2D Laplace-Domain Waveform Inversion of Field Data Using a Power Objective Function

The wavefield in the Laplace domain has a very small amplitude except only near the source point. In order to deal with this characteristic, the logarithmic objective function has been used in many Laplace domain inversion studies. The Laplace-domain waveform inversion using the logarithmic objective function has fewer local minima than the time- or frequency domain inversion. Recently, the power objective function was suggested as an alternative to the logarithmic objective function in the Laplace domain. Since amplitudes of wavefields are very small generally, a power <1 amplifies the wavefields especially at large offset. Therefore, the power objective function can enhance the Laplace-domain inversion results. In previous studies about synthetic datasets, it is confirmed that the inversion using a power objective function shows a similar result when compared with the inversion using a logarithmic objective function. In this paper, we apply an inversion algorithm using a power objective function to field datasets. We perform the waveform inversion using the power objective function and compare the result obtained by the logarithmic objective function. The Gulf of Mexico dataset is used for the comparison. When we use a power objective function in the inversion algorithm, it is important to choose the appropriate exponent. By testing the various exponents, we can select the range of the exponent from 5 × 10^?3 to 5 × 10^?8 in the Gulf of Mexico dataset. The results obtained from the power objective function with appropriate exponent are very similar to the results of the logarithmic objective function. Even though we do not get better results than the conventional method, we can confirm the possibility of applying the power objective function for field data. In addition, the power objective function shows good results in spite of little difference in the amplitude of the wavefield. Based on these results, we can expect that the power objective function will produce good results from the data with a small amplitude difference. Also, it can partially be utilized at the sections where the amplitude difference is very small.     

CPU/GPU协同计算在频率域二维全波形反演中的应用

全波形反演利用波场的运动学和动力学信息重建地下物理参数,是建立高精度速度模型的有效手段,巨大的计算量是制约其实用化的瓶颈之一。本文针对全波形反演中频率域正演的复杂计算问题,采用粗细结合的并行策略,将MPI技术应用于多炮间并行计算,同时利用GPU技术加速正演过程中大型稀疏线性代数方程组的求解,以提高频率域全波形反演的计算效率。通过理论模型验证本文方法的正确性和有效性,给出不同数据量与GPU计算效率的相关分析结论,提出频率域全波形反演CPU/GPU协同并行计算的制约瓶颈和发展方向。     

Passive Surface-Wave Waveform Inversion for Source-Velocity Joint Imaging

Surveys in Geophysics - Reliable dispersion measurement between two seismic stations is an essential basis of surface wave imaging. Noise source directivity has become an inescapable obstacle and a...     

用地质雷达数据资料反演二维地下介质的方法

从二维麦克斯韦方程组出发推导出反演介电常数和电导率等二维介质物性参数的反演公式.反演的步骤是: 建立初始猜测模型,利用电磁波时间域有限差分法模拟正演数据,用正演数据与观测数据之间的数据残差建立目标函数,通过引入一个由麦克斯韦方程计算的伴随场,将目标函数对介质参数的导数表示成显式形式,应用最优化理论得出对初始猜测模型的修改,用共轭梯度法迭代,最终得到反演结果.用合成数据反演具有粗糙地表的非导电介质的介电常数,用实验数据同时反演介电常数和电导率,并比较了麦克斯韦方程反演结果与声波方程反演结果、波动方程偏移剖面的差异.     

2-D Frequency-domain Waveform Inversion of Coupled Acoustic-Elastic Media with an Irregular Interface

In order to correctly interpret marine exploration data, which contain many elastic signals such as S waves, surface waves and converted waves, we have developed both a frequency-domain modeling algorithm for acoustic-elastic coupled media with an irregular interface, and the corresponding waveform inversion algorithm. By applying the continuity condition between acoustic (fluid) and elastic (solid) media, wave propagation can be properly simulated throughout the coupled domain. The arbitrary interface is represented by tessellating square and triangular finite elements. Although the resulting complex impedance matrix generated by finite element methods for the acoustic-elastic coupled wave equation is asymmetric, we can exploit the usual back-propagation algorithm used in the frequency domain through modern sparse matrix technology. By running numerical experiments on a synthetic model, we demonstrate that our inversion algorithm can successfully recover P- and S-wave velocity and density models from marine exploration data (pressure data only).     

