Seismic Waveform Inversion Research Articles

Porous media hydrogen storage at a synthetic, heterogeneous field site: numerical simulation of storage operation and geophysical monitoring

Large-scale energy storage such as porous media hydrogen storage will be required to mitigate shortages originating from fluctuating power production if renewables dominate the total supply. In order to assess the applicability of this storage option, a possible usage scenario is defined for an existing anticlinal structure in the North German Basin and the storage operation is numerically simulated. A heterogeneous and realistic parameter distribution is generated by a facies modelling approach. The storage operation, which is performed using five wells, consists of an initial filling of the storage with nitrogen used as cushion gas and hydrogen as well as several week-long withdrawal periods each followed by a refill and a shut-in period. Storage performance increases with the number of storage cycles and a total of 29 million m(3) of hydrogen gas at surface conditions can be produced in the long term, equating to 186,000 GJ of energy when assuming a re-electrification efficiency of 60 %. In addition to downhole pressure monitoring geophysical techniques such as seismic full waveform inversion (FWI), electrical resistivity tomography (ERT) and gravity methods can be used for site monitoring, if their individual detecting capabilities are sufficient. Investigation of the storage scenario by virtual application of these methods shows that FWI and ERT can be used to map the thin gas phase distribution in this heterogeneous formation with the individual methods conforming each other. However, a high spatial density of receivers in a crosswell geometry with less than 500 m distance between the observation wells is required for this. Gravity mapping also shows anomalies indicating mass changes caused by the storage operation. However, monitoring the filling state of this hydrogen storage site is not possible.

Estimation of dynamic friction of the Akatani landslide from seismic waveform inversion and numerical simulation

Estimation of dynamic friction of the Akatani landslide from seismic waveform inversion and numerical simulation

Unscented hybrid simulated annealing for fast inversion of tunnel seismic waves

A new hybridized global optimization method that combines simulated annealing global search with unscented Kalman filter minimization is proposed to solve waveform inversion for predicting ahead of the underground tunnel face. The authors demonstrate in this work fast and reliable convergence of this new algorithm through validation of optimization of a multi-minima test function and inversion of synthetic tunnel seismic waveforms to predict the geological structure ahead of the tunnel face. With regard to the engineering application, the successful identification of the true model by minimizing a multimodal misfit functional for wide feasible bounds of the model parameters confirms that waveform inversion by the improved global optimization method is promising for practical applications with real measurement data.

Full-waveform inversion on heterogeneous HPC systems

We present a spectral-element implementation of full seismic waveform inversion for large heterogeneous HPC systems. In this we address the optimal parallelisation configurations of individual simulations, the large I/O requirements of adjoint simulations, and the scheduling of large numbers of forward and adjoint solves, typical for realistic inversions. Using GPU accelerators allows us to achieve a 3.5–4 times performance improvement over the best known homogeneous implementation. We achieve GPU memory throughput varying from 60 to 80% of the peak bandwidth, thus providing good utilisation of hardware resources. We demonstrate the practical applicability of our developments in a real-data application in the western Mediterranean. With the help of GPU accelerators, we are able to model and invert seismic wave propagation in a frequency band that is broader than permitted by the use of CPUs alone, which helps bridging the traditional gap between crustal and mantle tomography.

A flexible, extendable, modular and computationally efficient approach to scattering-integral-based seismic full waveform inversion

A flexible, extendable, modular and computationally efficient approach to scattering-integral-based seismic full waveform inversion

A feasibility and efficiency study of seismic waveform inversion for time-lapse monitoring of onshore CO2 geological storage sites using reflection seismic acquisition geometries

