高阶面波频散曲线的提取及华北克拉通地区三维S波速度构建

目前面波成像主要使用的是基阶频散曲线，反演会存在非唯一性和不稳定等问题。在反演中加入高阶频散曲线可以提高反演模型的分辨率和增加反演的稳定性。然而在面波成像尤其是大尺度的面波成像中多阶频散曲线的提取是一个难点。目前很多从台阵数据提取多阶频散曲线的方法暗含了平面波假设。而最近提出的频率-贝塞尔变换法（F-J 法）没有平面波假设，适用于小区域频散曲线的提取。但使用 F-J 法提取频散曲线时，运行时间长，频散谱中频散曲线的分辨率较低。为此本文基于压缩感知对 F-J 法进行了改进。使用了两种方法来求解此压缩感知反演问题，一种方法是基于 𝑙1 范数的优化算法，另一种方法是贝叶斯方法。合成和实际数据测试用来验证此压缩感知方法的有效性。该压缩感知方法提取的频散曲线和 F-J 法提取的相一致。但与 F-J 法相比，该压缩感知方法具有运行时间短，频散能量图分辨率高和信噪比高的优点。该压缩感知方法能够快速提取高分辨率的多阶频散曲线，为地下速度结构反演提供了基础。

华北克拉通因其东部岩石圈遭到强烈破坏而吸引了大量的研究。目前对华北克拉通岩石圈的破坏范围，尤其是地壳的变形和破坏程度，破坏机制和大同火山的起源等还不是很清楚。精细的三维地壳和上地幔速度结构可以为理解这些问题提供约束。但以前的面波成像只使用了周期较长的基阶频散曲线，因此缺乏对地壳结构的约束。为了从背景噪音中提取多阶频散曲线，本文将 F-J 法应用到华北克拉通地区密集台站记录的背景噪音数据中。将整个研究地区划分成很多子区域，利用 F-J 法分别从每个子区域台阵记录的背景噪音中提取多阶频散曲线，构建了华北克拉通地区基阶和第一到第五高阶的相速度图。基阶相速度图在短周期与地表地质构造相吻合，基阶长周期和高阶相速度图显示在大同火山附近有大尺度的低速异常，可能为软流圈物质上涌引起。高阶频散曲线可以提供对地壳速度结构的约束，为后面精细三维地壳和上地幔速度模型的构建提供了基础。

为得到华北克拉通地区的速度结构，分别对每个子区域的频散曲线进行反演得到该子区域的一维 S 波速度结构，然后将所有子区域的一维 S 波速度结构进行插值，得到了华北克拉通地区精细的三维地壳及上地幔 S 波速度结构。在反演中，对于大多数子区域使用了频率更高的基阶频散曲线和高阶频散曲线，提高了地壳速度结构垂向分辨率。本文的三维 S 波速度模型显示，东部块体的地壳比较薄（∼30 km），中西部块体的地壳厚（∼40 km），中部造山带中北部的地壳厚度比中南部的大。在上地壳，陕西山西裂缝为线状的相对的低速异常，对应厚的沉积层。在上地幔，在该裂缝的北部为低速异常，其岩石圈可能发生了减薄，中南部存在一个明显的高速异常，可能为残留的太古代克拉通。该速度模型显示在中下地壳和上地幔，中西部块体的北部为大范围的低速区，且大同火山附近的低速异常幅值更低，推测可能是地幔深处的热物质上涌引起。该速度模型还显示在中部块体和西部块体的北部有广泛的中地壳低速层，这可能是由岩浆底侵作用造成的地壳物质部分熔融引起。本文构建的精细三维地壳和上地幔速度结构为研究华北克拉通的破坏范围，华北克拉通的地壳变形和大同火山的起源等问题提供了参考。

