Constrained Full Waveform Inversion for Borehole Multicomponent Seismic Data

Full-waveform inversion for borehole seismic data is an ill-posed problem and constraining the problem is crucial. Constraints can be imposed on the data and model space through covariance matrices. Usually, they are set to a diagonal matrix. For the data space, signal polarization information can be used to evaluate the data uncertainties. The inversion forces the synthetic data to fit the polarization of observed data. A synthetic inversion for a 2D-2C data estimating a 1D elastic model shows a clear improvement, especially at the level of the receivers. For the model space, horizontal and vertical spatial correlations using a Laplace distribution can be used to fill the model space covariance matrix. This approach reduces the degree of freedom of the inverse problem, which can be quantitatively evaluated. Strong horizontal spatial correlation distances favor a tabular geological model whenever it does not contradict the data. The relaxation of the spatial correlation distances from large to small during the iterative inversion process allows the recovery of geological objects of the same size, which regularizes the inverse problem. Synthetic constrained and unconstrained inversions for 2D-2C crosswell data show the clear improvement of the inversion results when constraints are used.

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Adding Prior Information in FWI through Relative Entropy

Entropy ◽

10.3390/e23050599 ◽

2021 ◽

Vol 23 (5) ◽

pp. 599

Author(s):

Danilo Cruz ◽

João de Araújo ◽

Carlos da Costa ◽

Carlos da Silva

Keyword(s):

Inverse Problem ◽

Relative Entropy ◽

Global Minimum ◽

Prior Information ◽

Waveform Inversion ◽

Petroleum Industry ◽

Synthetic Data ◽

Full Waveform Inversion ◽

Full Waveform

Full waveform inversion is an advantageous technique for obtaining high-resolution subsurface information. In the petroleum industry, mainly in reservoir characterisation, it is common to use information from wells as previous information to decrease the ambiguity of the obtained results. For this, we propose adding a relative entropy term to the formalism of the full waveform inversion. In this context, entropy will be just a nomenclature for regularisation and will have the role of helping the converge to the global minimum. The application of entropy in inverse problems usually involves formulating the problem, so that it is possible to use statistical concepts. To avoid this step, we propose a deterministic application to the full waveform inversion. We will discuss some aspects of relative entropy and show three different ways of using them to add prior information through entropy in the inverse problem. We use a dynamic weighting scheme to add prior information through entropy. The idea is that the prior information can help to find the path of the global minimum at the beginning of the inversion process. In all cases, the prior information can be incorporated very quickly into the full waveform inversion and lead the inversion to the desired solution. When we include the logarithmic weighting that constitutes entropy to the inverse problem, we will suppress the low-intensity ripples and sharpen the point events. Thus, the addition of entropy relative to full waveform inversion can provide a result with better resolution. In regions where salt is present in the BP 2004 model, we obtained a significant improvement by adding prior information through the relative entropy for synthetic data. We will show that the prior information added through entropy in full-waveform inversion formalism will prove to be a way to avoid local minimums.

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Seismic full-waveform inversion using minimization of virtual scattering sources

Geophysics ◽

10.1190/geo2019-0533.1 ◽

2020 ◽

Vol 85 (3) ◽

pp. R299-R311

Author(s):

Donguk Lee ◽

Sukjoon Pyun

Keyword(s):

Newton Method ◽

Scattering Problem ◽

Waveform Inversion ◽

Synthetic Data ◽

Inverse Scattering Problem ◽

Simulated Data ◽

Model Space ◽

Full Waveform Inversion ◽

Velocity Inversion ◽

Full Waveform

Full-waveform inversion (FWI) is a powerful tool for imaging underground structures with high resolution; however, this approach commonly suffers from the cycle-skipping issue. Recently, various FWI methods have been suggested to address this problem. Such methods are mainly classified into either data-space manipulation or model-space extension. We developed an alternative FWI method that belongs to the latter class. First, we define the virtual scattering source based on perturbation theory. The virtual scattering source is estimated by minimizing the differences between observed and simulated data with a regularization term penalizing the weighted virtual scattering source. The inverse problem for obtaining the virtual scattering source can be solved by the linear conjugate gradient method. The inverted virtual scattering source is used to update the wavefields; thus, it helps FWI to better approximate the nonlinearity of the inverse scattering problem. As the second step, the virtual scattering source is minimized to invert the velocity model. By assuming that the variation of the reconstructed wavefield is negligible, we can apply an approximated full Newton method to the velocity inversion with reasonable cost comparable to the Gauss-Newton method. From the numerical examples using synthetic data, we confirm that the proposed method performs better and more robust than the simple gradient-based FWI method. In addition, we show that our objective function has fewer local minima, which helps to mitigate the cycle-skipping problem.