Monitoring of the CO2 distribution at depth is imperative for onshore geological storage of CO2. Seismic methods are effective monitoring tools during and after the injection process, but are generally expensive and time consuming to perform. In this paper we perform a series of synthetic experiments in order to compare the seismic waveform inversion method with conventional seismic monitoring methods for time-lapse monitoring at CO2 geological storage sites. We mainly focus our study on seismic data sets with typical reflection acquisition geometries that is far offset limited. Two synthetic seismic data sets (consisting of one baseline and repeat) were generated by a third party 2D forward modeling code to compare the waveform inversion method with a conventional time-lapse procedure. The velocity models are based on a simplified structure of the Heletz site in Israel. The area into which CO2 is injected is on the order of a few hundred meters wide and a few 10s of meters high. We compare the waveform inversion results and conventional time-lapse results to determine how sparse spatial sampling affects the results by increasing both the shot and receiver spacing. We test the waveform inversion method for a synthetic time-lapse data set with different inversion strategies. First, we invert each data set independently by using both phase and amplitude information. Then we invert them by using only phase information. We also test the influence of the starting model. Finally, we test the double difference inversion method which is equivalent to only inverting the difference between the baseline and repeat data sets. During the test a relative coarse starting model and higher starting frequency were used in order to better represent real seismic reflection data. Our results show that, under certain noise conditions, it may be possible to use a combination of sparse spatial sampling geometries and seismic waveform inversion to monitor the velocity changes caused by CO2 injection. We conclude that seismic waveform inversion may be a good complement to standard CDP processing when monitoring CO2 injection.

Quantifying subsurface geophysical properties changes using double-difference seismic-waveform inversion with a modified total-variation regularization scheme

Quantifying subsurface geophysical properties changes using double-difference seismic-waveform inversion with a modified total-variation regularization scheme

Strategy and Application of Waveform Inversion Based on Seismic Data Subset

AbstractThe main difficulty in seismic full waveform inversion (FWI) is the strong nonlinearity, which is caused by the complexity of seismic wave propagation. Different components of elastic parameters result in different characteristics in seismic data. Meanwhile, different inversion quality is required in different stages of exploration or exploitation. So, there is no need to pursue matching all the seismic information during the inversion. Some problems can be solved by matching part of seismic information and the strong nonlinearity can also be avoided by this way. According to this consideration, a generalized FWI strategy and method based on seismic data subsets is presented. For different seismic data subsets, the gradients of the misfits have the same form and can be calculated by two times of seismic wave forward modeling just as traditional FWI. The only difference in calculating the gradients is the adjoint source. During the waveform inversion based on seismic data subsets, the responses of seismic data to different scales of perturbation on different media parameters should be analyzed intensively. Different seismic data subsets should be used in different stages of full waveform inversion. And then the residual of this seismic data subset is back‐projected along the reasonable sub‐kernels to decide where and which component of the model parameter need to be updated. As examples, envelope and reflection data subsets are used in FWI with synthetic and practical data to prove the validity and effectiveness of our presented FWI strategy and method. Especially, in the absence of low frequency contents, reasonable misfits can be used to recover the background compressional and shear velocity models using these FWI methods.

A proposal of seismic oceanography for temperature model inversion of the East Sea, Korea

Much attention has recently been paid to the East Sea because of the great influence it exerts on weather in the Korean peninsula as well as its peculiar oceanographic features. A large number of oceanographic observations have been made to probe the physical properties of the waters at the East Sea. However, until now, measuring the physical properties of a broad oceanic area simultaneously was impractical. To address this problem, this study presents a methodology to measure the physical properties of seawater by introducing seismic oceanography (SO) into marine seismic surveys. SO has been attracting attention as a new technology capable of concurrent analysis of a broad oceanic area; however, hardly any research of this type has been conducted in Korea to date. The technique proposed in this study involves derivation of a seawater temperature model based on the 1D seismic waveform inversion and Leroy equations using seismic data and non-stationary ARGO data. The proposed technique was validated through numerical model experiments using the seawater temperature information obtained at the East Sea in 2013, through which much insight into the ocean currents and seawater characteristics of the East Sea could be gained.

Application of the least-squares inversion method: Fourier series versus waveform inversion

We describe an implicit link between waveform inversion and Fourier series based on inversion methods such as gradient, Gauss–Newton, and full Newton methods. Fourier series have been widely used as a basic concept in studies on seismic data interpretation, and their coefficients are obtained in the classical Fourier analysis. We show that Fourier coefficients can also be obtained by inversion algorithms, and compare the method to seismic waveform inversion algorithms. In that case, Fourier coefficients correspond to model parameters (velocities, density or elastic constants), whereas cosine and sine functions correspond to components of the Jacobian matrix, that is, partial derivative wavefields in seismic inversion. In the classical Fourier analysis, optimal coefficients are determined by the sensitivity of a given function to sine and cosine functions. In the inversion method for Fourier series, Fourier coefficients are obtained by measuring the sensitivity of residuals between given functions and test functions (defined as the sum of weighted cosine and sine functions) to cosine and sine functions. The orthogonal property of cosine and sine functions makes the full or approximate Hessian matrix become a diagonal matrix in the inversion for Fourier series. In seismic waveform inversion, the Hessian matrix may or may not be a diagonal matrix, because partial derivative wavefields correlate with each other to some extent, making them semi-orthogonal. At the high-frequency limits, however, the Hessian matrix can be approximated by either a diagonal matrix or a diagonally-dominant matrix. Since we usually deal with relatively low frequencies in seismic waveform inversion, it is not diagonally dominant and thus it is prohibitively expensive to compute the full or approximate Hessian matrix. By interpreting Fourier series with the inversion algorithms, we note that the Fourier series can be computed at an iteration step using any inversion algorithms such as the gradient, full-Newton, and Gauss–Newton methods similar to waveform inversion.

