Full Waveform Inversion Research Articles

Automated salt model building: From compaction trend to final velocity model using waveform inversion

Conventional seismic velocity model building in complicated salt-affected areas requires the explicit identification of salt boundaries in migrated images and typically involves testing of possible subsurface scenarios through multiple generations. The resulting velocity models are slow to generate and may contain interpreter-driven features that are difficult to verify. We show that it is possible to build a full final velocity model using advanced forms of full-waveform inversion applied directly to raw field data, starting from a model that contains only a simple 1D compaction trend. This approach rapidly generates the final velocity model and migrates processed reflection data at least as accurately as conventionally generated models. We demonstrate this methodology using an ocean-bottom-node data set acquired in deep water over Walker Ridge in the Gulf of Mexico. Our approach does not require exceptionally long offsets or the deployment of special low-frequency sources. We restrict the inversion so it does not use significant energy below 3 Hz or offsets longer than 14 km. We use three advanced forms of waveform inversion to recover the final model. The first is adaptive waveform inversion to proceed from models that begin far from the true model. The second is nonlinear reflection waveform inversion to recover subsalt velocity structure from reflections and their long-period multiples. The third is constrained waveform inversion to produce salt- and sediment-like velocity floods without explicitly identifying salt boundaries or velocities. In combination, these three algorithms successively improve the velocity model so it fully predicts the raw field data and accurately migrates primary reflections, though explicit migration forms no part of the workflow. Thus, model building via waveform inversion is able to proceed from field data to the final model in just a few weeks. It entirely avoids the many cycles of model rebuilding that may otherwise be required.

Concurrent elastic inversion of Rayleigh and body waves with interleaved envelope-based and waveform-based misfit functions

Rayleigh and body waves are both solutions of the same propagation equation, but correspond to different wavenumber regions and boundary conditions, so their interaction with the elastic parameters (Vp, Vs and density) provides independent constraints during inversion. We develop and illustrate concurrent, elastic, full-waveform inversion of P and S body- and Rayleigh-waves using interleaved envelope- and waveform-based misfit functions, in a gradually-increasing frequency, multi-scale, inversion strategy. A wavelet and its envelope have different effective bandwidths, spectral shapes, and provide complementary frequency and wavenumber weighting in concurrent inversion. Because of the greater depth extent sampled by the exponentially decaying tail of a Rayleigh wave, compared to a body waveform, the depth extent of the model required to support both body and surface waves in concurrent inversion is defined by the Rayleigh waves. Correlation coefficients provide quantitative measures of the contributions of the data subsets to the fits of the solutions. For both smooth and constant starting models, concurrent interleaved inversion gives smaller data misfits than the envelope-only and waveform-only solutions. Treating the whole wavefield as a single data set means that it is not necessary to separate, or even to identify, different types of body and surface waves.

Implicit Seismic Full Waveform Inversion With Deep Neural Representation

AbstractFull waveform inversion (FWI) is arguably the current state‐of‐the‐art amongst methodologies for imaging subsurface structures and physical parameters with seismic data; however, important challenges are faced in its implementation and use. Keys amongst these are (a) building a suitable initial model, from which a local minimum is unlikely to be reached, and (b) availability of tools for evaluation of uncertainty. An algorithm we refer to as implicit full waveform inversion (IFWI), designed using continuously and implicitly defined deep neural representations, appears in principle to address both of these issues. We observe in IFWI, with its random initialization and deep learning optimization, improved convergence relative to standard FWI model initialization and optimization. Models close to the global minimum, capturing relatively high‐resolution subsurface structures, are obtained. In addition, uncertainty analysis, though not solved in IFWI, is meaningfully addressed by approximating Bayesian inference with the addition of dropout neurons. Numerical experimentation with a range of 2D geological models is suggestive that IFWI exhibits a strong capacity for generalization, and is likely well‐suited for multi‐scale joint geophysical inversion.

