earth
Calculates Earth parameters and Body Tide Love numbers
Provides gravitational and ellipsoidal parameters from Hofmann-Wellenhof and Moritz [29], Petit and Luzum [56]
General Methods
- class pyTMD.earth.datum(**kwargs)[source]
Class for gravitational and ellipsoidal parameters [29, 74]
- Parameters:
- ellipsoid: str, default ‘WGS84’
Reference ellipsoid name
'CLK66': Clarke 1866'CLK80': Clarke 1880'GRS67': Geodetic Reference System 1967'GRS80': Geodetic Reference System 1980'HGH80': Hughes 1980 Ellipsoid'WGS60': World Geodetic System 1960'WGS66': World Geodetic System 1966'WGS72': World Geodetic System 1972'WGS84': World Geodetic System 1984'ATS77': Quasi-earth centred ellipsoid for ATS77'NAD27': North American Datum 1927'NAD83': North American Datum 1983'INTER': International'KRASS': Krassovsky (USSR)'SGS90': Soviet Geodetic System 1990'HLMRT': Helmert 1906 Ellipsoid'HOUGH': Hough 1960 Ellipsoid'AIRY': Airy (1830)'MAIRY': Modified Airy (1849)'MERIT': MERIT 1983 ellipsoid'TOPEX': TOPEX/POSEIDON ellipsoid'EGM96': EGM 1996 gravity model'IAG75': International Association of Geodesy (1975)'IAU64': International Astronomical Union (1964)'IAU76': International Astronomical Union (1976)'IERS89': IERS Numerical Standards (1989)'IERS': IERS Numerical Standards (2010)
- units: str, default `MKS`
Output units
'MKS': meters, kilograms, seconds'CGS': centimeters, grams, seconds
- Attributes:
- a_axis: float
Semi-major axis of the ellipsoid
- flat: float
Flattening of the ellipsoid
- omega: float
Angular velocity of the Earth
- GM: float
Geocentric gravitational constant
- property rad_e: float
Average radius of the Earth with same volume as ellipsoid
- property b_axis: float
Semi-minor axis of the ellipsoid
- property ratio: float
Ratio between ellipsoidal axes
- property rad_p: float
Polar radius of curvature
- property ecc: float
Linear eccentricity
- property ecc1: float
First numerical eccentricity
- property ecc2: float
Second numerical eccentricity
- property m: float
\(m\) Parameter
- property f2: float
\(f_2\) component
- property f4: float
\(f_4\) component
- property q: float
\(q\) Parameter
- property q0: float
\(q_0\) Parameter
- property J2: float
Oblateness \(J_2\) coefficient
- property C20: float
Normalized \(C_{20}\) harmonic
- property gamma_a: float
Normal gravity at the equator
- property gamma_b: float
Normal gravity at the pole
- gamma_0(theta: float | ndarray) float[source]
Normal gravity at colatitudes
- Parameters:
- theta: float
Colatitudes (radians)
- gamma_h(theta: float | ndarray, height: float | ndarray) float[source]
Normal gravity at colatitudes and heights
- Parameters:
- theta: float
Colatitudes (radians)
- height: float
Height above ellipsoid (same as
units)
- property dk: float
Ratio between gravity at pole versus gravity at equator
- property U0: float
Normal potential at the ellipsoid
- property area: float
Surface area of the ellipsoid
- property volume: float
Volume of the ellipsoid
- property rho_e: float
Average density
- pyTMD.earth.love_numbers(omega: ndarray, model: str = 'PREM', **kwargs)[source]
Compute the body tide Love/Shida numbers for a given frequency [42, 75, 76, 78]
- Parameters:
- omega: np.ndarray
Angular frequency (radians per second)
- model: str, default ‘PREM’
Earth model to use for Love numbers
‘1066A’
‘1066A-N’ (neutral)
‘1066A-S’ (stable)
‘PEM-C’
‘C2’
‘PREM’
- astype: np.dtype, default np.float64
Data type for the output Love numbers
- Returns:
- h2: float
Degree-2 Love number of vertical displacement
- k2: float
Degree-2 Love number of gravitational potential
- l2: float
Degree-2 Love (Shida) number of horizontal displacement
- pyTMD.earth.complex_love_numbers(omega: ndarray, **kwargs)[source]
Compute the complex body tide Love/Shida numbers with in-phase and out-of-phase components for a given frequency [43, 44, 56]
- Parameters:
- omega: np.ndarray
Angular frequency (radians per second)
- kwargs: dict
Keyword arguments for
pyTMD.earth.love_numbers()
- Returns:
- h2: complex
Degree-2 Love number of vertical displacement
- k2: complex
Degree-2 Love number of gravitational potential
- l2: complex
Degree-2 Love (Shida) number of horizontal displacement
- pyTMD.earth.degree_love_numbers(l: int, model: str = 'Longman', **kwargs)[source]
Extracts body tide Love/Shida numbers for a given degree [46]
- Parameters:
- Returns:
- hl: float
Body tide Love number of vertical displacement
- kl: float
Body tide Love number of gravitational potential
- ll: float
Body tide Love (Shida) number of horizontal displacement