmonic synthesis matrix, $\mathbf{\Omega}$ is defined by the values in inputfileGriddedData and the expression value, $\mathbf{A}$ is the spherical harmonic analysis matrix. The resulting window matrix is written to a matrix file.
The spherical harmonic degree range, and coefficient numbering are defined by minDegree, maxDegree, and numbering.
Note that a proper window function $\mathbf{\Omega}$ should contain values in the range [0, 1]. The window function $\mathbf{\Omega}$ can feature a smooth transition between 0 and 1 to avoid ringing effects.
| Name | Type | Annotation |
|---|---|---|
outputfileWindowMatrix | filename | |
inputfileGriddedData | filename | gridded data which defines the window function in space domain |
value | expression | expression to compute the window function (input columns are named data0, data1, ...) |
kernel | kernel | kernel for windowing |
minDegree | uint | |
maxDegree | uint | |
GM | double | Geocentric gravitational constant |
R | double | reference radius |
numbering | sphericalHarmonicsNumbering | numbering scheme for solution vector |