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1.
In the second paper of this three part series, we studied the case of conventional and logarithmic phase‐only approaches to full‐waveform inversion. Here, we concentrate on deriving amplitude‐only approaches for both conventional‐ and logarithmic‐based methods. We define two amplitude‐only objective functions by simply assuming that the phase of the modelled wavefield is equal to that of the observed wavefield. We do this for both the conventional least‐squares approach and the logarithmic approach of Shin and Min. We show that these functions can be optimized using the same reverse‐time propagation algorithm of the full conventional methodology. Although the residuals in this case are not really residual wavefields, they can both be considered and utilized in that sense. In contrast to the case for our phase‐only algorithms, we show through numerical tests that the conventional amplitude‐only inversion is better than the logarithmic method. 相似文献
2.
The phase‐shift‐plus‐interpolation and extended‐split‐step‐Fourier methods are wavefield‐continuation algorithms for seismic migration imaging. These two methods can be applied to regions with complex geological structures. Based on their unified separable formulas, we show that these two methods have the same kinematic characteristics by using the theory of pseudodifferential operators. Numerical tests on a Marmousi model demonstrate this conclusion. Another important aspect of these two methods is the selection of reference velocities and we explore the influence of the selection of reference velocities by comparing the geometric progression method and the statistical method. We show that the geometric progression method is simple but does not take into account the velocity distribution while the statistical approach is relatively complex but reflects the velocity distribution. 相似文献
3.
This is the first in a series of three papers focused on using variants of a logarithmic objective function approach to full waveform inversion. In this article, we investigate waveform inversion using full logarithmic principles and compare the results with the conventional least squares approach. We demonstrate theoretically that logarithmic inversion is computational similar to the conventional method in the sense that it uses exactly the same back‐propagation technology as used in least‐squares inversion. In the sense that it produces better results for each of three numerical examples, we conclude that logarithmic inversion is also more robust. We argue that a major reason for the inherent robustness is the fact that the logarithmic approach produces a natural scaling of the amplitude of the residual wavefield by the amplitude of the modelled wavefield that tends to stabilize the computations and consequently improve the final result. We claim that any superiority of the logarithmic inversion is based on the fact that it tends to be tomographic in the early stage of the inversion and more dependent on amplitude differences in the latter stages. 相似文献
4.
In seismic waveform inversion, non‐linearity and non‐uniqueness require appropriate strategies. We formulate four types of L2 normed misfit functionals for Laplace‐Fourier domain waveform inversion: i) subtraction of complex‐valued observed data from complex‐valued predicted data (the ‘conventional phase‐amplitude’ residual), ii) a ‘conventional phase‐only’ residual in which amplitude variations are normalized, iii) a ‘logarithmic phase‐amplitude’ residual and finally iv) a ‘logarithmic phase‐only’ residual in which the only imaginary part of the logarithmic residual is used. We evaluate these misfit functionals by using a wide‐angle field Ocean Bottom Seismograph (OBS) data set with a maximum offset of 55 km. The conventional phase‐amplitude approach is restricted in illumination and delineates only shallow velocity structures. In contrast, the other three misfit functionals retrieve detailed velocity structures with clear lithological boundaries down to the deeper part of the model. We also test the performance of additional phase‐amplitude inversions starting from the logarithmic phase‐only inversion result. The resulting velocity updates are prominent only in the high‐wavenumber components, sharpening the lithological boundaries. We argue that the discrepancies in the behaviours of the misfit functionals are primarily caused by the sensitivities of the model gradient to strong amplitude variations in the data. As the observed data amplitudes are dominated by the near‐offset traces, the conventional phase‐amplitude inversion primarily updates the shallow structures as a result. In contrast, the other three misfit functionals eliminate the strong dependence on amplitude variation naturally and enhance the depth of illumination. We further suggest that the phase‐only inversions are sufficient to obtain robust and reliable velocity structures and the amplitude information is of secondary importance in constraining subsurface velocity models. 相似文献
5.
Numerical implementation of the gradient of the cost function in a gradient‐based full‐ waveform inversion (FWI) is essentially a migration operator used in wave equation migration. In FWI, minimizing different data residual norms results in different weighting strategies of data residuals at receiver locations prior to back‐propagation into the medium. In this paper, we propose different scaling methods to the receiver wavefield and compare their performances. Using time‐domain reverse‐time migration (RTM), we show that compared to conventional algorithms, this type of scaling is able to significantly suppress non‐Gaussian noise, i.e., outliers. Our tests also show that scaling by its absolute norm produces better results than other approaches. 相似文献
6.