Acoustic Full Waveform Inversion with Hamiltonian Monte Carlo Method

Full-Waveform Inversion (FWI) is a high-resolution technique used in geophysics to evaluate the physical parameters and construct subsurface models in a noisy and limited data scenario. The ill-posed nature of the FWI turns this a challenging problem since more than one model can match the observations. In a probabilistic way, solving the FWI problem demands efficient sampling techniques to infer information on parameters and to estimate the uncertainties in high-dimensional model spaces. We investigate the feasibility of applying the Hamiltonian Monte Carlo (HMC) method in the acoustic FWI by a reflection setup containing different noise level data. We propose a new strategy for tuning the mass matrix based on the acquisition geometry of the seismic survey. Our methodology significantly improves the ability of the HMC method in reconstructing reasonable seismic models with affordable computational efforts.

Near-Surface 2D Imaging via FWI of DAS Data: An Examination on the Impacts of FWI Starting Model

Full waveform inversion (FWI) and distributed acoustic sensing (DAS) are powerful tools with potential to improve how seismic site characterization is performed. FWI is able to provide true 2D or 3D images of the subsurface by inverting stress wave recordings collected over a wide variety of scales. DAS can be used to efficiently collect high-resolution stress wave recordings from long and complex fiber optic arrays and is well-suited for large-scale site characterization projects. Due to the relative novelty of combining FWI and DAS, there is presently little published literature regarding the application of FWI to DAS data for near-surface (depths < 30 m) site characterization. We perform 2D FWI on DAS data collected at a well-characterized site using four different, site-specific 1D and 2D starting models. We discuss the unique benefits and challenges associated with inverting DAS data compared to traditional geophone data. We examine the impacts of using the various starting models on the final 2D subsurface images. We demonstrate that while the inversions performed using all four starting models are able to fit the major features of the DAS waveforms with similar misfit values, the final subsurface images can be quite different from one another at depths greater than about 10 m. As such, the best representation(s) of the subsurface are evaluated based on: (1) their agreement with borehole lithology logs that were not used in the development of the starting models, and (2) consistency at shallow depths between the final inverted images derived from multiple starting models. Our results demonstrate that FWI applied to DAS data has significant potential as a tool for near-surface site characterization while also emphasizing the significant impact that starting model selection can have on FWI results.

Full waveform inversion for arterial viscoelasticity

Objective. Arterial viscosity is emerging as an important biomarker, in addition to the widely used arterial elasticity. This paper presents an approach to estimate arterial viscoelasticity using shear wave elastography (SWE). Approach. While dispersion characteristics are often used to estimate elasticity from SWE data, they are not sufficiently sensitive to viscosity. Driven by this, we develop a full waveform inversion (FWI) methodology, based on directly matching predicted and measured wall velocity in space and time, to simultaneously estimate both elasticity and viscosity. Specifically, we propose to minimize an objective function capturing the correlation between measured and predicted responses of the anterior wall of the artery. Results. The objective function is shown to be well-behaving (generally convex), leading us to effectively use gradient optimization to invert for both elasticity and viscosity. The resulting methodology is verified with synthetic data polluted with noise, leading to the conclusion that the proposed FWI is effective in estimating arterial viscoelasticity. Significance. Accurate estimation of arterial viscoelasticity, not just elasticity, provides a more precise characterization of arterial mechanical properties, potentially leading to a better indicator of arterial health.

Understanding Subsurface Fracture Evolution Dynamics Using Time‐Lapse Full Waveform Inversion of Continuous Active‐Source Seismic Monitoring Data

AbstractPredicting the behavior, geometry, and flow properties of subsurface fractures remains a challenging problem. Seismic models that can characterize fractures usually suffer from low spatiotemporal resolution. Here, we develop a correlative double‐difference time‐lapse full waveform inversion of continuous active source seismic monitoring data for determining high‐spatiotemporal‐resolution time‐lapse Vp models of in‐situ fracture evolution at a shallow contamination site in Wyoming, USA. Assisted by rock physics modeling, we find that (a) rapidly increasing pore pressure initializes and grows the fracture, increasing the porosity slightly (from ∼13.7% to ∼14.6%) in the tight clay formation, thus decreasing Vp (∼50 m/s); (b) the fluid injection continues decreasing Vp, likely through the introduction of gas bubbles in the injectate; and (c) final Vp reductions reach over ∼150 m/s due to a posited ∼4.5% gas saturation. Our results demonstrate that high‐resolution Vp changes are indicative of mechanical and fluid changes within the fracture zone during hydrofracturing.

