基于MINRES-QLP截断牛顿法的全波形反演

在全波形反演过程中,二阶梯度信息扮演着重要的作用.然而,由于其巨大的计算量和内存需求,限制了其在全波形反演问题中的应用.本文基于MINRES-QLP方法提出了一种高效的截断牛顿全波形反演方法.该全波形反演方法能够充分利用目标泛函的二阶梯度信息,提高反演精度.MINRES-QLP反演方法还能够利用Hessian阵负特征值信息,从而提高算法的重构分辨率和计算效率.针对Hessian阵计算难题,本文给出了一种矩阵向量相乘的快速算法.基于二维2004 BP模型,Sigsbee模型,验证了MINRES-QLP截断牛顿反演方法的有效性.数值结果表明MINRES-QLP截断牛顿法能充分利用二阶梯度信息和Hessian阵负特征值信息,从而加速算法收敛速度和提高成像精度.     

一维波动方程联合反演的分步正则化法

本文只用一个纵波信息,对一维波动方程的速度和震源函数进行联合反演.并考虑到波动方程的反问题是一不适定问题,对震源函数和波速分别用正则化法分步迭代求解,大大减少了反问题的计算工作量,改善了该反问题的计算稳定性.为计算实际一维地震数据提供了一种方法.文中给出了只用一个反问题补充条件同时进行多参数反演的详细公式,并对相应的数值算例进行了分析和比较.     

求解地震波反演问题的一类预处理共轭梯度方法

地质勘探中的全波形反演模型可以转化为一个求解带微分方程约束的最小二乘问题,这类模型通过扩大了搜索区域,减少了变量的储存,提高了计算效率.基于上述模型,采用有限差分方法离散Helmholtz方程,提出一类预处理共轭梯度法求解地震波场,并交替更新地层信息.数值实验中测试和比较了对角预处理、Gauss-Seidel预处理和不完全LU分解三种预处理方法,实验结果表明这类预处理方法应用到共轭梯度法中能够减少迭代步数、改善实验精度,加快反演迭代效率.     

基于模拟退火地震反演技术——以X油田某区为例

为了提高地震反演预测的分辨率和可信度,提出了线性反演与非线性反演二者相结合的反演方法——以稀疏脉冲反演结果为约束背景的基于模拟退火的反演方法,阐述了基于模拟退火法的反演机理,并以X油田某区为例,开展了基于模拟退火地球物理反演预测,从反演分辨率、可信度和误差三个方面进行分析和定量研究.结果表明,非线性的随机反演与线性反演相结合有效地提高了反演分辨率,纵向上能够精细到单砂体级,反演结果多个概率的实现最大程度上降低反演的多解性,并且,反演结果的精度较高,2m以上砂岩反演符合率均在90%以上.     

基于系统识别方法的围岩弹性模量及水平地应力反演分析

利用有限元软件建立隧道开挖正演模型,基于新奥法隧道施工现场实测围岩收敛数据,采用灵敏度分析建立了参数调整算法,利用系统识别方法对隧道围岩弹性模量及水平地应力进行了反演分析,并讨论了初始值的影响.结果表明,系统识别反演分析法具有自适应能力强、反演分析过程收敛计算稳定性好和计算速度快等优点,在隧道及地下工程领域具有广阔的应用前景.     

Abel变换数值反演的积分算子方法

本文研究了Abel变换的数值反演问题.利用Abel变换的理论反演公式与数值求导的积分算子法相结合的方法,对反演公式中奇异积分合理处理,获得Abel变换数值反演的一种算法,并进行了理论分析与数值实验. 结果表明该算法具有计算简单、数值稳定等优点.     