Surface wave methods are based on the inversion of observed Rayleigh wave phase‐velocity dispersion curves. The goal is to estimate mainly the shear‐wave velocity profile of the investigated site. The model used for the interpretation is 1D, hence results obtained wherever lateral variations are present cannot be considered reliable. In this paper, we study four synthetic models, all with a lateral heterogeneity. When we process the entire corresponding seismograms with traditional f‐k approach, the resulting 1D profiles are representative of the subsurface properties averaged over the whole length of the receivers lines. These results show that classical analysis disregards evidences of sharp lateral velocity changes even when they show up in the raw seismograms. In our research, we implement and test over the same synthetic models, a novel robust automated method to check the appropriateness of 1D model assumption and locate the discontinuities. This new approach is a development of the recent multi‐offset phase analysis with the following further advantages: it does not need previous noise evaluation and more than one shot. Only once the discontinuities are clearly identified, we confidently perform classical f‐k dispersion curve extraction and inversion separately on both sides of the discontinuity. Thus the final results, obtained by putting side by side the 1D profiles, are correct 2D reconstructions of the discontinuous S‐wave distributions obtained without any additional ad‐hoc hypotheses. 相似文献
7.
Ho Seuk Bae Changsoo Shin Young Ho Cha Yunseok Choi Dong‐Joo Min 《Geophysical Prospecting》2010,58(6):997-1010
Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and frequency‐domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non‐linear objective function and the unreliable low‐frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace‐domain waveform inversion has been proposed. The Laplace‐domain waveform inversion has been known to provide a long‐wavelength velocity model even for field data, which may be because it employs the zero‐frequency component of the damped wavefield and a well‐behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media. We extend the Laplace‐domain waveform inversion algorithm to a 2D acoustic‐elastic coupled medium, which is encountered in marine exploration environments. In 2D acoustic‐elastic coupled media, the Laplace‐domain pressures behave differently from those of 2D acoustic media, although the overall features are similar to each other. The main differences are that the pressure wavefields for acoustic‐elastic coupled media show negative values even for simple geological structures unlike in acoustic media, when the Laplace damping constant is small and the water depth is shallow. The negative values may result from more complicated wave propagation in elastic media and at fluid‐solid interfaces. Our Laplace‐domain waveform inversion algorithm is also based on the finite‐element method and logarithmic wavefields. To compute gradient direction, we apply the back‐propagation technique. Under the assumption that density is fixed, P‐ and S‐wave velocity models are inverted from the pressure data. We applied our inversion algorithm to the SEG/EAGE salt model and the numerical results showed that the Laplace‐domain waveform inversion successfully recovers the long‐wavelength structures of the P‐ and S‐wave velocity models from the noise‐free data. The models inverted by the Laplace‐domain waveform inversion were able to be successfully used as initial models in the subsequent frequency‐domain waveform inversion, which is performed to describe the short‐wavelength structures of the true models. 相似文献
8.
Multiple-point geostatistical simulation is used to simulate the spatial structures of geological phenomena. In contrast to conventional two-point variogram based geostatistical methods, the multiple-point approach is capable of simulating complex spatial patterns, shapes, and structures normally observed in geological media. A commonly used pattern based multiple-point geostatistical simulation algorithms is called FILTERSIM. In the conventional FILTERSIM algorithm, the patterns identified in training images are transformed into filter score space using fixed filters that are neither dependent on the training images nor on the characteristics of the patterns extracted from them. In this paper, we introduce two new methods, one for geostatistical simulation and another for conditioning the results. At first, new filters are designed using principal component analysis in such a way to include most structural information specific to the governing training images resulting in the selection of closer patterns in the filter score space. We then propose to combine adaptive filters with an overlap strategy along a raster path and an efficient conditioning method to develop an algorithm for reservoir simulation with high accuracy and continuity. We also combine image quilting with this algorithm to improve connectivity a lot. The proposed method, which we call random partitioning with adaptive filters simulation method, can be used both for continuous and discrete variables. The results of the proposed method show a significant improvement in recovering the expected shapes and structural continuity in the final simulated realizations as compared to those of conventional FILTERSIM algorithm and the algorithm is more than ten times faster than FILTERSIM because of using raster path and using small overlap specially when we use image quilting. 相似文献
9.
本文介绍了一个重建误差和扫描半径之间的关系,并在此关系的基础上提出了一种新的基于不同半径的两个同心圆轨道的算法,利用估算的重建误差改善重建结果。随后进行了数值仿真实验。通过数值模拟实验评价了此算法的性能,结果表明新的算法能比已有的同类算法更好地估计重建误差,从而获得更精确的重建结果,在锥角≤±10°时都能获得相当好的重建结果,在锥角更大时也能起到很好的改善作用。最后本文讨论了此类算法的局限性。 相似文献
10.