地震震源机制波形自动反演系统的研究现状与展望

震源机制解是地震学研究的重要组成部分, 它从一定程度上描述了震源的性质及其破裂过程, 对其正确、 全面地认识可深化理解地震的孕育、 发生和演化。 而地震波形自动反演系统的建立, 不仅实现了利用地震波形信息进行震源机制解的自动反演, 更重要的是加快了反演的速度, 充分体现了提取震源信息的实效性, 从而有力地帮助震情分析、 余震趋势预测、 震后救援等工作的展开。 本文系统地阐述了震源机制解反演方法, 总结了自动反演系统构建思路以及波形自动反演系统的实现, 为国内构建自动反演系统提供了可鉴的技术思路。     

Inversion of 2D spectral induced polarization imaging data

Laboratory measurements of various materials suggest that more information can be obtained by measuring the in‐phase and out‐of‐phase potentials at a number of frequencies. One common model used to describe the variation of the electrical properties with frequency is the Cole‐Cole model. Apart from the DC resistivity (ρ) and chargeability (m) parameters used in conventional induced‐polarization (IP) surveys, the Cole‐Cole model has two additional parameters, i.e. the time (τ) and relaxation (c) constants. Much research has been conducted on the use of the additional Cole‐Cole parameters to distinguish between different IP sources. Here, we propose a modified inversion method to recover the Cole‐Cole parameters from a 2D spectral IP (SIP) survey. In this method, an approximate inversion method is initially used to construct a non‐homogeneous starting model for the resistivity and chargeability values. The 2D model consists of a number of rectangular cells with constant resistivity (ρ), chargeability (m), time (τ) and relaxation (c) constant values in each cell. A regularized least‐squares optimization method is then used to recover the time and relaxation constant parameters as well as to refine the chargeability values in the 2D model. We present results from tests carried out with the proposed method for a synthetic data set as well as from a laboratory tank experiment.     

ELRIS2D: A MATLAB Package for the 2D Inversion of DC Resistivity/IP Data

ELRIS2D is an open source code written in MATLAB for the two-dimensional inversion of direct current resistivity (DCR) and time domain induced polarization (IP) data. The user interface of the program is designed for functionality and ease of use. All available settings of the program can be reached from the main window. The subsurface is discre-tized using a hybrid mesh generated by the combination of structured and unstructured meshes, which reduces the computational cost of the whole inversion procedure. The inversion routine is based on the smoothness constrained least squares method. In order to verify the program, responses of two test models and field data sets were inverted. The models inverted from the synthetic data sets are consistent with the original test models in both DC resistivity and IP cases. A field data set acquired in an archaeological site is also used for the verification of outcomes of the program in comparison with the excavation results.     

Computing the Sensitivity Kernels for 2.5-D Seismic Waveform Inversion in Heterogeneous,Anisotropic Media

2.5-D modeling and inversion techniques are much closer to reality than the simple and traditional 2-D seismic wave modeling and inversion. The sensitivity kernels required in full waveform seismic tomographic inversion are the Fréchet derivatives of the displacement vector with respect to the independent anisotropic model parameters of the subsurface. They give the sensitivity of the seismograms to changes in the model parameters. This paper applies two methods, called ‘the perturbation method’ and ‘the matrix method’, to derive the sensitivity kernels for 2.5-D seismic waveform inversion. We show that the two methods yield the same explicit expressions for the Fréchet derivatives using a constant-block model parameterization, and are available for both the line-source (2-D) and the point-source (2.5-D) cases. The method involves two Green’s function vectors and their gradients, as well as the derivatives of the elastic modulus tensor with respect to the independent model parameters. The two Green’s function vectors are the responses of the displacement vector to the two directed unit vectors located at the source and geophone positions, respectively; they can be generally obtained by numerical methods. The gradients of the Green’s function vectors may be approximated in the same manner as the differential computations in the forward modeling. The derivatives of the elastic modulus tensor with respect to the independent model parameters can be obtained analytically, dependent on the class of medium anisotropy. Explicit expressions are given for two special cases—isotropic and tilted transversely isotropic (TTI) media. Numerical examples are given for the latter case, which involves five independent elastic moduli (or Thomsen parameters) plus one angle defining the symmetry axis.     

Complex Frequency-Shifted Perfectly Matched Layers for 2.5D Frequency-Domain Marine Controlled-Source EM Field Simulations

Surveys in Geophysics - For geophysical electromagnetic (EM) forward modeling problems, the accuracy of solutions mainly depends on the numerical modeling method used and the corresponding boundary...     

