Seismic waveform modelling in a 3-D Earth using the Born approximation: Potential shortcomings and a remedy
Seismic waveform modelling in a 3-D Earth using the Born approximation: Potential shortcomings and a remedy
复制标题
使用玻恩近似在 3-D 地球中进行地震波形建模：潜在缺点和补救措施
DOI：
10.1111/j.1365-246x.2008.04050.x
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发表时间：
2009
影响因子：
2.8
通讯作者：
B. Romanowicz
中科院分区：
文献类型：
--
作者：
M. Panning;Y. Capdeville;B. Romanowicz
总结 虽然使用一阶玻恩近似来计算 3-D 地球模型中的地震观测值和灵敏度核显示出改进层析成像建模的希望，但与更标准的渐近方法相比，还需要做更多的工作来系统地确定此类方法对真实地震数据进行建模的效果。迄今为止，大多数工作都集中在辅助数据的分析上，例如相速度，而不是时域波形。我们在这里比较使用标准渐近近似（消除了对大圆平面上 3-D 结构的敏感性）为简单模型获得的合成波形，以及使用 3-D 线性 Born 近似获得的合成波形，以及精确的数值 3-D 合成。毫不奇怪，我们发现 3-D Born 可以更准确地模拟速度异常的扰动效应，这些速度异常的波长与第一菲涅尔区相当或小于第一菲涅尔区。然而，较大的波长和幅度异常很容易产生较大的相位延迟，导致一阶（线性）玻恩近似失效，而将相位异质性影响而不是波形幅度的异质性影响纳入其中的渐近方法则更为稳健。在玻恩计算的波形中加入路径平均相位延迟，可以显着提高长波长结构情况下的精度，同时仍然保留正确建模短波长结构效应的能力。在结构波长与现有全球地震模型一致的随机模型中进行的测试表明，线性玻恩近似在现实地球模型中经常崩溃，在所有测试距离（>20•）上，与基于大圆的近似相比，第一和第二轨道瑞利和更高模式表面波形的失配更严重。对于基本模式，使用线性玻恩形式计算的波形的平均失配非常差，特别是对于大于 60 • 的距离。修改后的玻恩形式持续改进了相对于线性玻恩波形的拟合，但仅优于高模表面波形的基于大圆的近似。然而，我们注意到，从玻恩近似开发的用于基模瑞利波相速度的多锥度测量的相位延迟内核并没有证明与线性波形内核相关的问题。与测量结果普遍一致，并且相对于路径平均近似预测的相位延迟有适度的改进。
S U M M A R Y Although the use of the first-order Born approximation for the computation of seismic observ-ables and sensitivity kernels in 3-D earth models shows promise for improving tomographic modelling, more work is necessary to systematically determine how well such methods forward model realistic seismic data compared with more standard asymptotic methods. Most work so far has been focused on the analysis of secondary data, such as phase velocity, rather than time domain waveforms. We here compare synthetic waveforms obtained for simple models using standard asymptotic approximations that collapse the sensitivity to 3-D structure on the great circle plane and those obtained using the 3-D linear Born approximation, with accurate numerical 3-D synthetics. We find, not surprisingly, that 3-D Born more accurately models the perturbation effects of velocity anomalies that are comparable in wavelength to or are smaller than the first Fresnel zone. However, larger wavelength and amplitude anomalies can easily produce large phase delays that cause the first-order (linear) Born approximation to break down, whereas asymptotic methods that incorporate the effect of heterogeneity in the phase rather than in the amplitude of the waveform are more robust. Including a path average phase delay to the Born calculated waveforms significantly improves their accuracy in the case of long-wavelength structure, while still retaining the ability to correctly model the effect of shorter-wavelength structure. Tests in random models with structural wavelengths consistent with existing global seismic models indicate that the linear Born approximation frequently breaks down in realistic earth models, with worse misfit for first and second orbit Rayleigh and higher mode surface waveforms than the great-circle based approximations at all distances tested (>20 •). For fundamental modes, the average misfit for the waveforms calculated with the linear Born formalism is quite poor, particularly for distances larger than 60 •. The modified Born formalism consistently improves the fit relative to the linear Born waveforms, but only outperforms the great-circle based approximations for the higher mode surface waveforms. We note, however, that phase delay kernels for multitaper measurements of fundamental mode Rayleigh wave phase velocities developed from the Born approximation do not demonstrate the problems associated with the linear waveform kernels. There is general agreement with measurements and moderate improvement relative to phase delays predicted by the path-average approximation.