A risk‐based life cycle cost strategy for optimal design and evaluation of control methods for nonlinear structures 
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下载免费PDF全文 The lack of direct correspondence between control objectives and hazard risks over the lifetime of systems is a key shortcoming of current control techniques. This along with the inability to objectively analyze the benefits and costs of control solutions compared with conventional methods has hindered widespread application of control systems in seismic regions. To address these gaps, this paper offers 2 new contributions. First, it introduces risk‐based life cycle–cost (LCC) optimal control algorithms, where LCC is incorporated as the performance objective in the control design. Two strategies called risk‐based linear quadratic regulator and unconstrained risk‐based regulator are subsequently proposed. The considered costs include the initial cost of the structure and control system, LCC of maintenance, and probabilistically derived estimates of seismic‐induced repair costs and losses associated with downtime, injuries, and casualties throughout the life of the structure. This risk‐based framework accounts for uncertainties in both system properties and hazard excitations and uses outcrossing rate theory to estimate fragilities for various damage states. The second contribution of this work is a risk‐based probabilistic framework for LCC analysis of existing and proposed control strategies. The proposed control designs are applied to the nonlinear model of a 4‐story building subjected to seismic excitations. Results show that these control methods reduce the LCC of the structure significantly compared with the status quo option (benefits of up to $1 351 000). The advancements offered in this paper enhance the cost‐effectiveness of control systems and objectively showcase their benefits for risk‐informed decision making. 相似文献
11.
The conventional design methods for seismically loaded piles still concentrate in providing adequate resistance from the pile to withstand only the inertial bending moments generated from the oscillation of the superstructure, thus neglecting the effect of kinematic interaction between pile and soil. By contrast there has been extensive research on kinematic effects induced by earthquakes and a number of simplified methods are available for a preliminary evaluation of kinematic bending moments at the interface between two soil layers. Less attention has been paid to the effects of kinematic interaction at the pile‐head. The paper summarizes recent research work on kinematic response analysis of fixed‐head piles aimed at the performance evaluation of a piled foundation. Results from an extensive parametric study, undertaken by means of three‐dimensional FE analyses, suggest a new criterion to predict kinematic bending effects at the pile head, where the combination of kinematic and inertial effect may be critical. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
12.
We propose a mathematical representation to qualitatively describe the spatio-temporal slip evolution during earthquake rupture
in an efficient and easy-to-use manner for numerical simulations of strong ground motion. It is based on three basis functions
and associated expansion coefficients. It is an extension of the approach of Ide and Takeo, (J Geophys Res, 102:27379–27391, 1997). We compare our approach and theirs using simple kinematic source models to illustrate differences
between the two approaches, and show that our approach more accurately represents the spatio-temporal slip evolution. We also
propose a technique based on our representation for extracting a spatio-temporal slip velocity function from a kinematic source
model obtained by the conventional source inversion. We then demonstrate the feasibility of our procedure with application
to an inverted source model of the 26 March 1997 Northwestern Kagoshima, Japan, earthquake (M
W6.1). In the simulations for actual earthquakes, source models obtained from kinematic source inversions are commonly employed.
Our scheme could be used as an interpolation method of slip time functions from relatively coarse finite-source models obtained
by conventional kinematic source inversions. 相似文献
13.
In this paper we calculate a synthetic medium surface displacement response that is consistent with real measurement data by applying the least-square principle and a niche genetic algorithm to the parameters inversion problem of the wave equation in a two-phase medium. We propose a niche genetic multi-parameter (including porosity, solid phase density and fluid phase density) joint inversion algorithm based on a two-phase fractured medium in the BISQ model. We take the two-phase fractured medium of the BISQ model in a two-dimensional half space as an example, and carry out the numerical reservoir parameters inversion. Results show that this method is very convenient for solving the parameters inversion problem for the wave equation in a two-phase medium, and has the advantage of strong noise rejection. Relative to conventional genetic algorithms, the niche genetic algorithm based on a sharing function can not only significantly speed up the convergence, but also improve the inversion precision. 相似文献
14.
Acoustic transversely isotropic models are widely used in seismic exploration for P‐wave processing and analysis. In isotropic acoustic media only P‐wave can propagate, while in an acoustic transversely isotropic medium both P and S waves propagate. In this paper, we focus on kinematic properties of S‐wave in acoustic transversely isotropic media. We define new parameters better suited for S‐wave kinematics analysis. We also establish the travel time and relative geometrical spreading equations and analyse their properties. To illustrate the behaviour of the S‐wave in multi‐layered acoustic transversely isotropic media, we define the Dix‐type equations that are different from the ones widely used for the P‐wave propagation. 相似文献
15.