一种确保收敛的弹性波反演迭代解法

本文研究弹性波反演的数值解法,文中通过不断构造虚拟震源,变换优化解法的目标函数,使得对任何初始背景计算都能收敛于真实解;该方法不仅解次了优化法的收敛问题,还通过改变目标函数曲面的性态,提高了收敛速度。     

某些数学方法在地震波反演问题求解中的应用

本文以地震波广义散射（包括透射、折射、反射、绕射等）为背景，对其反演问题的发展状况做了一个回顾．文中着重介绍了在地震波逆散射问题研究过程中，各种数学、物理的基本理论和基本假设是如何被应用于非线性偏微分方程这一复杂问题的求解过程的，同时，结合对地震波逆散射问题的认识，简单介绍了与之相关的数学方法及其在应用中存在的问题。     

应用地震反演技术预测储层

为了解决开发过程中储层精细刻画难题,提出将曲线重构地震反演技术引入带储层预测工作中,根据曲线不同频带范围对砂岩敏感性特征,开展基于高频恢复、低频补偿原来的曲线重构技术开展地震反演预测.通过对南八区西部的地震反演实例表明:对于大于2m砂岩分辨能力较高的,隔层太小时,两套砂岩只能当一套砂岩组合反演出来;对于小于2米的砂岩,只有当隔层大于4m条件下才能清晰识别.地震反演能很好的推测地下岩层结构和物性参数的空间分布,有效的提高了薄储层预测精度.     

一些反演关系的反演链

本文主要提出和讨论了一般反演关系的反演链和反演对的理论.在此基础上,具体给出Gould-Hsu反演的两类反演链和Gould-Hsu反演的q-模拟的相关问题.最后,本文结合一些常用的反演对,建立了众多的组合恒等式.     

On Quadratic Wasserstein Metric with Squaring Scaling for Seismic Velocity Inversion

The quadratic Wasserstein metric has shown its power in comparing probability densities. It is successfully applied in waveform inversion by generating objective functions robust to cycle skipping and insensitive to data noise. As an alternative approach that converts seismic signals to probability densities, the squaring scaling method has good convexity and thus is worth exploring. In this work, we apply the quadratic Wasserstein metric with squaring scaling to regional seismic tomography. However, there may be interference between different seismic phases in a broad time window. The squaring scaling distorts the signal by magnifying the unbalance of the mass of different seismic phases and also breaks the linear superposition property. As a result, illegal mass transportation between different seismic phases will occur when comparing signals using the quadratic Wasserstein metric. Furthermore, it gives inaccurate Fréchet derivative, which in turn affects the inversion results. By combining the prior seismic knowledge of clear seismic phase separation and carefully designing the normalization method, we overcome the above problems. Therefore, we develop a robust and efficient inversion method based on optimal transport theory to reveal subsurface velocity structures. Several numerical experiments are conducted to verify our method.     

A NEW INVERSION METHOD OF TIME-LAPSE SEISMIC

Time-Lapse Seismic improves oil recovery ratio by dynamic reservoir monitoring. Because of the large number of seismic explorations in the process of time-lapse seismic inversion, traditional methods need plenty of inversion calculations which cost high computational works. The method is therefore inefficient. In this paper, in order to reduce the repeating computations in traditional, a new time-lapse seismic inversion method is put forward. Firstly a homotopy-regularization method is proposed for the first time inversion. Secondly, with the first time inversion results as the initial value of following model, a model of the second time inversion is rebuilt by analyzing the characters of time-lapse seismic and localized inversion method is designed by using the model. Finally, through simulation, the comparison between traditional method and the new scheme is given. Our simulation results show that the new scheme could save the algorithm computations greatly.     

Forward and Inverse Viscoacoustic Modelling in a Tunnel Environment

In this work, the goal is to model forward acoustic waves in a tunnel environment with attenuation and to do full waveform inversion. In reality, there is no material without attenuation. Some materials, such as rocks, have so low attenuation that, in a small domain, the waves are almost not damped at all. At the same time, there are materials with high attenuation. In an environment with such materials, the attenuation has to be taken into account in order to model the waves properly. In this study, attenuation effect is integrated into acoustic equation by using Kolsky-Futterman model ( [1], [2]) which only replaces velocity field with a complex-valued field in frequency domain. Apart from attenuation, another objective is to consider an inhomogeneous density field. Mainly, acoustic equation with a constant density field is referred to in many studies. In many cases, it may suffice to model waves appropriately. However, in reality, the density field of ground can be highly inhomogeneous. The objective is to investigate the effect of the inhomogeneity in waves, and to search for density field ρ and attenuation parameter Q as well as pressure wave velocity c using full waveform inversion. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hierarchical approach of seismic full waveform inversion