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Elastic envelope inversion using multicomponent seismic data without low frequency

Nonlinear Processes in Geophysics Discussions ◽

10.5194/npgd-1-1757-2014 ◽

2014 ◽

Vol 1 (2) ◽

pp. 1757-1802

Author(s):

C. Huang ◽

L. Dong ◽

Y. Liu ◽

B. Chi

Keyword(s):

Seismic Data ◽

Waveform Inversion ◽

Synthetic Data ◽

Low Frequency ◽

Velocity Model ◽

Inversion Method ◽

Full Waveform Inversion ◽

S Wave ◽

Full Waveform ◽

Multicomponent Data

Abstract. Low frequency is a key issue to reduce the nonlinearity of elastic full waveform inversion. Hence, the lack of low frequency in recorded seismic data is one of the most challenging problems in elastic full waveform inversion. Theoretical derivations and numerical analysis are presented in this paper to show that envelope operator can retrieve strong low frequency modulation signal demodulated in multicomponent data, no matter what the frequency bands of the data is. With the benefit of such low frequency information, we use elastic envelope of multicomponent data to construct the objective function and present an elastic envelope inversion method to recover the long-wavelength components of the subsurface model, especially for the S-wave velocity model. Numerical tests using synthetic data for the Marmousi-II model prove the effectiveness of the proposed elastic envelope inversion method, especially when low frequency is missing in multicomponent data and when initial model is far from the true model. The elastic envelope can reduce the nonlinearity of inversion and can provide an excellent starting model.

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True-amplitude versus trace-normalized full waveform inversion

Geophysical Journal International ◽

10.1093/gji/ggz532 ◽

2019 ◽

Vol 220 (2) ◽

pp. 1421-1435

Author(s):

Zhikai Wang ◽

Satish C Singh ◽

Mark Noble

Keyword(s):

Seismic Data ◽

Waveform Inversion ◽

Synthetic Data ◽

Physical Parameters ◽

Full Waveform Inversion ◽

Full Waveform ◽

Velocity Relationship ◽

Gradient Calculation ◽

The Time Domain ◽

Viscoelastic Modelling

SUMMARY Full waveform inversion (FWI) is a powerful method to estimate high-resolution physical parameters of the subsurface by iteratively minimizing the misfit between the observed and synthetic seismic data. Standard FWI algorithms measure seismic misfit between amplitude-preserved seismic data (true-amplitude FWI). However, in order to mitigate the variations in sources and recording systems acquired on complex geological structures and the physics that cannot be modelled using an approximation of the seismic wave equation, the observed and synthetic seismic data are normalized trace-by-trace and then used to perform FWI. Trace-by-trace normalization removes the amplitude effects related to offset variations and only keeps the phase information. Furthermore, trace-by-trace normalization changes the true amplitude difference because of different normalization factors used for the corresponding synthetic and observed traces. In this paper, we study the performance of true-amplitude FWI and trace-normalized-residual-based FWI in the time domain. The misfit function of trace-normalized-residual-based FWI is defined such that the adjoint source used in gradient calculation is the trace-normalized seismic residual. We compare the two inversion schemes with synthetic seismic data simulated on laterally invariant models and the more complex 2-D Marmousi model. In order to simulate realistic scenarios, we perform the elastic FWI ignoring attenuation to noisy seismic data and to the synthetic data modelled using a viscoelastic modelling scheme. Comparisons of seismic data and adjoint sources show that trace-by-trace normalization increases the magnitude of seismic data at far offsets, which are usually more cycle-skipped than those at near offsets. The inverted results on linear-gradient models demonstrate that trace-by-trace normalization increases the non-linearity of FWI, so an initial model with sufficient accuracy is required to guarantee the convergence to the global minimum. The inverted results and the final seismic residuals computed using seismic data without trace-by-trace normalization demonstrate that true-amplitude FWI provides inverted models with higher accuracy than trace-normalized-residual-based FWI, even when the unknown density is updated using density–velocity relationship in inversion or in the presence of noise and complex physics, such as attenuation.

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Elastic Full-Waveform Inversion Using Migration‑Based Depth Reflector Representation in the Data Domain

10.20944/preprints202011.0663.v1 ◽

2020 ◽

Author(s):

Vladimir Cheverda

Keyword(s):

Seismic Data ◽

Optimization Problem ◽

Waveform Inversion ◽

Nonlinear Least Squares ◽

Model Space ◽

Full Waveform Inversion ◽

Brute Force ◽

Data Inversion ◽

Full Waveform ◽

Least Squares Optimization

Full-waveform seismic data inversion has given rise to hope for the simultaneous and automated execution of tomography and imaging by solving a nonlinear least-squares optimization problem. As previously recognized, brute force minimization by classical methods is hopeless if the data lacks low temporal frequencies. The article developed a reliable numerical method for recovering smooth velocity using model space decomposition. We present realistic synthetic examples to test the presented algorithm.

