gen_harmonics

Converts data from the spatial domain to spherical harmonic coefficients
Does not compute the solid Earth elastic response or convert units

Calling Sequence

from gravity_toolkit.gen_harmonics import gen_harmonics
from gravity_toolkit.associated_legendre import plm_holmes
PLM, dPLM = plm_holmes(LMAX, np.cos(th))
Ylms = gen_harmonics(data, lon, lat, LMAX=LMAX, PLM=PLM)

Source code

gravity_toolkit.gen_harmonics(data, lon, lat, **kwargs)[source]

Converts data from the spatial domain to spherical harmonic coefficients

Parameters:

data: np.ndarray

data magnitude

lon: np.ndarray

longitude array

lat: np.ndarray

latitude array

LMAX: int, default 60

Upper bound of Spherical Harmonic Degrees

MMAX: int or NoneType, default None

Upper bound of Spherical Harmonic Orders

PLM: np.ndarray, default 0

Fully normalized associated Legendre polynomials or Fourier coefficients of Legendre polynomials

METHOD: str, default ‘integration’

Conversion method for calculating harmonics

'integration': for global grids

'fourier': for regional or global grids

Returns:

clm: np.ndarray: cosine spherical harmonic coefficients (4-pi normalized)
slm: np.ndarray: sine spherical harmonic coefficients (4-pi normalized)
l: np.ndarray: spherical harmonic degree to LMAX
m: np.ndarray: spherical harmonic order to MMAX

gravity_toolkit.gen_harmonics.integration(data, lon, lat, LMAX=60, MMAX=None, PLM=0, **kwargs)[source]

Converts data from the spatial domain to spherical harmonic coefficients

Parameters:

data: float: data magnitude
lon: float: longitude array
lat: float: latitude array
LMAX: int, default 60: Upper bound of Spherical Harmonic Degrees
MMAX: int or NoneType, default None: Upper bound of Spherical Harmonic Orders
PLM: float, default 0: input Legendre polynomials

Returns:

clm: float: cosine spherical harmonic coefficients
slm: float: sine spherical harmonic coefficients
l: int: spherical harmonic degree to LMAX
m: int: spherical harmonic order to MMAX

gravity_toolkit.gen_harmonics.fourier(data, lon, lat, LMAX=60, MMAX=None, PLM=0, **kwargs)[source]

Computes the spherical harmonic coefficients of a spatial field

Parameters:

data: float: data magnitude
lon: float: longitude array
lat: float: latitude array
LMAX: int, default 60: Upper bound of Spherical Harmonic Degrees
MMAX: int or NoneType, default None: Upper bound of Spherical Harmonic Orders
PLM: float, default 0: input Fourier coefficients of Legendre polynomials

Returns:

clm: float: cosine spherical harmonic coefficients
slm: float: sine spherical harmonic coefficients
l: int: spherical harmonic degree to LMAX
m: int: spherical harmonic order to MMAX