SUMMARY Isostasy explains why observed gravity anomalies are generally much weaker than what is expected from topography alone, and why planetary crusts can support high topography without breaking up. On Earth, it is used to subtract from gravity anomalies the contribution of nearly compensated surface topography. On icy moons and dwarf planets, it constrains the compensation depth which is identified with the thickness of the rigid layer above a soft layer or a global subsurface ocean. Classical isostasy, however, is not self-consistent, neglects internal stresses and geoid contributions to topographical support, and yields ambiguous predictions of geoid anomalies. Isostasy should instead be defined either by minimizing deviatoric elastic stresses within the silicate crust or icy shell, or by studying the dynamic response of the body in the long-time limit. In this paper, I implement the first option by formulating Airy isostatic equilibrium as the linear response of an elastic shell to a combination of surface and internal loads. Isostatic ratios are defined in terms of deviatoric Love numbers which quantify deviations with respect to a fluid state. The Love number approach separates the physics of isostasy from the technicalities of elastic-gravitational spherical deformations, and provides flexibility in the choice of the interior structure. Since elastic isostasy is invariant under a global rescaling of the shell shear modulus, it can be defined in the fluid shell limit, which is simpler and reveals the deep connection with the asymptotic state of dynamic isostasy. If the shell is homogeneous, minimum stress isostasy is dual to a variant of elastic isostasy called zero deflection isostasy, which is less physical but simpler to compute. Each isostatic model is combined with general boundary conditions applied at the surface and bottom of the shell, resulting in one-parameter isostatic families. At long wavelength, the thin shell limit is a good approximation, in which case the influence of boundary conditions disappears as all isostatic families members yield the same isostatic ratios. At short wavelength, topography is supported by shallow stresses so that Airy isostasy becomes similar to either pure top loading or pure bottom loading. The isostatic ratios of incompressible bodies with three homogeneous layers are given in analytical form in the text and in complementary software.

中文翻译：

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爱的平衡 - I：弹性平衡

总结 等稳态解释了为什么观测到的重力异常通常比仅从地形中预期的要弱得多，以及为什么行星地壳可以支持高地形而不破裂。在地球上，它用于从重力异常中减去几乎补偿的表面地形的贡献。在冰冷的卫星和矮行星上，它限制了补偿深度，该补偿深度与软层或全球地下海洋之上的刚性层的厚度相同。然而，经典的均衡不是自洽的，忽略了内部应力和大地水准面对地形支撑的贡献，并产生了对大地水准面异常的模棱两可的预测。相反，应通过最小化硅酸盐壳或冰壳内的偏弹性应力来定义等稳态，或者通过研究身体在长时间极限内的动态响应。在本文中，我通过将 Airy 等静压平衡公式化为弹性壳对表面和内部载荷组合的线性响应来实现第一个选项。等静压比率是根据偏爱数定义的，它量化相对于流体状态的偏差。洛夫数方法将平衡物理学与弹性重力球形变形的技术分开，并为内部结构的选择提供了灵活性。由于弹性均衡在壳剪切模量的全局重新缩放下是不变的，因此可以在流体壳极限中定义，这更简单，并揭示了与动态均衡的渐近状态的深层联系。如果壳是均匀的，最小应力均衡与称为零偏转均衡的弹性均衡变体是双重的，后者物理性较差但计算更简单。每个等静压模型与应用在壳体表面和底部的一般边界条件相结合，从而形成单参数等静压系列。在长波长处，薄壳极限是一个很好的近似值，在这种情况下，边界条件的影响消失了，因为所有等静压族成员产生相同的等静压比。在短波长下，形貌由浅应力支持，因此艾里平衡变得类似于纯顶部加载或纯底部加载。具有三个均匀层的不可压缩物体的等静压比在正文和补充软件中以解析形式给出。