利用1-HzGPS波形数据反演2011年日本北大地震震源破裂过程

利用1-Hz GPS数据反演2011年3月日本东北大地震的时空破裂过程,通过理论波形图与观测波形图的拟合,以及ABIC准则的判定,反演得到滑移分布的稳定估计.结果表明:破裂集中在震源附近,并在震中以下30 km处达到最大位错量,约72 m,在岩手和福岛靠近海岸线处有两个较小的破裂区,断层的南半段破裂很小,同时也是余震最为密集的地方.整个破裂过程由3个破裂阶段组成,发震后断层从震源向周围缓慢破裂,在50～60 s破裂延伸至地表(海沟);60～90 s在震中下方迅速发生强烈破裂,形成了最大位错区,这一阶段主要是倾向上的双边破裂;90～120 s在断层最北西处和断层南半段发生较小破裂,整个破裂过程持续大约120 s.反演得到的地震矩为3.8×1022 Nm,相应的矩震级为MW 9.0.     

Source Parameters of Weak Crustal Earthquakes of the Vrancea Region from Short-period Waveform Inversion

High-frequency records of nine low magnitude shallow earthquakes of the Vrancea (Romania) seismic region are inverted for the seismic moment tensor (MT). An approach is suggested regarding how to obtain at least a rough estimate of the MT when the information on the structure of the crust is poor. Here simple 1-D layered models are used in the Greens function synthesis despite the fact that the structure of the region is undoubtedly very complex. Different 1-D models were used for different source-station paths to approximate lateral variations. Record of a station located on a ray path which crosses a structure differing substantially from a 1-D model may however bias the retrieved MT essentially. Therefore, we did not collectively process all records, but subsets of stations separately. We check the consistency of the MTs resulting from these individual bootstrap solutions, and reject those which differ substantially, assuming that this is due to the oversimplification of the forward modeling. Thereafter, the averaged moment tensor yielded by the consistent subsets is accepted. Moreover, the distribution of the T, N and P axes from the moment tensors used for averaging provides a rough estimate of their reliability.Following this simplistic procedure, we found seven acceptably constrained solutions among nine events processed. Their P axes are compared with the general trend of the stress in the area: three comply with it, the others should be attributed to the complex stress field active in the region.Acknowledgment This research has been made possible by MURST (40% and 60%), by UNESCO-IGCP project 414 Realistic Modelling of Seismic Input for Megacities and Large Urban Areas and NATO SfP 972266. Partial support issued from the Grant Agency of Czech Rep. (Grant 205/02/0383) and from the National Agency for Science, Technology and Innovation of Romania (Grant 6185 GR/2000).     

准实时中小地震震源机制波形自动反演系统的构建及在首都圈地区的应用

基于Cut And Paste(CAP)全波形拟合反演震源机制解方法, 依托中国地震局地震预测研究所准实时地震波形数据服务系统, 通过接收区域实时连续波形数据, 构建了首都圈地区准实时准自动波形反演系统, 使系统实现当地震大于3.5级时, 可自动、 迅速反演得到震源机制解。 同时考虑到一些台站的地震波形质量或信噪比等因素, 系统也可通过人为干预方式重新反演求得相关结果。 文中详细阐述了震源机制解波形反演系统的运行流程及该系统的基本构建思路, 并对实例进行对比分析, 表明该系统具有较好的实用性。     

A Comparison of Strategies for Seismic Interferometry

The extraction of the response from field fluctuations excited by random sources has received considerable attention in a variety of different fields. We present three methods for the extraction of the systems response that are based on cross-correlation, deconvolution, and the solution of an integral equation, respectively. For systems that are invariant for time-reversal the correlation method requires random sources on a bounding surface only, but when time-reversal invariance is broken, for example by attenuation, a volume distribution of sources is needed. For this reason the correlation method is not useful for diffusive or strongly attenuating systems. We provide examples of the three methods and compare their merits and drawbacks. We show that the extracted field may satisfy different boundary conditions than does the physical field. This can be used, for example, to suppress surface-related multiples in exploration seismology, to study the coupling of buildings to the subsurface, and to remove the airwave in controlled source electromagnetics (CSEM).     

