Tidal Tomography: From the Moon to Mars and Beyond
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Where
Dr. Alexander Berne
Postdoctoral Research Associate
Lunar and Planetary Laboratory
University of Arizona
Tides raised by host planets and stars periodically deform satellite planetary bodies, producing small temporal variations in their gravity fields. For a spherically symmetric interior, forcing at a given spherical harmonic degree and order drives deformation only at that same degree and order. However, lateral heterogeneity in internal structure couples with tidal forcing to excite deformation at other harmonics (for example, degree-3 gravity signals in response to degree-2 tides). Whereas the static gravity field is weighted towards density structure in the shallow interior, these coupled time-varying signals are most sensitive to lateral variations in the shear modulus of the mantle. Tidal tomography (that is, the inference of lateral variations in interior structure from a body’s time-variable response to tidal forcing) therefore provides a means to probe the deep interior from orbit. In this seminar, we present recent work applying tidal tomography to the Moon and Mars, followed by a discussion of future applications to other planetary bodies.
At the Moon, we use tracking data from NASA’s GRAIL mission to recover a degree-3 tidal Love number of 𝑘3 = 0.0163 ± 0.0007, roughly 72% larger than the value expected for a spherically symmetric interior. This anomalous response can be explained if the shear modulus of the lunar mantle varies by 2–3% between the nearside and farside (that is, an ℓ = 1, 𝑚 = 1 pattern). A compositional (for example, iron-rich) origin for this asymmetry would produce a centre-of-mass–centre-of-figure (COM–COF) offset at least 15 times larger than observed. By contrast, a temperature difference of roughly 100–200 K can produce the required variation with a sufficiently small change in mantle density, suggesting preservation of the thermal anomaly that formed the lunar maria 3–4 billion years ago.
At Mars, we extend this approach using 16 years of tracking data from the Mars Global Surveyor, Mars Odyssey and Mars Reconnaissance Orbiter spacecraft. We find that degree-3 components of the seasonal (that is, 687-day) time-variable gravity field deviate by up to 300% from predictions for a spherically symmetric planet. These deviations can be explained if the effective shear modulus of the mantle varies by more than 20% over a hemispheric pattern that closely tracks the crustal dichotomy, with lower/higher values beneath the southern highlands/northern lowlands. Note that this variation represents an average over the full depth of the mantle. What could generate such a large contrast? Because the effective shear modulus of olivine is roughly 15–20 times more sensitive to temperature at the seasonal period than at seismic periods, we infer a 200–400 K thermal anomaly in the present-day mantle below the southern highlands. This anomaly may reflect insulation by the thick highlands crust or regional mantle convection persisting over several billion years.
Future orbiters with dedicated gravity experiments could extend tidal tomography to other bodies that exhibit pronounced low-order asymmetries. For example, radio science measurements from BepiColombo could test whether Mercury’s north–south (that is, ℓ = 1, 𝑚 = 0) crustal dichotomy extends into the deeper mantle, as we infer for Mars. At Ganymede, tracking of the JUICE spacecraft, which will orbit the moon in the 2030s, could constrain lateral variations in the thickness of the ice shell overlying its subsurface ocean. At Enceladus, an ice shell that thins to a few kilometres beneath the South Polar Terrain may couple strongly with diurnal tides, such that a future orbiter could map the structure that modulates tidally driven fault motion and jet activity along the tiger stripes. Because tidal tomography does not require a landed spacecraft (unlike seismology), it represents a powerful tool for characterizing the deep interiors of planetary bodies throughout the Solar System.