Abstract The pseudo-spectral form of the sea level equation (SLE) requires the approximation of a radially-symmetric visco-elastic Earth. Thus, the resulting predictions of sea level change (SLC) and glacial isostatic adjustment (GIA) often ignore lateral variations in the Earth structure. Here, we assess the capabilities of a Multiple 1D Earth Approach (M1DEA) applied to large-scale ice load components with different Earth structures to account for these variations. In this approach the total SLC and GIA responses result from the superposition of individual responses from each load component, each computed globally assuming locally-appropriate 1D Earth structures. We apply the M1DEA to three separate regions (East Antarctica, West Antarctica, and outside Antarctica) to analyze uplift rates for a range of Earth structures and different ice loads at various distances. We find that the uplift response is mostly sensitive to the local Earth structure, which supports the usefulness of the M1DEA. However, stresses transmitted across rheological boundaries (e.g., producing peripheral bulges) present challenges for the M1DEA, but can be minimized under two conditions: (1) If the considered time period of ice loading for each component is consistent with the relaxation time of the local Earth structure. (2) If the load components can be subdivided according to the scale of the lateral variations in Earth structure. Overall, our results indicate that M1DEA could be a computationally much cheaper alternative to 3D finite element models, but further work is needed to quantify the relative accuracy of both methods for different resolutions, loads, and Earth structure variations.

中文翻译：

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一种多一维地球方法 (M1DEA)，用于解释海平面方程解中的横向粘度变化：南极冰川消融对冰川均衡调整的应用

摘要 海平面方程 (SLE) 的伪谱形式需要径向对称粘弹性地球的近似值。因此，由此产生的对海平面变化 (SLC) 和冰川均衡调整 (GIA) 的预测通常会忽略地球结构的横向变化。在这里，我们评估了应用于具有不同地球结构的大规模冰载荷分量的多一维地球方法 (M1DEA) 的能力，以解释这些变化。在这种方法中，总的 SLC 和 GIA 响应来自每个载荷分量的单个响应的叠加，每个载荷分量都是在假设局部合适的一维地球结构的情况下全局计算的。我们将 M1DEA 应用于三个不同的区域（南极洲东部、南极洲西部、和南极洲以外）以分析一系列地球结构和不同距离的不同冰荷载的抬升率。我们发现隆起响应对当地的地球结构最敏感，这支持了 M1DEA 的有用性。然而，跨流变边界传递的应力（例如，产生外围凸起）对 M1DEA 提出了挑战，但可以在两种情况下最小化：（1）如果考虑的每个组件的冰加载时间段与 M1DEA 的松弛时间一致当地的地球结构。(2)是否可以根据土体结构横向变化的尺度对荷载分量进行细分。总体而言，我们的结果表明 M1DEA 可能是 3D 有限元模型的计算成本低得多的替代方案，