Current surface wave tomography mainly used dispersion curves of fundamental mode surface waves, and thus the inversion of dispersion curves suffered from nonuniqueness and instability. The addition of higher modes to the inversion can improve the resolution of inverted models and strengthen the stability of the inversion. However, the extraction of multimodal dispersion curves from seismic data is a challenge in surface wave tomography, especially in large-scale surface wave tomography. For most methods of extracting multimodal dispersion curves from array data, the assumption of plane wave propagation is implied. The recently proposed frequency-Bessel transform (F-J) method doesn’t make the assumption of plane wave propagation, so it is more suitable for the extraction of dispersion curves from array data in a small region. However, the F-J method takes long running time and the spectrograms obtained by the F-J method have a low resolution. In this study, the F-J method is improved based on compressed sensing (CS). The CS inverse problem is solved by using two methods: an 𝑙1-based optimization algorithm and a Bayesian method. Synthetic and field data tests are conducted to validate the CS method. The dispersion curves extracted by the CS methods are consistent with those extracted by the F-J method, but the CS methods are more efficient and the spectrograms extracted by the CS methods can have a higher resolution and higher signal-to-noise ratio than those by the F-J method. The CS methods can quickly extract high-resolution multimodes from ambient noise, thereby providing a basis for the inversion for the subsurface velocity structure.

The North China Craton (NCC) has attracted a large number of geophysical studies because of its strong cratonic lithosphere destruction in the eastern block. Now there are still a number of issues that are not very clear in the NCC, such as the spatial distribution of the cratonic destruction, especially crustal deformation and the extent of crustal destruction, the destruction mechanism and the origin of the Datong volcanoes. A fine three-dimentional (3-D) velocity model of the crust and uppermost mantle in the NCC can provide constraints on understanding these questions. However, only fundamental-mode dispersion curves of long periods are used in previous surface wave tomography studies beneath the NCC, and the detailed constraints on the crustal structure of the NCC are lacked. To extract multimodal dispersion curves from ambient noise, the F-J method is applied to the ambient noise data recorded by the dense stations in the NCC. The entire study region is divided into many sub-regions, the F-J method is used to extract multimodal dispersion curves from the ambient noise recorded by each sub-regional stations and phase velocity maps of the fundamental and first to fifth higher modes are constructed in the NCC. The phase velocity maps of the fundamental mode at the short periods are consistent with the surface geological structures. The fundamental-mode phase velocity maps at the long periods and the phase velocity maps of the higher modes show a large-scale low-velocity anomaly near the Datong volcanoes, which may be caused by the upwelling of asthenospheric material. The dispersion curves of higher-mode surface waves can provide additional constraints on the crustal structure, which can provide a basis for imaging a high-resolution 3-D S-wave velocity model of the crust and uppermost mantle in the NCC.

To obtain a more reliable velocity model in the NCC, the dispersion curves are inverted to obtain a one-dimensional (1-D) S-wave velocity structure for each sub-region, and then the 1-D S-wave velocity models of all sub-regions are integrated to obtain a fine 3-D S-wave velocity structure of the crust and uppermost mantle in the NCC. A high-frequency fundamental mode and higher modes are used in the inversion for most sub-regions, so the vertical resolution of the crustal velocity structure is improved. The 3-D S-wave velocity structure shows that the eastern block has a thin crust (∼30 km), the Trans-North China Orogen (TNCO) and western bock have a thick crust (∼40 km) and the central-northern part of the TNCO has a thicker crust than that of the central-southern part. In the upper crust, the Shaanxi-Shanxi rift shows a linearly relative low-velocity anomaly, which corresponds to thick sediments. In the upper mantle, the north of the rift is characterized by low velocities, indicating its lithosphere may be thinned and the central-southern part of the rift is imaged as an apparent high-velocity patch, a possible remnant of a Archean craton. The model shows that in the middle-lower crust and upper mantle, a large-scale low-velocity area is observed at the northern part of the TNCO and western block, and the low-velocity anomaly near the Datong volcanoes has a lower amplitude, which may be caused by the upwelling of hot materials in the deep upper mantle. The results also show extensive low-velocity layers exist in the middle crust beneath the north of the TNCO and western block, which may be caused by partial melting of the middle crust associated with magmatic underplating. The detailed 3-D crustal and upper-mantle velocity model of the NCC constructed in this study can provide a reference for studying the spatial extent of the cratonic destruction, crustal deformation of the NCC and the origin of the Datong volcanoes.

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