An elastic layer plays an important role in deformation of the crust. At active volcanoes, its thickness would be effectively thinned by a higher geothermal gradient, particularly in a region beneath which magmatic activity is relatively high. This study examines the influence of elastic thickness non-uniformity on viscoelastic crustal deformation by magma emplacement. A 3-D linear Maxwell viscoelastic model is employed, in which an elastic layer underlain by a viscoelastic layer with a spatially uniform viscosity is thinned to be h_i in the volcano centre, compared with h_i + Δh in the peripheral regions, and a sill-like magma emplacement occurs in the upper layer beneath the centre. It is found that the post-emplacement viscoelastic subsidence is diminished or enhanced by the elastic thickness non-uniformity, depending on whether or not the horizontal width of the magma emplacement (ω_s) is greater than the horizontal width (ω_e) over which the elastic layer is thinner. The available signature of the non-uniformity is explored by comparison with a model that has a spatially uniform elastic thickness of h_i. If an apparent viscosity (η_a) of the uniform elastic thickness model is adjusted so that the difference in post-emplacement subsidence is minimised at the deformation centre, the non-uniformity appears in the overall deformation field as a displacement anomaly over the perimeter of the sill in which viscoelastic subsidence is greater for the non-uniform model. The anomaly is, however, by no more than the magnitude of ∼15 per cent of the maximal syn-emplacement uplift, though η_a is necessarily modified to be ∼0.2–10 times the non-uniform model viscosity (η_c). If ω_e is larger than a few times ω_s, a weak signature is no longer expected in the deformation field, and η_a is not significantly deviated from η_c. Since the signature appears so faintly in a displacement field, the InSAR data in the Kutcharo caldera for a period from 13 August 1993 to 9 June 1998 do not allow us to capture the non-uniformity. However, it can be concluded that if ω_e beneath the caldera is comparable with or greater than the topographic caldera diameter (ω_c) as implied by the spatial variation of the geothermal gradient, the non-uniformity has no significant influence. Otherwise, if ω_e < ω_c, the non-uniformity influences the estimation of the crustal viscosity, but does not affect the overall deformation field. The elastic thickness non-uniformity can be theoretically captured in the deformation field, but in practice, its influence, particularly on estimating crustal viscosity, cannot be properly inferred without other geophysical data such as the geothermal gradient in and around the caldera.

中文翻译：

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弹性厚度的不均匀性对岩浆对粘弹性地壳反应的影响：在日本北海道东部的鹿头町破火山口中的应用

弹性层在地壳的变形中起重要作用。在活火山中，其厚度将通过较高的地热梯度有效地变薄，特别是在岩浆活动相对较高的区域。这项研究探讨了岩浆位置对弹性厚度非均匀性对粘弹性地壳变形的影响。使用3-D线性麦克斯韦粘弹性模型，其中与h _i + Δh相比，在火山中心处由在空间上均一的粘度下粘弹性层支撑的弹性层变薄为h _i在外围区域，在中心下方的上层发生了基石状的岩浆。据发现，后炮位粘弹性沉降由弹性厚度非均匀性减弱或增强，这取决于是否岩浆炮位的水平宽度（ω_小号）大于水平宽度（ω _ë）在其上弹性层较薄。通过与具有空间均匀弹性厚度h _i的模型进行比较，探索了非均匀性的可用特征。如果表观粘度（η_一个调整均匀弹性厚度模型的），以使位移后沉降的差异在变形中心处最小化，在整个变形场中，非均匀性会在粘弹性沉降为基础的门槛周围出现位移异常对于非均匀模型更大。异常，然而，不超过的每〜15的最大顺式炮位隆起的百分之大小，虽然η_一个必然修改为~0.2-10倍不均匀模型粘度（η _Ç）。如果ω _Ë是多几次较大的ω_小号，弱签名不再在形变场预期，而η_一个不显著偏离η _Ç。由于签名在位移场上显得微弱，所以从1993年8月13日至1998年6月9日的Kutcharo破火山口中的InSAR数据使我们无法捕获不均匀性。然而，可以得出结论，如果ω _Ë火山口的下方是具有比地形火山口直径相当或更大（ω _Ç）通过地热梯度的空间变化所暗示，非均匀性没有影响显著。否则，如果ω _Ë < ω _Ç，不均匀性会影响地壳粘度的估算，但不会影响整体形变场。弹性厚度的不均匀性在理论上可以在变形场中捕获，但是在实践中，如果没有其他地球物理数据（如破火山口内和周围的地热梯度），就无法正确推断出其影响，尤其是对地壳粘度的估计。