利用地震同震形变精确反演地震震源参数和地下结构具有重要意义。然而，在研究地表形变与断层活动参数之间的关系时，为了简化模型，常常会忽略地形和分层介质因素。目前，地形因素和分层介质因素对同震形变的定量影响需要深入研究。2013年，四川芦山发生了Ms7.0地震，由于芦山地震断层两侧的地形梯度变化较大，地质构造复杂，忽略地形和分层介质因素会对反演结果造成一定偏差。因此，定量研究芦山区域地形和分层介质因素对同震形变的影响，有助于全面认识地震同震形变的机制。本文基于平面断层几何模型，采用谱元法探究了地形和分层介质对地表同震形变的影响，主要研究成果如下：

(1)谱元法能够量化地形因素对地表同震形变的影响。本文分别针对走滑、倾滑、张裂断层模型进行了研究，将其结果与Okada解析解进行对比分析，得出谱元法模拟结果与Okada解析解的吻合度较高，最大差异不超过3%。通过模拟计算了抛物线小山模型的同震位移场，并将其与基于平面模型计算的结果进行了比较。结果表明，地形因素不仅改变了同震位移场的分布形态，而且影响同震位移的量值。因此，本文认为在进行同震形变反演时，必须考虑地形因素的影响。

(2)地震同震形变研究中，地形因素和分层介质发挥着重要作用。本文利用芦山地区的地形数据、介质参数模型以及断层模型，基于谱元法计算了地形因素和分层介质对2013年芦山Ms7.0地震同震形变的影响。结果表明，相较于分层介质，地形因素对芦山地震同震形变的影响更为显著。地形因素对沿断层走向方向上同震形变分量的最大影响可达~17.3%，对垂直断层走向方向上同震形变分量的最大影响可达~20.6%，而分层介质对沿断层走向方向和垂直断层走向方向上同震形变分量的影响分别为~3.6%和~2.2%。综合考虑地形和分层介质因素时，其对沿断层走向方向和垂直断层走向方向上同震形变分量的影响分别为~17.5%和~18.3%。

(3)在考虑地形因素的芦山地震断层模型基础上，探讨了改变断层参数时地形效应的变化。研究结果表明，当断层倾角在30°到40°之间时，地形因素对同震形变的影响为~18%，当断层倾角在45°到65°之间时，地形因素对同震形变的影响为~15%，当断层倾角在70°到90°之间时，地形因素对同震形变的影响大于18%；随着震源深度的增加，地形效应随之减小；而改变断层滑动量的大小，地形因素的影响不明显。

The accurate inversion of earthquake source parameters and subsurface structures using seismic coseismic deformation is of great significance. However, in studying the relationship between surface deformation and fault activity parameters, the simplification of models often leads to the neglect of topographic and layered medium factors. Currently, there is a need for in-depth research into the quantitative effects of topographic and layered medium factors on coseismic deformation. In 2013, the Ms7.0 earthquake occurred in Lushan, Sichuan Province, China. Due to significant changes in topographic gradients on both sides of the Lushan seismic fault and the complex geological structure, ignoring topographic and layered medium factors can introduce certain biases into inversion results. Therefore, quantitatively studying the effects of topographic and layered medium factors on coseismic deformation in the Lushan region can contribute to a comprehensive understanding of the mechanism of seismic coseismic deformation. In this study, based on a planar fault geometry model, the spectral element method was employed to investigate the effects of topographic and layered medium factors on surface coseismic deformation. The main research results are as follows:

       (1) The spectral element approach quantifies the effect of topographic factors on ground surface coseismic deformation. In this work, we looked at several fault models, including strike-slip, dip-slip, and tensional faults, and compared their results to the Okada analytical solution. Our investigation demonstrates that the simulation results generated using the spectral element method closely match the Okada analytical solution, with a maximum variation of only 3%. We also estimated the coseismic displacement field using the parabolic hill model and compared it to the results obtained using the planar model. Our findings show that topographic parameters influence both the distribution pattern and the amplitude of coseismic displacement.  Consequently, we conclude that the impact of topographic factors must be considered when inverting coseismic deformation.

(2) In the study of seismic coseismic deformation, both topographic and layered media play important roles. This paper utilizes topographic data, media parameter models, and fault models particular to the Lushan region to investigate the impact of topographic factors and layered media on the coseismic deformation of the 2013 Lushan Ms7.0 earthquake using the spectral element approach. The results demonstrate that compared to layered media, topographic factors exert a more pronounced influence on the coseismic deformation of the Lushan earthquake. The maximum impact of topographic factors on the coseismic deformation component along the fault strike direction reaches ~17.3%, while for the component along the vertical fault strike direction, it reaches ~20.6%. In contrast, the influence of layered media on the coseismic deformation components along the fault strike direction and the vertical fault strike direction is ~3.6% and ~2.2%, respectively. When considering both topographic and layered media factors comprehensively, their effects on the coseismic deformation components along the fault strike direction and the vertical fault strike direction are ~17.5% and ~18.3%, respectively.

(3) Based on the fault model of the Lushan earthquake considering topographic factors, the variations in topographic effects were explored when changing fault parameters. The research findings indicate that when the fault dip ranges between 30° and 40°, the impact of topographic factors on coseismic deformation is approximately ~18%. When the fault dip is between 45° and 65°, this impact decreases to ~15%, and when the fault dip ranges between 70° and 90°, the influence of topographic factors exceeds 18%. As the depth of the earthquake source increases, the topographic effect diminishes. However, altering the magnitude of fault slip does not significantly affect the influence of topographic factors.

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