An efficient method of 3-D elastic full waveform inversion using a finite-difference injection method for time-lapse imaging

Seismic full waveform inversion is an objective method to estimate elastic properties of the subsurface and is an important area of research, particularly in seismic exploration community. It is a data-fitting approach, where the difference between observed and synthetic data is minimized iteratively. Due to a very high computational cost, the practical implementation of waveform inversion has so far been restricted to a 2-D geometry with different levels of physics incorporated in it (e.g. elasticity/viscoelasticity) or to a 3-D geometry but using an acoustic approximation. However, the earth is three-dimensional, elastic and heterogeneous and therefore a full 3-D elastic inversion is required in order to obtain more accurate and valuable models of the subsurface. Despite the recent increase in computing power, the application of 3-D elastic full waveform inversion to real-scale problems remains quite challenging on the current computer architecture. Here, we present an efficient method to perform 3-D elastic full waveform inversion for time-lapse seismic data using a finite-difference injection method. In this method, the wavefield is computed in the whole model and is stored on a surface above a finite volume where the model is perturbed and localized inversion is performed. Comparison of the final results using the 3-D finite-difference injection method and conventional 3-D inversion performed within the whole volume shows that our new method provides significant reductions in computational time and memory requirements without any notable loss in accuracy. Our approach shows a big potential for efficient reservoir monitoring in real time-lapse experiments.

2-D ocean temperature and salinity images from pre-stack seismic waveform inversion methods: an example from the South China Sea

2-D ocean temperature and salinity images from pre-stack seismic waveform inversion methods: an example from the South China Sea

Full waveform inversion in the frequency domain using direct iterative T-matrix methods

We present two direct iterative solutions to the nonlinear seismic waveform inversion problem that are based on volume integral equation methods for seismic forward modelling in the acoustic approximation. The solutions are presented in the frequency domain, where accurate inversion results can often be obtained using a relatively low number of frequency components. Our inverse scattering approach effectively replaces an ill-posed nonlinear inverse problem with a series of linear ill-posed inverse problems, for which there already exist efficient (regularized) solution methods. Both these solutions update the wavefield within the scattering domain after each iteration. The main difference is that the background medium Green functions are kept fixed in the first solution, but updated after each iteration in the second solution. This means that our solutions are very similar to the Born iterative (BI) and the distorted Born iterative (DBI) methods that are commonly used in acoustic and electromagnetic inverse scattering. However, we have eliminated the need to perform a full forward simulation (or to invert a huge matrix) at each iteration via the use of an iterative T-matrix method for fixed background media for the BI method and a variational T-matrix method for dynamic background media for the DBI method. The T-matrix (variation) is linearly related with the seismic wavefield data (residuals), but related with the unknown scattering potential model parameter (updates) in a non-linear manner, which is independent of the source-receiver configuration. This mathematical structure, which allows one to peel off the effects of the source-receiver configuration, is very attractive when dealing with multiple (simultaneous) sources, and is also compatible with the (future) use of renormalization methods for dealing with local minima problems. To illustrate the performance and potential of the two direct iterative methods for FWI, we performed a series of numerical experiments on synthetic seismic waveform data associated with a simple 2D model and the more complicated Marmousi model. The results of these numerical experiments suggest that the use of a fixed (e.g. smooth and ray-tracing friendly) background medium may be adequate for some applications with moderately large velocity contrasts, but the solution based on a dynamic (non-smooth and constantly updated) background medium will normally provide superiour inversion results; also in the case of low signal-to-noise ratios.

