Smoothness criteria in surface wave tomography
Smoothness criteria in surface wave tomography
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DOI：
10.1111/j.1365-246x.1990.tb00530.x
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发表时间：
1990-07
影响因子：
2.8
通讯作者：
T. Yanovskaya;P. Ditmar
中科院分区：
文献类型：
--
作者：
T. Yanovskaya;P. Ditmar
本文在几何射线近似的框架下，对表面波层析成像方法作了进一步的讨论和发展。用于确定横向相位或群速度分布的一般方法（其是标准的2-D层析成像问题）涉及线性化、将未知函数表示为在一些基函数中的级数以及通过线性代数方法评估系数。如果波路径不均匀地覆盖被调查的区域，则不应先验地选择基函数，而应根据路径的图案来构造基函数。比较了构造基函数的不同准则，并考虑了它们之间的关系。一种更可取的方法是联合解释不同时期的相速度和群速度数据，因为它允许由于使用群速度数据而扩大关于相速度变化的信息。相位和群走时都表示为未知相位慢度校正的线性泛函。数据核的特定形式允许基函数被表示为两个函数的乘积，一个取决于水平坐标，另一个取决于频率。
SUMMARY We discuss and develop further the methods of surface wave tomography in the frame of the geometric ray approximation. The general approach for determining the lateral phase or group velocity distribution, which is a standard 2-D tomography problem, involves linearization, representation of the unknown function as a series in some basis functions, and evaluation of the coefficients by the methods of linear algebra. If the wave paths cover the area under investigation non-uniformly, the basis functions should not be chosen a priori, but constructed proceeding from the pattern of paths. Different criteria for constructing the basis functions are compared, and a relation between them is considered. A more preferable approach is joint interpretation of phase and group velocity data for different periods, because it allows the information about phase velocity variations to be enlarged due to the use of the group velocity data. Both the phase and group traveltimes are represented as linear functionals of the unknown phase slowness corrections. A specific form of the data kernels allows the basis functions to be represented as a product of two functions, one depending on the horizontal coordinates, and the other on frequency.