| 利用反透射系数确定理论地震图计算过程中的积分限阈值 |
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| 引用本文： | 吴永祺,张海明.利用反透射系数确定理论地震图计算过程中的积分限阈值[J].地震学报,2018,40(6):719-727. |
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| 作者姓名： | 吴永祺 张海明 |
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| 作者单位： | 中国北京100871北京大学地球与空间科学学院 |
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| 基金项目： | 国家自然科学基金（41674050）资助 |
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| 摘 要： | 本文尝试基于理论分析来求解积分限阈值kc，即通过反透射系数来确定kc。根据计算理论地震图的广义反透射系数法，在反透射系数中进行求逆运算的矩阵行列式的零点将会使得被积函数产生较大的变化，通过具体实例显示出自由界面处的反射系数中含有的零点可以作为合适的kc。多种情况的实例显示，通过反射系数来确定kc具有较好的普适性。通过与经验公式的计算结果进行比对，表明根据本文方案所确定的kc在保证准确性的同时可以有效地提高计算效率。
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| 关 键 词： | 分层半空间 理论地震图 瑞雷函数 数值积分 峰谷平均法 |
| 收稿时间： | 2018-01-15 |
Determining the threshold value in upper limit of wavenumber integration by reflection-transmission coefficient in theoretical seismograms calculation |
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| Affiliation: | School of Earth and Space Sciences，Peking University，Beijing 100871，China |
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| Abstract: | In multi-layered half-space, the displacement field is expressed as the integration of wavenumber k using reflection-transmission (R/T) coefficient when the seismogram is calculated in numerical ways in the frequency domain. Therefore, some special methods were introduced to solve those kinds of integration as to accelerate computation. For example, when the depth of source is equal or close to that of receiver, the peak-trough averaging method (PTAM) is applied. To apply PTAM, however, one must determine the threshold value called kc after which the integration oscillates regularly. In previous studies, kc was estimated empirically without theoretical support. In this study, a scheme based on theoretical analysis to determine kc is proposed, and kc is related to the R/T coefficients. According to the generalized R/T coefficient method, violent variation of integrand will occur when the determinant of relevant R/T coefficient vanishes. We show by examples that for a given frequency, root of the determinant of the reflection coefficient on the free surface is a proper value for kc. Compared with the method calculated with empirical formula, the new method to determine kc will be more efficient for a given precision to prove the validity. |
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