Earth tide

Definition
An Earth tide, also called a solid‑earth tide or body tide, is the elastic deformation of the solid portion of the Earth caused by the gravitational forces exerted primarily by the Moon and, to a lesser extent, the Sun. These deformations are analogous to oceanic tides but involve the crust, mantle, and, to a very small degree, the core.

Mechanism
The tidal force arises from the differential gravitational pull on the near side of the Earth compared with its far side. The Moon, being closer, produces a larger tidal potential than the Sun; however, the Sun’s much larger mass results in a secondary contribution of about 46 % of the lunar effect. The combined tidal potential can be expressed as a sum of spherical harmonic components, the most significant being the semidiurnal (M₂) and diurnal (O₁, K₁) constituents.

Amplitude and Frequency
Typical vertical displacements of the Earth's surface range from 10 cm to 40 cm, with horizontal motions of 5 cm to 20 cm. The dominant periods are:

The exact amplitude varies with geographic location, latitude, and the Earth’s elastic structure.

Measurement Techniques
Earth tides are monitored using a variety of high‑precision instruments:

• Superconducting gravimeters detect minute changes in the local gravitational acceleration (∼10⁻⁹ g).
• Very Long Baseline Interferometry (VLBI) and Global Navigation Satellite System (GNSS) networks measure surface displacements at the millimetre level.
• Strainmeters and tiltmeters record the deformation of the crust directly.

Data from these instruments are routinely used to calibrate geodetic models, correct satellite orbits, and investigate Earth’s interior rheology.

Scientific Significance

1. Geophysical Modeling – Earth‑tidal observations constrain the elastic and anelastic properties of the mantle and crust, aiding the development of global Earth models such as PREM (Preliminary Reference Earth Model).
2. Seismology – Tidal stresses can modulate the timing of micro‑earthquakes and volcanic tremor, providing insight into fault mechanics and triggering thresholds.
3. Oceanography and Atmospheric Science – Solid‑earth tide models improve the accuracy of sea‑level and ocean‑loading corrections in satellite altimetry.
4. Spacecraft Navigation – Precise tidal models are incorporated into the force models used for low‑Earth‑orbit satellite orbit determination.

Related Phenomena

• Ocean tide – The movement of seawater driven by the same lunar‑solar gravitational forces; ocean tides exert additional loading on the solid Earth, known as ocean‑loading tides.
• Atmospheric tide – Periodic variations in atmospheric pressure caused by solar heating; contributes a minor component to surface loading.
• Tidal forcing of the Earth’s rotation – Redistribution of mass associated with tides leads to small variations in the Earth’s rotation rate (length‑of‑day changes).

Historical Context
The concept of solid‑earth tides was first proposed in the 19th century by astronomers such as George Biddell Airy and George Howard Darwin. Systematic observational confirmation came with the advent of superconducting gravimeters in the 1960s and the development of global GNSS networks in the late 20th century.

Current Research
Active areas of investigation include:

• High‑resolution modeling of tidal deformation in regions with complex topography and heterogeneous crustal structure.
• Interaction between Earth tides and fluid‐pressure changes in hydrothermal systems and fault zones.
• Integration of tidal signals into real‑time geodetic monitoring for early‑warning systems.

References

1. Wahr, J. (1981). “Body tides on an elliptical, rotating, self‑gravitating Earth.” Geophysical Journal International, 64(3), 705‑724.
2. Agnew, D. C. (2007). “Earth Tides.” Treatise on Geophysics, 3, 163‑215.
3. Koot, G., et al. (2016). “Solid Earth tide: Global observations from the International GNSS Service.” Journal of Geodesy, 90, 1175‑1195.

(This entry reflects the state of knowledge up to June 2026.)