New insights into the generation of the 2013 Lushan Earthquake (Ms 7.0), China

AbstractGlobal seismic waveform inversion can provide information on where the 2013 Ms 7.0 Lushan earthquake occurred in Sichuan Province, China, and how its aftershock sequence expanded. To investigate the generation mechanism of the Lushan earthquake and its relation to the 2008 Wenchuan earthquake (Ms 8.0), 50 temporary seismic stations were installed in the source area following the Lushan earthquake. Crustal stress data were also collected along the Longmen‐Shan Fault zone (LMFZ) to reveal its influence on the generation of the Lushan earthquake. Seismic imaging and crustal stress analysis have revealed that the Lushan earthquake occurred in a distinct area with high velocity (Vp, Vs), low Poisson's ratio (σ), and high crustal stress. The high‐velocity zone at the Lushan source may reflect Precambrian metasedimentary or igneous rock in the seismogenic layer, which enables the accumulation of high crustal stress to generate large earthquakes. However, a sharply contrasting gap zone with low‐velocity, high‐σ anomalies is clearly imaged in the upper crust under the concatenated area between the Lushan and Wenchuan earthquakes. Seismic images indicate that the low‐velocity gap zone is associated with fluid‐bearing ductile flow from the lower crustal materials of Tibet being pushed into a weakened segment of the LMFZ. This study suggests that the 2013 Lushan earthquake may have been triggered by high crustal stress accumulation together with high coseismic stress further increased by the Wenchuan earthquake in the metamafic seismogenic layer. Contrasting rheological variations in the crust and crustal stress changes along the LMFZ control the rupture processes that generated the Lushan and Wenchuan earthquakes, as well as the generation of new earthquakes in the future.

Waveform inversion in triclinic anisotropic media—a resolution study

Seismic full waveform inversion (FWI) has been applied to simple elastic problems with certain symmetries, such as isotropic, transverse isotropic or vertical transversely isotropic media. In this study, the FWI concept is extended to the most general anisotropic case with 21 independent elastic material parameters and no symmetry plane (triclinic). Beside a short description of the 3-D finite-difference scheme to solve the forward problem and the FWI optimization algorithm, we present a sensitivity study for a simple anisotropic medium. This test problem consists of a homogenous triclinic anisotropic full space, which contains 21 spatially separated spheres. In each sphere one component of the elastic tensor deviates by 5 per cent from the background medium. The resolution of the different spheres, ambiguities between the different elastic parameters, as well as the effect of the acquisition geometry can be systematically investigated. Due to the high computational costs of the triclinic forward problem a few compromises have to be made regarding the acquisition geometries. Point sources are replaced by plane wave sources which lead to a limitation of incidence angles and therefore a strong decrease in resolution of the nondiagonal elastic tensor components. It is shown that, despite these limitations, a tomographic acquisition geometry would be able to resolve to some extent a monoclinic symmetry via FWI. Restricting the acquisition geometries (e.g. VSP combined with reflection seismic or reflection seismic only) significantly reduces the number of resolvable tensor elements in strict dependence of the covered incidence angles.

Full Seismic Waveform Inversion for the Japanese Islands

Full Seismic Waveform Inversion for the Japanese Islands

An adaptive subspace trust-region method for frequency-domain seismic full waveform inversion

Full waveform inversion is currently considered as a promising seismic imaging method to obtain high-resolution and quantitative images of the subsurface. It is a nonlinear ill-posed inverse problem, the main difficulty of which that prevents the full waveform inversion from widespread applying to real data is the sensitivity to incorrect initial models and noisy data. Local optimization theories including Newton's method and gradient method always lead the convergence to local minima, while global optimization algorithms such as simulated annealing are computationally costly. To confront this issue, in this paper we investigate the possibility of applying the trust-region method to the full waveform inversion problem. Different from line search methods, trust-region methods force the new trial step within a certain neighborhood of the current iterate point. Theoretically, the trust-region methods are reliable and robust, and they have very strong convergence properties. The capability of this inversion technique is tested with the synthetic Marmousi velocity model and the SEG/EAGE Salt model. Numerical examples demonstrate that the adaptive subspace trust-region method can provide solutions closer to the global minima compared to the conventional Approximate Hessian approach and the L-BFGS method with a higher convergence rate. In addition, the match between the inverted model and the true model is still excellent even when the initial model deviates far from the true model. Inversion results with noisy data also exhibit the remarkable capability of the adaptive subspace trust-region method for low signal-to-noise data inversions. Promising numerical results suggest this adaptive subspace trust-region method is suitable for full waveform inversion, as it has stronger convergence and higher convergence rate.