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Full-Waveform Inversion for Imaging Faulted Structures: A Case Study from the Japan Trench Forearc Slope

Pure and Applied Geophysics ◽

10.1007/s00024-021-02727-w ◽

2021 ◽

Author(s):

Ehsan Jamali Hondori ◽

Chen Guo ◽

Hitoshi Mikada ◽

Jin-Oh Park

Keyword(s):

Seismic Data ◽

Initial Velocity ◽

Waveform Inversion ◽

Velocity Model ◽

Control Measures ◽

Japan Trench ◽

Full Waveform Inversion ◽

Full Waveform ◽

Time Migration ◽

Shallow Sediments

AbstractFull-waveform inversion (FWI) of limited-offset marine seismic data is a challenging task due to the lack of refracted energy and diving waves from the shallow sediments, which are fundamentally required to update the long-wavelength background velocity model in a tomographic fashion. When these events are absent, a reliable initial velocity model is necessary to ensure that the observed and simulated waveforms kinematically fit within an error of less than half a wavelength to protect the FWI iterative local optimization scheme from cycle skipping. We use a migration-based velocity analysis (MVA) method, including a combination of the layer-stripping approach and iterations of Kirchhoff prestack depth migration (KPSDM), to build an accurate initial velocity model for the FWI application on 2D seismic data with a maximum offset of 5.8 km. The data are acquired in the Japan Trench subduction zone, and we focus on the area where the shallow sediments overlying a highly reflective basement on top of the Cretaceous erosional unconformity are severely faulted and deformed. Despite the limited offsets available in the seismic data, our carefully designed workflow for data preconditioning, initial model building, and waveform inversion provides a velocity model that could improve the depth images down to almost 3.5 km. We present several quality control measures to assess the reliability of the resulting FWI model, including ray path illuminations, sensitivity kernels, reverse time migration (RTM) images, and KPSDM common image gathers. A direct comparison between the FWI and MVA velocity profiles reveals a sharp boundary at the Cretaceous basement interface, a feature that could not be observed in the MVA velocity model. The normal faults caused by the basal erosion of the upper plate in the study area reach the seafloor with evident subsidence of the shallow strata, implying that the faults are active.

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Multi-scale time-frequency domain full waveform inversion with a weighted local correlation-phase misfit function

Journal of Geophysics and Engineering ◽

10.1093/jge/gxz062 ◽

2019 ◽

Vol 16 (6) ◽

pp. 1017-1031 ◽

Cited By ~ 5

Author(s):

Yong Hu ◽

Liguo Han ◽

Rushan Wu ◽

Yongzhong Xu

Keyword(s):

Frequency Domain ◽

Seismic Data ◽

Waveform Inversion ◽

Low Frequency ◽

Full Waveform Inversion ◽

Local Correlation ◽

Time Frequency ◽

Model Dependence ◽

Full Waveform ◽

Frequency Components

Abstract Full Waveform Inversion (FWI) is based on the least squares algorithm to minimize the difference between the synthetic and observed data, which is a promising technique for high-resolution velocity inversion. However, the FWI method is characterized by strong model dependence, because the ultra-low-frequency components in the field seismic data are usually not available. In this work, to reduce the model dependence of the FWI method, we introduce a Weighted Local Correlation-phase based FWI method (WLCFWI), which emphasizes the correlation phase between the synthetic and observed data in the time-frequency domain. The local correlation-phase misfit function combines the advantages of phase and normalized correlation function, and has an enormous potential for reducing the model dependence and improving FWI results. Besides, in the correlation-phase misfit function, the amplitude information is treated as a weighting factor, which emphasizes the phase similarity between synthetic and observed data. Numerical examples and the analysis of the misfit function show that the WLCFWI method has a strong ability to reduce model dependence, even if the seismic data are devoid of low-frequency components and contain strong Gaussian noise.

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Restricted model domain time Radon transforms

Geophysics ◽

10.1190/geo2016-0270.1 ◽

2016 ◽

Vol 81 (6) ◽

pp. A17-A21 ◽

Cited By ~ 7

Author(s):

Juan I. Sabbione ◽

Mauricio D. Sacchi

Keyword(s):

Inverse Problem ◽

Seismic Data ◽

Computational Cost ◽

Synthetic Data ◽

Model Space ◽

Radon Transforms ◽

Iterative Solver ◽

Hard Thresholding ◽

Restricted Model ◽

Marine Data

The coefficients that synthesize seismic data via the hyperbolic Radon transform (HRT) are estimated by solving a linear-inverse problem. In the classical HRT, the computational cost of the inverse problem is proportional to the size of the data and the number of Radon coefficients. We have developed a strategy that significantly speeds up the implementation of time-domain HRTs. For this purpose, we have defined a restricted model space of coefficients applying hard thresholding to an initial low-resolution Radon gather. Then, an iterative solver that operated on the restricted model space was used to estimate the group of coefficients that synthesized the data. The method is illustrated with synthetic data and tested with a marine data example.

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