Full waveform inversion (FWI) of seismic traces recorded at the free surface allows the reconstruction of the physical parameters structure on the underlying medium. For such a reconstruction, an optimization problem is defined, where synthetic traces, obtained through numerical techniques as finite-difference or finite-element methods in a given model of the subsurface, should match the observed traces. The number of data samples is routinely around 1 billion for 2D problems and 1 trillion for 3D problems while the number of parameters ranges from 1 million to 10 million degrees of freedom. Moreover, if one defines the mismatch as the standard least-squares norm between values sampled in time/frequency and space, the misfit function has a significant number of secondary minima related to the ill-posedness and the nonlinearity of the inversion problem linked to the so-called cycle skipping. Taking into account the size of the problem, we consider a local linearized method where gradient is computed using the adjoint formulation of the seismic wave propagation problem. Starting for an initial model, we consider a quasi-Newtonian method, which allows us to formulate the reconstruction of various parameters such as P and S waves velocities or density or attenuation factors. A hierarchical strategy based on the incremental increase of the data complexity starting from low-frequency content to high-frequency content, from initial wavelets to later phases in the data space from narrow azimuths to wide azimuths and from simple observables to more complex ones. Different synthetic examples on realistic structures illustrate the efficiency of this strategy based on the data manipulation. This strategy related to the data space has to be inserted into a more global framework where we could improve significantly the probability to converge to the global minimum. When considering the model space, we may rely on the construction of the initial model or add constraints such as smoothness of the searched model and/or prior informations collected by other means. An alternative strategy concerns the building of the objective function and various possibilities must be considered, which may increase the linearity of the inversion procedure.     

基于贝叶斯一稀疏约束正则化方法的地震波形反演

将稀疏约束正则化方法应用于地震波形反演问题.为了减弱对稀疏约束项的光滑性要求,引入贝叶斯推断,产生一组收敛于后验分布的采样点.通过数值算例记录了采样点的条件期望、方差、置信区间等具有统计意义的结果.数值结果表明,在没有光滑性的要求下,稀疏约束正则化方法对孔洞模型和分层模型中的介质边缘有良好的识别能力.特别地,当减少观测数据时,稀疏约束正则化方法仍能获得较好的反演结果.     

多偏移距电磁波数值成像的高阶FDTD法研究

数值模拟是数据处理和反演解释的重要环节,为提高高频电磁波层析成像技术在工程勘察中的解译准确性,采用高阶时间域有限差分法(FDTD(2阶时间精度,4阶空间精度))模拟电磁波在溶洞地电模型下的数值成像,并采用多偏移距模式采集电磁波道集.分析了电磁波的波场快照图和波形剖面图,总结了电磁波在溶洞地质体中的传播规律,为实际工程勘察工作提供可靠依据.数值试验结果表明,FDTD(2,4)能高精度模拟电磁波在溶洞复杂介质中的数值成像和多偏移距采集模式具有高效性和灵活性.     

High-performance computer simulation of wave processes in geological media in seismic exploration

A class of problems arising in seismic exploration are investigated, namely, seismic signal propagation in multilayered geological rock and near-surface disturbance propagation in massive rock with heterogeneities, such as empty or filled fractures and cavities. Numerical solutions are obtained for wave propagation in such highly heterogeneous media, including those taking into account the plastic properties of the rock, which can be manifested near a seismic gap or a wellbore. All types of explosion-generated elastic and elastoplastic waves and waves reflected from fractures and the boundaries of the integration domain are analyzed. The identification of waves in seismograms recorded with near-surface receivers is addressed. The grid-characteristic method is used on triangular, parallelepipedal, and tetrahedral meshes with boundary conditions set on the rock-fracture interface and on free surfaces in explicit form. The numerical method proposed is suitable for the study of the interaction between seismic waves and heterogeneous inclusions, since it ensures the most correct design of computational algorithms on the boundaries of the integration domain and at media interfaces. A parallel software code implemented with the help of OpenMP and MPI was used to execute computations on parallelepipedal and tetrahedral grids.