earth-tides

earth-tides computes solid Earth tides: the Love numbers of a rotating, flattened, layered, anelastic and self-gravitating Earth, and the tidal displacement of a station that follows from them. The Love numbers are computed directly on the flattened Earth by a spectral method (Chebyshev collocation in radius, Galerkin projection along the level surfaces), without generalized spherical harmonics or hand-derived perturbation theory. The package is pure Python (NumPy and SciPy).

Quick start

earth-tides has no graphical interface and no icon to click: everything happens in a terminal. Open one (Windows: Command Prompt or PowerShell; macOS: Terminal; Linux: any shell), then type each command below and press Enter, waiting for one to finish before starting the next.

Step 1: install earth-tides (requires Python 3.10 or newer with pip):

pip install earth-tides

Nothing works until this step has completed successfully.

Step 2: get the examples and the manual:

earthtides-examples

This copies five worked examples and the PDF user manual into a new directory earthtides-examples in your current location (give a different name as argument if you prefer, e.g. earthtides-examples my_dir). If the command is not found, step 1 did not finish successfully: read its error messages.

Open earthtides_manual_v1.0.pdf first. It explains the conventions of tidal Love numbers, how the solver works, the two programs and every example.

Step 3: compute something. The body tide at Onsala for one day, hourly, with the Love numbers of the IERS Conventions (columns: MJD, up, north, east in metres):

etide 57.395 11.926 --start 2026-01-01 --days 1

The Love numbers of PREM for every wave group of the tidal catalogue (about 12 seconds), and the same body tide computed with them:

earthtides-love -o love.json
etide 57.395 11.926 --start 2026-01-01 --days 1 --love love.json

Step 4: run an example. Each example runs from its own directory and prints the numbers of its .out file:

cd earthtides-examples/ex1
python swing.py

Programs

All print their options with --help.

From Python

from earthtides.model import EarthModel
from earthtides.love import model_path
from earthtides.geometry import ClairautGeometry, OMEGA_EARTH
from earthtides.solver import TidalSolver
from earthtides.iers import iers_fit

md = EarthModel(str(model_path('PREM')))   # PREM with a fluid outer core
g = ClairautGeometry(md)                     # hydrostatic flattening (Clairaut)
S = TidalSolver(md, g, m=2, K=5, N=30, omega_f=0.0, coriolis=OMEGA_EARTH,
                omega_t=1.4053e-4, omega_rot=OMEGA_EARTH,
                dyn_fluid=True, consistent_reference=True)   # M2
S.solve()
print(iers_fit(S, g))     # h0 = 0.60243, h2 = -0.00049, l0 = 0.08361, l1 = 0.00099, ...

Verification

Every part of the method is checked against a known answer: homogeneous spheres (exact Bessel solution), a spherical Earth on a distorted mesh (round-off), an exact homogeneous spheroid (round-off), the analytical flattened Earth of Greff-Lefftz et al. (2005) (5e-6), Hough's free core nutation (2e-4), and elastic hydrostatic PREM against Dehant, Defraigne & Wahr (1999) (1e-5 at M2). etide reproduces the IERS routine DEHANTTIDEINEL to 0.1 mm rms.

Reference

If you use earth-tides in your research, please cite:

Bos, M.S. (2026). What the IERS body-tide model assumes: Love numbers of a flattened, rotating, anelastic Earth. Journal of Geodesy (submitted).

License

Free for academic, research, and educational use. Commercial use requires a separate license from TeroMovigo – Earth Innovation Lda. See LICENSE for the full terms.