Multiscale Seismic Tomography
Multiscale Seismic Tomography
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DOI：
10.1007/978-4-431-55360-1
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发表时间：
2015-02
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影响因子：
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通讯作者：
Dapeng Zhao
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文献类型：
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作者：
Dapeng Zhao
地震走时层析成像通常是离散化的截断展开所追求的模型在选定的基函数。参数化是否会影响给定数据集的实际分辨率以及由此产生的地球模型的鲁棒性长期以来一直存在严重争议。然而，从模型分辨率的角度来看，地震层析成像的参数化问题的一个重要方面尚未得到系统的探讨，即所选参数化的空间频率局部化。事实上，这两种最常见的参数化倾向于在它们各自的特定域中强制解析。也就是说，在具有全局支持的球面谐波方面的参数化倾向于强调光谱分辨率，同时牺牲空间分辨率，而compensated支持的像素倾向于以相反的方式表现。当处理非均匀采样的数据集时，层析模型之间的一些显著差异很可能是这种效应的表现。以S-SKStraveltimes层析反演D″层横向横波非均匀性为例，给出了一种基于多分辨率表示的参数化方法。不像以前的尝试调用像素的大小可变的多尺度反演，或覆盖几层的镶嵌与不同的网格间隔，我们的配方调用双正交广义Harr小波的球体。我们表明，多分辨率表示可以很容易地从现有的基于块的离散化。所追求的模型结构的自然尺度层次结构受给定采样的分辨率的约束被嵌入在所获得的解决方案中。它提供了一种基于实际射线路径采样的自然正则化方案，因此不受大多数正则化方案固有的优先偏见的影响。与通过球谐函数或球形块获得的解决方案，往往崩溃的结构到射线路径上，我们的参数化施加区域变化的奈奎斯特限制，也就是说，鲁棒性可分辨的本地波长带内获得的解决方案。
Seismic traveltime tomography is commonly discretized by a truncated expansion of the pursued model in terms of chosen basis functions. Whether parametrization affects the actual resolving power of a given data set as well as the robustness of the resulting earth model has long been seriously debated. From the perspective of the model resolution, however, there is one important aspect of the parametrization issue of seismic tomography that has yet to be systematically explored, that is, the space–frequency localization of a chosen parametrization. In fact, the two most common parametrizations tend to enforce resolution in each of their own particular domains. Namely, parametrization in terms of spherical harmonics with global support tends to emphasize spectral resolution while sacrificing the spatial resolution, whereas the compactly supported pixels tend to behave in the opposite manner. Some of the significant discrepancies among tomographic models are very likely to be manifestations of this effect, when dealing with data sets with non-uniform sampling. With an example of the tomographic inversion for the lateral shear wave heterogeneity of the D″ layer usingS–SKStraveltimes, we demonstrate an alternative parametrization in terms of the multiresolution representation of the pursued model function. Unlike previous attempts of multiscale inversion that invoke pixels with variable sizes, or overlay several layers of tessellation with different grid intervals, our formulation invokes biorthogonal generalized Harr wavelets on a sphere. We show that multiresolution representation can be constructed very easily from an existing block-based discretization. A natural scale hierarchy of the pursued model structure constrained by the resolving power of the given sampling is embedded within the solution obtained. It provides a natural regularization scheme based on the actual ray-path sampling and is thus free froma prioriprejudices intrinsic to most regularization schemes. Unlike solutions obtained through spherical harmonics or spherical blocks that tend to collapse structures onto ray paths, our parametrization imposes regionally varying Nyquist limits, that is, robustly resolvable local wavelength bands within the obtained solution.