harmonic_summation

  • Returns the spatial field for a series of spherical harmonics

Calling Sequence

from gravity_toolkit.harmonic_summation import harmonic_summation
spatial = harmonic_summation(clm,slm,lon,lat,LMAX=60)

Source code

gravity_toolkit.harmonic_summation(clm1, slm1, lon, lat, LMIN=0, LMAX=60, MMAX=None, PLM=None)[source]

Converts data from spherical harmonic coefficients to a spatial field

Parameters:
clm1: float

cosine spherical harmonic coefficients in output units

slm1: float

sine spherical harmonic coefficients in output units

lon: float

longitude array

lat: float

latitude array

LMIN: int, default 0

Lower bound of Spherical Harmonic Degrees

LMAX: int, default 60

Upper bound of Spherical Harmonic Degrees

MMAX: int or NoneType, default None

Upper bound of Spherical Harmonic Orders

PLM: float or NoneType, default None

Fully-normalized associated Legendre polynomials

Returns:
spatial: float

spatial field

gravity_toolkit.harmonic_transform(clm1, slm1, lon, lat, LMIN=0, LMAX=60, MMAX=None, PLM=None)[source]

Converts data from spherical harmonic coefficients to a spatial field using Fast-Fourier Transforms

Parameters:
clm1: float

cosine spherical harmonic coefficients in output units

slm1: float

sine spherical harmonic coefficients in output units

lon: float

longitude array

lat: float

latitude array

LMIN: int, default 0

Lower bound of Spherical Harmonic Degrees

LMAX: int, default 60

Upper bound of Spherical Harmonic Degrees

MMAX: int or NoneType, default None

Upper bound of Spherical Harmonic Orders

PLM: float or NoneType, default None

Fully-normalized associated Legendre polynomials

Returns:
spatial: float

spatial field

gravity_toolkit.stokes_summation(clm1, slm1, lon, lat, LMIN=0, LMAX=60, MMAX=None, RAD=0, UNITS=0, LOVE=None, PLM=None)[source]

Converts data from spherical harmonic coefficients to a spatial field [73]

Parameters:
clm1: np.ndarray

cosine spherical harmonic coefficients

slm1: np.ndarray

sine spherical harmonic coefficients

lon: np.ndarray

longitude array

lat: np.ndarray

latitude array

LMIN: int, default 0

Lower bound of Spherical Harmonic Degrees

LMAX: int, default 60

Upper bound of Spherical Harmonic Degrees

MMAX: int or NoneType, default None

Upper bound of Spherical Harmonic Orders

RAD: float, default 0.0

Gaussian smoothing radius (km)

UNITS: int, default 0

Output data units

  • 1: cm water equivalent thickness (cm w.e., g/cm2)

  • 2: mm geoid height

  • 3: mm elastic crustal deformation [15]

  • 4: microGal gravitational perturbation

  • 5: mbar equivalent surface pressure

  • 6: cm viscoelastic crustal uplift (GIA) [76]

  • list: custom degree-dependent unit conversion factor

LMAX: int, default 0

Upper bound of Spherical Harmonic Degrees

LOVE: tuple or NoneType, default None

Load Love numbers up to degree LMAX (hl, kl, ll)

PLM: np.ndarray or NoneType, default None

Fully-normalized associated Legendre polynomials

Returns:
spatial: np.ndarray

spatial field