Energy balance of glacial isostatic adjustment: importance of the rotational feedback

Patočka,; Čadek, O.; Martinec, Zdenĕk

doi:10.1093/gji/ggx469

Cited by 5 publications

(13 citation statements)

References 26 publications

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“…The second set is the LE, which takes deformation of the body as input and returns the changes in the rotation vector ω on output. The here employed numerical method was benchmarked and described in more detail in Patočka et al (2018), and it is only briefly repeated below.…”

Section: Methodsmentioning

confidence: 99%

“…where e r is the radial unit vector, u r is the radial component of displacement, 𝐴𝐴 [𝜌𝜌0]𝑎𝑎 = 𝜌𝜌0(𝑎𝑎) is the density jump at the outer surface, and σ L is the surface mass density of the prescribed surface load. A similar condition can be imposed at the bottom boundary, on Earth corresponding to the core-mantle boundary (see Patočka et al, 2018;Souček et al, 2016).…”

Section: Methodsmentioning

confidence: 99%

“…Surface loads are represented by a non-zero surface mass density σ L in Equation 7. After emplacing a surface load, the body instantaneously deforms due to the elastic response to the surface traction, and then the load's geoid signal continues to weaken as a result of viscous flow in the mantle (i.e., the model tends toward isostasy, see Section 4.2 in Patočka et al, 2018). Fixed load, on the other hand, has a predefined, time-constant inertia tensor contribution, and it ends up at the equator unless it is counterbalanced by another load.…”

Section: Model Setupmentioning

confidence: 99%

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True Polar Wander on Dynamic Planets: Approximative Methods Versus Full Solution

Patočka

2021

JGR Planets

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Internal and external planetary processes such as mantle convection, deglaciation, or large meteorite impacts cause bodies to move as a whole relative to their rotation axis. The rotation poles of planets and moons thus wander on their surfaces, as shown by paleomagnetic, astrometric, and geodetic measurements (e.g., Mitrovica & Wahr, 2011). Such reorientation in space is commonly referred to as true polar wander (TPW).The TPW mechanism can be described as follows. Let us assume that a rotating planet in hydrostatic equilibrium is subject to a sudden loading with a positive geoid anomaly, shifting the principal directions of the planet's inertia tensor in effect (the principal direction that has the largest associated moment of inertia is hereafter referred to as the main inertia axis, MIA). When viewed by an observer on the surface of the planet, the rotation axis will start a circular motion, known as free oscillations, around the new MIA. As soon as free oscillations dampen out (Nakada & Karato, 2012), the resulting position of the rotation pole will be closer to the principal axis of the load than in the initial state. Such motion of the rotation axis misaligns it with the hydrostatic rotational bulge, which effectively prevents the rotation axis from moving further toward the load axis (see figure 1 in Matsuyama et al., 2014). Gold (1955) argued that the stabilization is only transient, because the rotational bulge will eventually adjust to the new direction of rotation. The planet is then free to reorient further, and the process gradually

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Model Setupmentioning

confidence: 99%

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True Polar Wander on Dynamic Planets: Approximative Methods Versus Full Solution

Patočka

2021

JGR Planets

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“…by freezing water that is already on the planet for the case of ice caps. Note also that in this study I do not employ any correction to the initial tensor of inertia, while to fit the original benchmark a correction is needed (see Patočka et al, 2018, for a detailed discussion).…”

Section: Model Setupmentioning

confidence: 99%

“…To provide a rigorous framework for comparing the full LE solution with the approximative methods, I employ formulae from Patočka et al (2018) and compute the energy balance associated with the reorientation process. A perhaps surprising result of the energetical analysis is that the ω||MMOI approximation conserves energy.…”

Section: Introductionmentioning

confidence: 99%

True Polar Wander on Dynamic Planets: Approximative Methods vs. Full Solution

Patočka

2021

Preprint

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Almost three decades ago, the problem of long term polar wander on a dynamic planet was formulated and simplified within the framework of normal mode theory. The underlying simplifications have been debated ever since, recently in a series of papers by Hu et al. (2017bHu et al. ( , 2017aHu et al. ( , 2019, who clarify the role of neglecting short-term relaxation modes of the body. However, the authors still do not solve the governing equations in full, because they make approximations to the Liouville equation (LE). In this paper I use a time domain approach and for previously studied test loads I solve both the relaxation of the body and the LE in full. I also compute the energy balance of true polar wander (TPW) in order to analyze the existing LE approximations. For fast rotating bodies such as the Earth, I show that the rotation axis is always aligned with the maximum principal axis of inertia (ω||MMOI) once free oscillations are damped. The ω||MMOI assumption is also re-derived theoretically. Contrary to previous beliefs, I demonstrate that it is not necessarily linked to the quasi-fluid simplification of the body's viscoelastic response to loading and rotation, but that it is an expression of neglecting the Coriolis and Euler forces in the equation of motion. For slowly rotating bodies such as Venus, the full LE together with energy analysis indicate that previous estimates of TPW in the normal direction need to be revisited. The numerical code LIOUSHELL is made freely available.

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Dynamic reorientation of tidally locked bodies: Application to Pluto

Patočka

Kihoulou

2023

Earth and Planetary Science Letters

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Energy balance of glacial isostatic adjustment: importance of the rotational feedback

Cited by 5 publications

References 26 publications

True Polar Wander on Dynamic Planets: Approximative Methods Versus Full Solution

True Polar Wander on Dynamic Planets: Approximative Methods Versus Full Solution

True Polar Wander on Dynamic Planets: Approximative Methods vs. Full Solution

Dynamic reorientation of tidally locked bodies: Application to Pluto

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