Conventional Full-waveform Inversion Methods Research Articles

Robust joint adaptive multiparameter waveform inversion with attenuation compensation in viscoacoustic media

Full-waveform inversion (FWI) has been proven as an effective method to estimate subsurface parameters by iteratively reducing the data residual between the predictions and the observations. Nevertheless, FWI is greatly dependent on the initial model, and a poor initial model will lead to an incorrect solution. Furthermore, owing to the anelasticity of the earth, seismic waves will attenuate during propagation, which results in an attenuated gradient and makes the convergence rate of FWI even worse in viscoacoustic medium. Commonly, multiparameter (e.g. velocity and Q) waveform inversion can be used to mitigate these problems. Benefiting from the theory of Q-compensated wavefield propagation, we develop a Q-compensated joint multiparameter waveform inversion method to weaken the nonlinearity of the FWI objective function, which enables it to cope with challenges related with attenuation-induced gradient energy loss and cycle skipping simultaneously. We refer to our Q-compensated joint multiparameter FWI scheme as QJMFWI. The main contributions of QJMFWI are as follows: (1) given the difficulty associated with the estimation of velocity and Q simultaneously in viscoacoustic media, QJMFWI provides a straightforward waveform inversion method for velocity and Q model construction, by which we can obtain velocity and Q information with improved accuracy and resolution; and (2) compared with conventional FWI methods, QJMFWI relaxes the requirement for a good initial velocity and Q model, which can avoid trapping into local minima. Numerical and field data examples demonstrate that QJMFWI is an effective method to invert for accurate subsurface parameters in viscoacoustic media.

Wide‐spectrum reconstruction of a velocity model based on the wave equation reflection inversion method and its application

AbstractMost seismic data used for conventional exploration lack far‐offset signals and effective low‐frequency components. This makes it difficult for conventional full waveform inversion methods to recover the low‐wavenumber components of mid‐ and deep‐layer models. To resolve the bottleneck of ray‐theoretical reflection traveltime tomography, wave equations, such as reflection inversion methods, are receiving increasing attention. We reconstructed a wide‐spectrum velocity model based on the multiscale wave‐equation reflection inversion method for model decomposition. First, using the dynamic image warping method to obtain reflection traveltime residuals, the wave‐equation reflection traveltime inversion was used to recover the low‐wavenumber components of the background model, which also solved the cycle‐skipping problem. Second, the medium‐wavenumber component of the model is then supplemented by the reflection waveform inversion, while the reflectivity model is obtained relying on the least‐squares reverse time migration method. Based on this method, the background and perturbation models are updated alternately and iteratively. At the same time, the stratum structural tensor information was extracted using the perturbed model image to construct a preconditioned operator for the stratum structural constraint, suppress unreasonably high‐wavenumber components in the generalized gradient and improve the geological consistency of the inversion results. Testing of the model using the Sigsbee2b model and seismic field data from the East China Sea showed that, compared with the conventional reflection traveltime tomography method based on prestack depth migration, the wave‐equation reflection inversion strategy with well‐matched information from traveltimes to waveforms significantly improved the accuracy of the middle and deep velocity modelling and enhanced the imaging quality of the whole body.

Seismic velocity inversion transformer

Velocity model inversion is one of the most challenging tasks in seismic exploration, and an accurate velocity model is essential for high-resolution seismic imaging. Recently, velocity inversion methods based on deep learning (DL), particularly convolutional neural networks (CNNs), have attracted considerable attention from the seismic exploration community. These researchers aim to directly estimate the velocity model from raw seismograms using a well-trained model. Although CNN-based velocity inversion methods have demonstrated remarkable performance in terms of intelligence and automation, their inversion performance is often constrained by a limited long-range dependence. Specifically, when conducting a convolutional operation on raw seismic data using small kernels (i.e., 1 × 1, 3 × 3, 5 × 5, and 7 × 7), CNN-based methods extract only the local features and neglect the weak spatial correlation between different local features that reflect the information of the same interface. This correlation could assist CNN in providing an overview of the seismic data and promote inversion performance when using DL. Furthermore, the time-varying properties of seismic data pose a challenge to the weight sharing of CNNs. Here, we have developed a new DL framework based on a transformer, called the seismic velocity inversion transformer (SVIT), to address the problem of velocity inversion. SVIT uses a self-attention mechanism to capture the long-range dependence of seismic data, rather than stacking multiple convolutional layers as in CNNs. Thus, SVIT can provide more informative remote features for building velocity models. The validity and reliability of the proposed method are demonstrated through numerical experiments using synthetic models. Compared with the conventional full-waveform inversion method and an existing CNN-based velocity inversion method, our SVIT indicates greater consistency with the target in terms of the velocity value, subsurface structures, and geologic interfaces and is expected to provide a new DL-based solution to resolve inversion problems.

