Introduction

Once raw gravity data has been obtained, several corrections must be applied to isolate the geological signal. Earth tide correction is the process of removing the gravity changes caused by the sun and moon’s tidal forces, along with related effects such as polar tides and length-of-day tides, to account for celestial and related environmental effects in gravity data so the remaining data reflects subsurface mass changes rather than celestial forcing. For geophysicists and gravimeter users, this sits alongside instrument specific corrections such as drift, tilt, and ambient temperature and pressure.

SMG Gravimeters to date have utilised Longman earth tide corrections but in our upcoming software update will now support an improved Earth Tide model greatly reducing tidal correction errors.

In this article we explore what factors affect earth tides, the approaches used to correct for them, including body tide correction and ocean loading, and the analysis of model and software improvements that can improve accuracy.

Gravimeter noise, drift, instrument tilt, ambient temperature etc can all affect the quality of the gravity signal measured by an instrument, whereas tidal corrections are slightly different. These are real forces that affect the actual gravity acceleration experienced by the gravimeter and so tidal effects must be removed to observe the gravity variations associated with the distribution of mass in the subsurface.

Lunisolar (the combined sun and moon) tides can affect the experienced strength of gravity daily by >100 µGal, as they deform the solid Earth by ~0.4 m. Even across a small survey area, this temporal change can be larger than the gravity variations caused by local geology, meaning measurements taken at different times cannot be compared reliably without an accurate tidal correction.

Other planets also lead to an Earth tidal effect, however the effects are very small. At its greatest the impact of Venus this 0.0053% the force of the lunar tide - well below the precision a gravimeter can detect.

Components of Earth Tides and Tidal Forces

When one observes the tidal response of the Earth, the most familiar component typically considered is the twice daily oceanic tides. These tidal phenomena arise from tidal forces because gravitational attraction varies with the distance between two bodies. The Moon’s gravitational force causes ocean water to bulge outward, forming two tidal bulges, one in the Moon’s direction and one on the opposite side, and these shift relative to a fixed position on the Earth’s surface as the Earth rotates. Although the most visually dramatic, this has only a minor impact on the gravitational acceleration observed in a given location. The major component is the solid Earth response, which causes a gravitational change of up to 100 µGal with a near instantaneous response, this is termed the body tide.

Ocean tides commonly produce two high tides and two low tides daily, and spring tides occur when the Sun, Moon, and Earth align.

The other components are:

• Ocean loading: The gravitational pull from water that has moved with the tides, as well as the change from how that water's movement deforms the Earth.
• Polar tides: The changes in the pole of rotation of the Earth that modify how the tidal deformation field maps onto locations on the Earth.
• Length of Day tides: Slight variations in the rotation rate of the Earth linked to Earth's rotation due to pulls from other bodies, leading to minor gravitational variations from that predicted by a fixed rotation rate.

Correcting for Body Tides in Tidal Gravity Observations

For correcting body tides, there are two approaches:

• Direct computation using a precise description of the position of the sun and moon and the tide generating potential to find how gravity varies at any given point. This method was derived by Longman (1959) and is very efficient as a practical lower-accuracy approach, but has residual errors of 15 µGal.
• Harmonic computation, by decomposing the gravitational pull of the sun and moon into a series of waves at different frequencies with a set of coefficients for each. These equations are based on spherical harmonics by degree and period, and high-accuracy implementations typically follow the IERS Conventions Technical Note No. 32. This is less efficient, but can be highly precise down to sub-nanogal if required.

The GAIA-FIELD 1.1 launched with the Longman tide correction, which removes the majority of the error allowing tide free data to be observed but for highest accuracy results would still require post-processing to observe more subtle features as the model may contain errors of up to ~15 µGal. This is not ideal as it could prevent a field user from observing anomalous readings when they are taken, and being able to re-take the measurement to verify them. Thus, in high precision geodetic work, strict adherence to earth tide correction standards is required.

To improve this, we are implementing a spherical harmonic based correction. Specifically we will be using the 1,200 waves with parameters outlined by Tamura (1987). This calculates body tides with an accuracy better than 1 nGal, effectively removing body tides as a source of error.

Body tide effect modelled for the SMG offices over several days in July 2026 highlighting the differences between tidal models.

We are implementing an adaptation of the ETERNA program, with modifications that allow it to run efficiently on GAIA. The solid Earth’s response to lunisolar forces is highly predictable, allowing modern harmonic models to calculate the gravity variation with high accuracy. This represents a clear improvement over the Longman model.

Ocean Loading from Ocean Tides

Ocean loading is significantly more complex than body tides to calculate because ocean tides and tidal loading depend on both the ocean model and the Earth’s deformation response. It requires a global tidal model to understand how ocean movements vary across the Earth and with differing tidal conditions. Following this, how these movements of water affect gravity can then be calculated. In some bays, tides can exceed 10 meters, so loading magnitude varies strongly by location.

Near to coastlines, ocean loading can reach 20 µGal, but in continental interiors this effect is < 2 µGal. Due to the impact of this being below the resolution of the GAIA in the mid-continent, and the high complexity of calculating ocean loading, it is not currently planned to be implemented onto the device.

For surveys occurring near to coastline, many packages are available to calculate this effect such as the ocean loading aspect of the ETERNA package, or SPOTL.

In Summary

Lunisolar tides greatly impact the gravity signal measured by a gravimeter by 100 µGal over a day. This can prevent field users from spotting anomalous data readings if not corrected on device. Earth tide correction also matters beyond field gravimetry, including absolute gravity measurements used for long-term deformation monitoring and separating vertical crustal movements.

SMG gravimeters have historically used the Longman earth-tide correction. Our upcoming software update will introduce an improved Earth-tide model, reducing residual tidal error in continental interiors to approximately 2 µGal, with ocean loading remaining the principal unmodelled tidal contribution. In high-precision geodetic work, strict adherence to recognised Earth-tide correction standards is essential, while for field gravity surveys the improved correction provides more reliable on-device data and greater confidence when identifying subtle geological anomalies.

Author Philip Couldery - SMG Gravity
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