复杂二维/三维大地电磁的有限单元法正演模拟策略

复杂二维和三维大地电磁模型的正演数值模拟具有一定的挑战性。对于复杂的二维和三维大地电磁正演问题,我们采用有限单元法进行求解。有限单元法最后形成一个线性方程组,系数矩阵是大型稀疏的带状对称复系数矩阵,并且其条件数远大于1,为严重病态矩阵,求解其对应方程组会遇到很多困难。不完全LU分解处理的Bi-CGSTAB迭代方法可用于该线性方程组的求解,并且具有速度快、精度高和稳定性好等优点;为了模拟无穷远边界及满足计算机的内存需求,在保证计算精度的情况下设计了非均匀网格剖分;在程序编制中,只存储有限元系数矩阵的非零元素,大大减少了正演计算的时间。通过对二维和三维模型电磁响应的计算,验证了算法的正确性。     

Inversion of multi-frequency electromagnetic induction data for 3D characterization of hydraulic conductivity

Electromagnetic induction (EMI) instruments provide rapid, noninvasive, and spatially dense data for characterization of soil and groundwater properties. Data from multi-frequency EMI tools can be inverted to provide quantitative electrical conductivity estimates as a function of depth. In this study, multi-frequency EMI data collected across an abandoned uranium mill site near Naturita, Colorado, USA, are inverted to produce vertical distribution of electrical conductivity (EC) across the site. The relation between measured apparent electrical conductivity (EC_a) and hydraulic conductivity (K) is weak (correlation coefficient of 0.20), whereas the correlation between the depth dependent EC obtained from the inversions, and K is sufficiently strong to be used for hydrologic estimation (correlation coefficient of ? 0.62). Depth-specific EC values were correlated with co-located K measurements to develop a site-specific ln(EC)–ln(K) relation. This petrophysical relation was applied to produce a spatially detailed map of K across the study area. A synthetic example based on EC_a values at the site was used to assess model resolution and correlation loss given variations in depth and/or measurement error. Results from synthetic modeling indicate that optimum correlation with K occurs at ~ 0.5 m followed by a gradual correlation loss of 90% at 2.3 m. These results are consistent with an analysis of depth of investigation (DOI) given the range of frequencies, transmitter–receiver separation, and measurement errors for the field data. DOIs were estimated at 2.0 ± 0.5 m depending on the soil conductivities. A 4-layer model, with varying thicknesses, was used to invert the EC_a to maximize available information within the aquifer region for improved correlations with K. Results show improved correlation between K and the corresponding inverted EC at similar depths, underscoring the importance of inversion in using multi-frequency EMI data for hydrologic estimation.     

Modeling Coastal Salinity in Quasi 2D and 3D Using a DUALEM‐421 and Inversion Software

Rising sea levels, owing to climate change, are a threat to fresh water coastal aquifers. This is because saline intrusions are caused by increases and intensification of medium‐large scale influences including sea level rise, wave climate, tidal cycles, and shifts in beach morphology. Methods are therefore required to understand the dynamics of these interactions. While traditional borehole and galvanic contact resistivity (GCR) techniques have been successful they are time‐consuming. Alternatively, frequency‐domain electromagnetic (FEM) induction is potentially useful as physical contact with the ground is not required. A DUALEM‐421 and EM4Soil inversion software package are used to develop a quasi two‐ (2D) and quasi three‐dimensional (3D) electromagnetic conductivity images (EMCI) across Long Reef Beach located north of Sydney Harbour, New South Wales, Australia. The quasi 2D models discern: the dry sand (<10 mS/m) associated with the incipient dune; sand with fresh water (10 to 20 mS/m); mixing of fresh and saline water (20 to 500 mS/m), and; saline sand of varying moisture (more than 500 mS/m). The quasi 3D EMCIs generated for low and high tides suggest that daily tidal cycles do not have a significant effect on local groundwater salinity. Instead, the saline intrusion is most likely influenced by medium‐large scale drivers including local wave climate and morphology along this wave‐dominated beach. Further research is required to elucidate the influence of spring‐neap tidal cycles, contrasting beach morphological states and sea level rise.     

逆时偏移中波形光滑性分析与波形校正研究

针对RTM成像波形不光滑的问题进行研究,利用简单模型分析了空间、时间采样间隔对成像波形光滑性的影响。结果表明,空间采样间隔对波形光滑性的影响较大,而时间采样间隔的改变并不能改变波形光滑性。利用三次样条插值,在空间上对RTM成像波形进行插值,可以解决波形不光滑问题。通过复杂模型进行验证,也证明了该方法的有效性。同时对RTM成像剖面沿层地震属性(瞬时振幅、瞬时频率、瞬时相位)进行了分析,结果表明波形经过光滑校正后可以提高地震属性的横向空变稳定性。