地震层析成像是计算地球物理学中的重要问题，也是计算数学中的交叉性前沿课题。近年来，随着计算机性能的高速发展，研究者们可以通过求解复杂的波动方程来获得地下参数的成像。与基于高频近似的传统射线层析成像方法相比，波形伴随层析成像方法不仅可以更精确地描述地震波的传播过程，而且还利用了地震波的后续振幅信息来约束地下结构，进而获得更高分辨率的模型。在实际问题中，地震波传播是具有衰减的，在以往的成像研究中，往往只关注地震波速度信息而忽略了地震波衰减的信息，这是由于对衰减的建模存在诸多困难。本文针对地震波衰减的波形伴随层析成像存在的计算代价高、速度-衰减容易产生伪影的困难，提出了若干的解决方案。在正演方面，本文选用基于图形处理器加速的粘弹性波方程求解方法。该方法基于一般标准线性固体的相关理论，结合谱元法精确地模拟了地震波的衰减效应，相比于弹性波方程数值求解方法增加的计算代价较少。此外，对于传统的基于 ?2 范数的方法广泛存在的速度-衰减串扰问题，本研究在层析成像中选用了基于包络的振幅目标函数。该目标函数将衰减特征与速度特征分离，可以有效地压制了多参数串扰现象。在反演的过程中，不同于一般的全批量梯度方法，本文的研究中引入小批量梯度下降方法。该方法以较小的计算代价近似计算敏感核，进而加速反演的过程。本文结合上述方法改进了基于全波形的衰减伴随层析成像算法。针对中国川滇地区以及南北地震带地区的实际数据，利用改进的基于全波形的衰减伴随层析成像算法，反演得到了中国川滇地区以及南北地震带地区地壳和上地幔的剪切波衰减模型。多组合成数据的测试表明了改进方法相对于传统方法的优越性，其中的分辨率测试展现出衰减模型具有良好的分辨率。生成的剪切波衰减模型详细地揭示了川滇地区和南北地震带区域上地幔的结构详细特征。实际资料的成像结果表明，大地震频繁发生在强衰减区域和强弱衰减过渡带上，提供了强震孕育机制的辅助推断。此外，成像结果中的强衰减异常为中下地壳流通道假说提供了新的证据，帮助我们更加深入地理解青藏高原东南缘的构造演化过程。
Seismic tomography is an important problem in computational geophysics and a cross-disciplinary frontier topic in computational mathematics. In recent years, with the rapid development of computer performance, researchers can solve complex wave equations to obtain imaging of underground parameters. Compared with the traditional ray-tracing tomography theory based on high-frequency approximations, the waveform tomography method can not only model seismic waves more accurately but also use the subsequent amplitude information of seismic waves to constrain the underground structure and obtain higher resolution models. In practical seismic problems, seismic wave propagation is attenuated, and the information of seismic wave attenuation was often ignored in previous imaging studies, which was due to the difficulties of modeling attenuation.In this paper, we propose multiple solutions to the difficulties of high computational cost and the artifacts in velocity-attenuation waveform inversion tomography. This paper employs a sophisticated graphics processing unit-accelerated viscoelastic wave equation simulation in forward modeling. This method is based on the general theory of linear solids and employs the spectral element method to precisely simulate the attenuation effect of seismic waves, with a lower computational cost compared to elastic wave equation simulation. Furthermore, in contrast to the widely encountered velocity-attenuation crosstalk problem in the traditional $L_{2}$ norm, this study employs an envelope-based amplitude objective function, which effectively isolates the attenuation feature from the velocity feature and suppresses multi-parameter crosstalk. In the inversion process, instead of using the general full-batch gradient method, this study employs a small-batch gradient descent method, which is a stochastic gradient descent method that approximates the sensitive kernel acceleration inversion process with a relatively smaller computational cost. By integrating the aforementioned approaches, an enhanced full-waveform attenuation adjoint tomography algorithm is developed.Based on real data from the Sichuan-Yunnan region and the North-South seismic zone in China, shear wave attenuation models of the crust and upper mantle of these regions are inverted using the enhanced full-waveform attenuation tomography algorithm. Multiple synthetic tests demonstrate the superiority of the improved method over traditional methods, and resolution tests indicate that the attenuation models are well resolved. The generated shear wave attenuation models reveal detailed structural features of the upper mantle in the Sichuan-Yunnan region and the North-South seismic zone. Tomography results from real data show that strong earthquakes frequently occur in areas of strong attenuation and in transition zones with strong and weak attenuation, providing auxiliary inference for the mechanism of strong earthquake generation. Additionally, the strong attenuation anomalies in the imaging results provide new evidence for the hypothesis of mid-lower crustal flow channels, helping us to better understand the tectonic evolution process of the southeastern margin of the Qinghai-Tibet Plateau.