Physics-driven self-supervised learning system for seismic velocity inversion

Seismic velocity inversion plays a vital role in various applied seismology processes. A series of deep learning methods have been developed that rely purely on manually provided labels for supervision; however, their performances depend heavily on using large training data sets with corresponding velocity models. Because no physical laws are used in the training phase, it is usually challenging to generalize trained neural networks to a new data domain. To mitigate these issues, we have embedded a seismic forward modeling step at the end of a network to remap the inversion result back to seismic data and thus train the neural network through self-supervised loss, i.e., the misfit between the network input and output. As a result, we eliminate the need for many labeled velocity models, and physical laws are introduced when back-propagating gradients through the seismic forward modeling step. We verify the effectiveness of our approach through comprehensive experiments on synthetic data sets, where self-supervised learning outperforms the fully supervised approach, which accesses much more labeled data. The superior performance is even more significant when compared with a new data domain that has velocity models with faults and more geologic layers. Finally, in case of unknown and more complex data types, we develop a network-constrained full-waveform inversion (FWI) method. This method refines the initial prediction of the network by iteratively optimizing network parameters other than the velocity model, as found with the conventional FWI method, and demonstrates clear advantages in terms of interface and velocity accuracy. With these measures (self-supervised learning and network-constrained FWI), our physics-driven self-supervised learning system successfully mitigates issues such as the dependence on large labeled data sets, the absence of physical laws, and the difficulty in adapting to new data domains.

Acoustic- and elastic-waveform inversion with total generalized p-variation regularization

Geophysical models usually contain both sharp interfaces and smooth variations, and it is difficult to accurately account for both of these two types of medium parameter variations using conventional full-waveform inversion methods. We develop a novel full-waveform inversion method for acoustic and elastic waves using a total generalized p-variation regularization scheme to address these challenging problems. We decompose the full-waveform inversion into two subproblems and solve these two minimization subproblems using an alternating-direction minimization strategy. One important advantage of the total generalized p-variation regularization scheme is that it can simultaneously reconstruct sharp interfaces and smooth background variations of geophysical parameters. Such capability can also effectively suppress the noises in source-encoded inversion and sparse-data inversion, or inversion of noisy data. We demonstrate the advantages of our full-waveform inversion method using a checkerboard model, a modified elastic SEG/EAGE overthrust model, and a land field seismic data set. Our results of synthetic and field seismic data demonstrate that our method reconstructs both smooth background variations and sharp interfaces of subsurface geophysical properties accurately, and provides a useful tool for accurate and reliable inversion of field seismic data.

Full waveform inversion using oriented time‐domain imaging method for vertical transverse isotropic media

ABSTRACTFull waveform inversion for reflection events is limited by its linearised update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate, the resulting gradient can have an inaccurate update direction leading the inversion to converge what we refer to as local minima of the objective function. In our approach, we consider mild lateral variation in the model and, thus, use a gradient given by the oriented time‐domain imaging method. Specifically, we apply the oriented time‐domain imaging on the data residual to obtain the geometrical features of the velocity perturbation. After updating the model in the time domain, we convert the perturbation from the time domain to depth using the average velocity. Considering density is constant, we can expand the conventional 1D impedance inversion method to two‐dimensional or three‐dimensional velocity inversion within the process of full waveform inversion. This method is not only capable of inverting for velocity, but it is also capable of retrieving anisotropic parameters relying on linearised representations of the reflection response. To eliminate the crosstalk artifacts between different parameters, we utilise what we consider being an optimal parametrisation for this step. To do so, we extend the prestack time‐domain migration image in incident angle dimension to incorporate angular dependence needed by the multiparameter inversion. For simple models, this approach provides an efficient and stable way to do full waveform inversion or modified seismic inversion and makes the anisotropic inversion more practicable. The proposed method still needs kinematically accurate initial models since it only recovers the high‐wavenumber part as conventional full waveform inversion method does. Results on synthetic data of isotropic and anisotropic cases illustrate the benefits and limitations of this method.

Frequency-domain auto-adapting full waveform inversion with blended source and frequency-group encoding

As a high quality seismic imaging method, full waveform inversion (FWI) can accurately reconstruct the physical parameter model for the subsurface medium. However, application of the FWI in seismic data processing is computationally expensive, especially for the three-dimension complex medium inversion. Introducing blended source technology into the frequency-domain FWI can greatly reduce the computational burden and improve the efficiency of the inversion. However, this method has two issues: first, crosstalk noise is caused by interference between the sources involved in the encoding, resulting in an inversion result with some artifacts; second, it is more sensitive to ambient noise compared to conventional FWI, therefore noisy data results in a poor inversion. This paper introduces a frequency-group encoding method to suppress crosstalk noise, and presents a frequency-domain auto-adapting FWI based on source-encoding technology. The conventional FWI method and source-encoding based FWI method are combined using an auto-adapting mechanism. This improvement can both guarantee the quality of the inversion result and maximize the inversion efficiency.

Improved Full-Waveform Inversion of Normalised Seismic Wavefield Data

The full-waveform inversion algorithm using normalised seismic wavefields can avoid potential inversion errors due to source estimation required in conventional full-waveform inversion methods. In this paper, we have modified the inversion scheme to install a weighted smoothness constraint for better resolution, and to implement a staged approach using normalised wavefields in order of increasing frequency instead of inverting all frequency components simultaneously. The newly developed scheme is verified by using a simple two-dimensional fault model. One of the most significant improvements is based on introducing weights in model parameters, which can be derived from integrated sensitivities. The model-parameter weighting matrix is effective in selectively relaxing the smoothness constraint and in reducing artefacts in the reconstructed image. Simultaneous multiplefrequency inversion can almost be replicated by multiple singlefrequency inversions. In particular, consecutively ordered singlefrequency inversion, in which lower frequencies are used first, is useful for computation efficiency.