Noise cross-correlation sensitivity kernels
Noise cross-correlation sensitivity kernels
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DOI：
10.1111/j.1365-246x.2010.04721.x
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发表时间：
2010-11
影响因子：
2.8
通讯作者：
J. Tromp;Yang Luo;S. Hanasoge;D. Peter
中科院分区：
文献类型：
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作者：
J. Tromp;Yang Luo;S. Hanasoge;D. Peter
摘要我们根据噪声互相关测量确定地震干涉测量的有限频率灵敏度核。在噪声空间不相关但不均匀的假设下，我们确定了两个地理位置不同的合成地震记录之间的整体平均互相关。通过最大限度地减少观测和模拟合奏互相关之间的差异的措施，受约束的模拟波场满足地震波方程，我们获得合奏灵敏度内核。这些集合核反映了集合互相关测量对模型参数变化的敏感性，例如质量密度、剪切和压缩波速度以及噪声的空间分布。基于两个波场之间的相互作用来计算集合核：集合前向波场和集合伴随波场。为了获得系综前向波场，首先计算通过在第一接收器的位置处插入由噪声的特性确定的信号而获得的生成波场，将该计算的结果保存在生成噪声的位置处，即，通常在地球表面（的一部分）上。接下来，使用该生成波场作为与第一接收器相关联的总体前向波场的源。集合伴随波场是通过使用模拟和观测集合互相关之间的测量作为位于第二接收器处的震源来获得的。系综前向波场和伴随波场之间的相互作用'绘制'系综灵敏度核。我们说明了合奏内核的建设和他们的性质在二维和三维使用谱元素的方法。除了连接两个接收器的"香蕉甜甜圈"功能之外，如在传统的有限频率地震层析成像中，一些噪声互相关灵敏度内核表现出从每个接收器在远离另一个接收器的方向上突出的双曲线"射流"。在全局模型中，对于长周期（T> 50 s）非均匀噪声的包络灵敏度核表现出沿沿着次弧和主弧的灵敏度。这些内核反映了这样一个事实，即测量通常涉及包括多轨道表面波的长时间序列。像自由振荡一样，这种测量对通过两个接收器的沿着大圆的结构敏感。从噪声互相关层析成像的角度来看，我们讨论了在地面和日震反演的策略。
SUMMARY We determine finite-frequency sensitivity kernels for seismic interferometry based upon noise cross-correlation measurements. Under the assumptions that noise is spatially uncorrelated but non-uniform, we determine ensemble-averaged cross correlations between synthetic seismograms at two geographically distinct locations. By minimizing a measure of the difference between observed and simulated ensemble cross correlations—subject to the constraint that the simulated wavefield satisfies the seismic wave equation—we obtain ensemble sensitivity kernels. These ensemble kernels reflect the sensitivity of ensemble cross-correlation measurements to variations in model parameters, for example, mass density, shear and compressional wave speeds and the spatial distribution of noise. Ensemble kernels are calculated based upon the interaction between two wavefields: an ensemble forward wavefield and an ensemble adjoint wavefield. To obtain the ensemble forward wavefield, one first calculates a generating wavefield obtained by inserting a signal determined by the characteristics of the noise at the location of the first receiver, saving the results of this calculation at locations where noise is generated, that is, typically on (a portion of) the Earth's surface. Next, one uses this generating wavefield as the source of the ensemble forward wavefield associated with the first receiver. The ensemble adjoint wavefield is obtained by using measurements between simulated and observed ensemble cross correlations as a seismic source located at the second receiver. The interaction between ensemble forward and adjoint wavefields ‘paints’ ensemble sensitivity kernels. We illustrate the construction of ensemble kernels and their nature in two and three dimensions using a spectral-element method. In addition to a ‘banana-doughnut’ feature connecting the two receivers, as in traditional finite-frequency earthquake tomography, some noise cross-correlation sensitivity kernels exhibit hyperbolic ‘jets’ protruding from each receiver in a direction away from the other receiver. Ensemble sensitivity kernels for long-period (T > ∼ 50 s) non-uniform noise in global models exhibit sensitivity along the minor and major arcs. These kernels reflect the fact that measurements typically involve long time-series that include multi-orbit surface waves. Like free oscillations, such measurements are sensitive to structure along the great circle through the two receivers. From the perspective of noise cross-correlation tomography, we discuss strategies for inversions in terrestrial and helioseismology.