Full Waveform Inversion Using Student’s t Distribution: a Numerical Study for Elastic Waveform Inversion and Simultaneous-Source Method

Seismic full waveform inversion (FWI) has primarily been based on a least-squares optimization problem for data residuals. However, the least-squares objective function can suffer from its weakness and sensitivity to noise. There have been numerous studies to enhance the robustness of FWI by using robust objective functions, such as l 1-norm-based objective functions. However, the l 1-norm can suffer from a singularity problem when the residual wavefield is very close to zero. Recently, Student’s t distribution has been applied to acoustic FWI to give reasonable results for noisy data. Student’s t distribution has an overdispersed density function compared with the normal distribution, and is thus useful for data with outliers. In this study, we investigate the feasibility of Student’s t distribution for elastic FWI by comparing its basic properties with those of the l 2-norm and l 1-norm objective functions and by applying the three methods to noisy data. Our experiments show that the l 2-norm is sensitive to noise, whereas the l 1-norm and Student’s t distribution objective functions give relatively stable and reasonable results for noisy data. When noise patterns are complicated, i.e., due to a combination of missing traces, unexpected outliers, and random noise, FWI based on Student’s t distribution gives better results than l 1- and l 2-norm FWI. We also examine the application of simultaneous-source methods to acoustic FWI based on Student’s t distribution. Computing the expectation of the coefficients of gradient and crosstalk noise terms and plotting the signal-to-noise ratio with iteration, we were able to confirm that crosstalk noise is suppressed as the iteration progresses, even when simultaneous-source FWI is combined with Student’s t distribution. From our experiments, we conclude that FWI based on Student’s t distribution can retrieve subsurface material properties with less distortion from noise than l 1- and l 2-norm FWI, and the simultaneous-source method can be adopted to improve the computational efficiency of FWI based on Student’s t distribution.

Multicomponent, multi-azimuth pre-stack seismic waveform inversion for azimuthally anisotropic media using a parallel and computationally efficient non-dominated sorting genetic algorithm

Multicomponent, multi-azimuth pre-stack seismic waveform inversion for azimuthally anisotropic media using a parallel and computationally efficient non-dominated sorting genetic algorithm

탄성파 파형역산을 이용한 엔지니어링 목적의 단일채널 탄성파 탐사자료에서의 속도모델 도출

최근 엔지니어링 목적의 단일채널 탄성파 탐사가 많이 수행되고 있다. 단일채널 탄성파 탐사는 일반적으로 특별한 자료처리 없이 효율적으로 지하 지질구조를 파악할 수 있는 장점이 있지만, 복잡한 지질구조에 대한 정확한 영상화에는 한계를 가진다. 자원개발 목적의 다중채널 탄성파 탐사에서는 최근 파형역산에 대한 연구가 활발히 진행되고 있으며, 복잡한 지하구조에 대해서도 정확한 지하영상화 결과를 제시하고 있다. 이에 본 논문에서는 단일채널 탄성파 탐사 자료를 이용하여 지하 속도모델을 구하기 위한 탄성파 파형역산 알고리즘을 제안하였다. 제안한 알고리즘은 단일채널 탄성파 탐사를 고려하여 지하 매질을 1차원으로 가정하였으며, 벌림에 의한 지연시간을 제거하여 벌림에 의한 효과를 보정하였다. 파형역산은 안정적인 해의 계산이 가능한 가우스-뉴턴법을 이용하였다. 알고리즘은 수정된 Marmousi2 모델에 적용하여 검증하였으며, 부산항에서 얻은 현장자료에 적용해 보았다. Recently, single channel seismic survey for engineering purpose have been used widely taking advantage of simple processing. However it is very difficult to obtain high fidelity subsurface image by single channel seismic due to insufficient fold coverage. Recently, seismic waveform inversion in multi channel seismic survey is utilized for accurate subsurface imaging even in complex terrains. In this paper, we propose the seismic waveform inversion algorithm for velocity model building using a single channel seismic data. We utilize the Gauss-Newton method and assume that subsurface model is 1-Dimensional. Seismic source estimation technique is used and offset effect is also corrected by removing delay time by offset. Proposed algorithm is verified by applying modified Marmousi2 model, and applied to field data set obtained in port of Busan.