As exploration targets have become deeper, cable lengths have increased accordingly, making the conventional two term hyperbolic traveltime approximation produce increasingly erroneous traveltimes. To overcome this problem, many traveltime formulas were proposed in the literature that provide approximations of different quality. In this paper, we concentrate on simple traveltime approximations that depend on a single anisotropy parameter. We give an overview of a collection of such traveltime approximations found in the literature and compare their quality. Moreover, we propose some new single‐parameter traveltime approximations based on the approximations found in the literature. The main advantage of our approximations is that some of them are rather simple analytic expressions that make them easy to use, while achieving the same quality as the better of the established formulas. 相似文献
16.
Seismic inversion has drawn the attention of researchers due to its capability of building an accurate earth model. Such a model will need to be discretised finely, and the dimensions of the inversion problem will be very high. In this paper, we propose an efficient differential evolution algorithm and apply it to high‐dimensional seismic inversion. Our method takes into account the differences among individuals, which are disregarded in conventional differential evolution methods, resulting to a better balance between exploration and exploitation. We divide the entire population into three subpopulations and propose a novel mutation strategy with two phases. Furthermore, we optimise the crossover operator by applying the components having the best objective function values into the crossover operator. We embed this strategy into a cooperative coevolutionary differential evolution and propose a new differential evolution algorithm referred to as a differential evolution with subpopulations. Then, we apply our scheme to both synthetic and field data; the results of high‐dimensional seismic inversion have shown that the proposed differential evolution with subpopulations achieves faster convergence and a higher‐quality solution for seismic inversion. 相似文献
17.
We have developed a straightforward and ray based methodology to estimate both the maximum offset and reflection imaging radius for multi‐layered velocity models, which can be used for a 2D/3D VSP survey design. Through numerical examples, we demonstrate that the presence of a high‐velocity layer above a target zone significantly reduces the maximum offset and reflection imaging radius. Our numerical examples also show that including in a migration VSP data acquired beyond a recommended maximum offset, radically degrades the quality of the final VSP image. In addition, unlike the conventional straight‐line based approximation that often produces an incorrect large reflection imaging radius, our methodology predicts the VSP imaging radius with more accuracy than does the conventional approximation. 相似文献
18.
射线参数水平分量是立体层析数据空间中最为重要的参数信息,梯度平方结构张量算法是一种针对图像的边缘检测快速算法.本文将叠前地震数据集视为图像,将梯度平方结构张量算法用于射线参数水平分量的提取,提高了立体层析数据空间的准备效率.高效率的数据空间提取使得高密度立体层析反演成为可能,数据空间加密后的立体层析反演精度以及叠前深度成像质量相比常规流程得到明显提高.基于二维理论数据与南海某二维深水数据的严格测试证实了该方法的有效性与稳健性. 相似文献
19.
Romain Teyssier 《地球物理与天体物理流体动力学》2013,107(3-4):199-225
We propose to extend the well-known MUSCL-Hancock scheme for Euler equations to the induction equation modeling the magnetic field evolution in kinematic dynamo problems. The scheme is based on an integral form of the underlying conservation law which, in our formulation, results in a “finite-surface” scheme for the induction equation. This naturally leads to the well-known “constrained transport” method, with additional continuity requirement on the magnetic field representation. The second ingredient in the MUSCL scheme is the predictor step that ensures second order accuracy both in space and time. We explore specific constraints that the mathematical properties of the induction equations place on this predictor step, showing that three possible variants can be considered. We show that the most aggressive formulations reach the same level of accuracy than the other ones, at a lower computational cost. More interestingly, these schemes are compatible with the Adaptive Mesh Refinement (AMR) framework. It has been implemented in the AMR code RAMSES. It offers a novel and efficient implementation of a second order scheme for the induction equation. The scheme is then adaptated to solve for the full MHD equations using the same methodology. Through a series of test problems, we illustrate the performances of this new code using two different MHD Riemann solvers (Lax–Friedrich and Roe) and the need of the Adaptive Mesh Refinement capabilities in some cases. Finally, we show its versatility by applying it to the ABC dynamo problem and to the collapse of a magnetized cloud core. 相似文献
20.
In order to account for the effects of elastic wave propagation in marine seismic data, we develop a waveform inversion algorithm for acoustic‐elastic media based on a frequency‐domain finite‐element modelling technique. In our algorithm we minimize residuals using the conjugate gradient method, which back‐propagates the errors using reverse time migration without directly computing the partial derivative wavefields. Unlike a purely acoustic or purely elastic inversion algorithm, the Green's function matrix for our acoustic‐elastic algorithm is asymmetric. We are nonetheless able to achieve computational efficiency using modern numerical methods. Numerical examples show that our coupled inversion algorithm produces better velocity models than a purely acoustic inversion algorithm in a wide variety of cases, including both single‐ and multi‐component data and low‐cut filtered data. We also show that our algorithm performs at least equally well on real field data gathered in the Korean continental shelf. 相似文献