Spectral finite element approach to postseismic deformation in a viscoelastic self-gravitating spherical Earth
Spectral finite element approach to postseismic deformation in a viscoelastic self-gravitating spherical Earth
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DOI：
10.1111/j.1365-246x.2008.04015.x
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发表时间：
2009-03
影响因子：
2.8
通讯作者：
Yoshiyuki Tanaka;V. Klemann;K. Fleming;Z. Martinec
中科院分区：
文献类型：
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作者：
Yoshiyuki Tanaka;V. Klemann;K. Fleming;Z. Martinec
摘要：本文推导了球形地球的粘弹性松弛理论模型，用于模拟大地震（m>7）在年代际尺度上引起的大尺度震后变形。大多数现有的震后变形模型都没有考虑到地幔黏度的强横向非均质性，特别是在发生这种事件的俯冲板块。此外，自引力效应通常只被近似地处理。当对GPS和GRACE等空间大地测量技术的观测结果进行解释时，这两种效应都变得很重要。在本文中，我们提出了一种允许以严格的方式考虑这两种效应的谱有限元方法。用这种方法，可以处理比摄动技术大得多的横向粘度变化。我们以双偶力的形式推导了任意剪切断层的界面条件，等效于规定的位错，并模拟了具有三维粘弹性结构的不可压缩麦克斯韦地球的松弛过程。采用基于拉普拉斯逆变换积分的独立方法对球对称模型的计算结果进行了验证，得到了较好的一致性。以2004年苏门答腊-安达曼地震为例，通过正演计算模拟了大尺度的震后重力势变化。在有厚板存在的情况下，波长超过500公里的大地水准面高度变化的长期变化比没有厚板的情况减少30%。当软流圈黏度为10 ~ 19 Pa s时，平板对短期变化的影响可超过0.3 mm yr−1，大于GRACE的观测误差。对于一个位移场，由于包含了一块板，变形率的降低可以达到70%，这可以用GPS等大地测量观测来检测。由于平板的水平尺度小于其空间分辨率，因此平板的影响在较长波长的重力场中减弱。因此，在解释由俯冲带的大逆冲事件引起的观测到的震后松弛时，应考虑由板块引起的横向黏度非均质性。
SUMMARY Theoretical models of the viscoelastic relaxation of a spherical Earth are derived to model large-scale postseismic deformation resulting from great earthquakes (M > 7) over decadal timescales. Most existing models of postseismic deformation do not consider strong lateral heterogeneities in mantle viscosity, in particular in the subducting slab where such events occur. In addition, the self-gravitation effect is often treated only approximately. Both effects become important when observations from space geodetic techniques such as GPS and GRACE are interpreted. In this paper, we present a spectral finite-element approach that allows these two effects to be considered in a rigorous way. In this way, much larger lateral viscosity variations can be handled than by perturbation techniques. We derive interface conditions for an arbitrary shear fault in the form of double-couple forces that are equivalent to a prescribed dislocation and simulate a relaxation process for an incompressible Maxwell earth with a 3-D viscoelastic structure. Computational results are validated for a spherically symmetric model by an independent method based on the inverse Laplace integration, and good agreement is obtained. As an example, we apply this approach to the 2004 Sumatra–Andaman earthquake and simulate a large-scale postseismic gravity potential variation by a forward calculation. In the presence of a slab, the secular variation in geoid height change decreases by 30 per cent for wavelengths longer than 500 km, with respect to the case excluding the slab. The effect of the slab can exceed 0.3 mm yr −1 for short-term variations when the asthenosphere viscosity is 10 19 Pa s, which are larger than the observation errors of GRACE. For a displacement field, a decrease in deformation rates can amount to 70 per cent due to the inclusion of a slab, which is detectable with geodetic observations such as GPS. The effect of the slab is attenuated in the gravity field for such longer wavelengths since horizontal scales of the slab are smaller than its spatial resolution. Lateral heterogeneities in viscosity due to a slab should therefore be considered for interpreting observed postseismic relaxation due to a large thrust event in a subduction zone.