Waveform inversion via reduced order modeling

We introduce a novel approach to waveform inversion based on a data-driven reduced order model (ROM) of the wave operator. The presentation is for the acoustic wave equation, but the approach can be extended to elastic or electromagnetic waves. The data are time resolved measurements of the pressure wave gathered by an acquisition system that probes the unknown medium with pulses and measures the generated waves. We propose to solve the inverse problem of velocity estimation by minimizing the square misfit between the ROM computed from the recorded data and the ROM computed from the modeled data, at the current guess of the velocity. We give a step by step computation of the ROM, which depends nonlinearly on the data and yet can be obtained from them in a noniterative fashion, using efficient methods from linear algebra. We also explain how to make the ROM robust to data inaccuracy. The ROM computation requires the full array response matrix gathered with colocated sources and receivers. However, we find that the computation can deal with an approximation of this matrix, obtained from towed-streamer data using interpolation and reciprocity on-the-fly. Although the full-waveform inversion approach of nonlinear least-squares data fitting is challenging without low-frequency information, due to multiple minima of the data fit objective function, we find that the ROM misfit objective function has better behavior, even for a poor initial guess. We also find by explicit computation of the objective functions in a simple setting that the ROM misfit objective function has convexity properties, whereas the least-squares data fit objective function displays multiple local minima.

Evaluation of starting model approaches and effective source wavelet variations for high-frequency ground-penetrating radar full-waveform inversion

High-frequency ground-penetrating radar (GPR) full-waveform inversion (FWI) can enhance the characterization of small-scale structures in the subsurface below the decimeter scale. We have investigated the potential and requirements to use FWI for higher-frequency data. Thereby, we focus on the two most important criteria to achieve reliable FWI results: adequate starting models that fulfill the half-wavelength criterion and the accuracy of the effective source wavelet. Therefore, we have defined a realistic reference model, generated synthetic GPR data sets (200, 450, and 700 MHz), and tested different standard ray-based starting model methods and frequency-hopping approaches to derive results close to our reference model. Although standard starting models provide good parameter reconstruction for lower-frequency data, a frequency-hopping approach is required for the 700 MHz data. In addition, we have seen that the reconstruction of the conductivity results is more sensitive to the presence of noise (25 dB) than the permittivity tomograms. The definition of the effective source wavelets is directly linked to the accuracy of the starting models; therefore, we investigate the effect on the FWI results for high-frequency data by varying the source wavelets in terms of starting time and/or amplitude. Considering the multiparameter nature of FWI, we observe that time shifts have a greater influence on the performance of the FWI than amplitude variations. Large time shifts of approximately 0.1 ns for the 700 MHz data may lead to the failure of the inversion, whereas amplitude variations (±5% of the maximum amplitude) affect the quantitative conductivity results only (no effect on permittivity) with an increased root-mean-square error of the data of up to 20%. Using a stochastically perturbed synthetic model, we determine an improved parameter reconstruction for higher frequencies. On the basis of our findings, we develop a workflow to obtain reliable results for high-frequency GPR FWI for future users.

Stepsize sharing in time-lapse full-waveform inversion

Full-waveform inversion (FWI) methods can produce high-resolution images of the physical properties of the subsurface. FWI has become a powerful tool for time-lapse or 4D seismic inversion, with applications in the monitoring of reservoir changes with injection and production, and potentially long-term storage of carbon. Current time-lapse FWI strategies include the parallel strategy (PRS), the sequential strategy, the double-difference strategy (DDS), the common-model strategy (CMS), and the central-difference strategy (CDS). PRS time-lapse inversion is affected by convergence differences between the baseline and monitoring inversions, as well as nonrepeatable noise and nonrepeatable acquisition geometries between surveys. The other strategies are largely efforts to fix the sensitivities of PRS, but robust solutions are still sought. We hypothesize that several problems in time-lapse FWI arise from the independence of step lengths during updating. This is supported by synthetic data tests, which indicate that stepsize sharing reduces artifacts caused by the variability in PRS convergence. Two strategies, which we refer to as stepsize-sharing PRS (SSPRS) and stepsize-sharing CMS, are then designed to address these remaining issues. In this paper, we have tested our methods in five scenarios, including noise-free data, nonrepeated noises, nonrepeatable source positions, biased starting models, and a combination of the latter three. The comparisons between the SSPRS and other strategies indicate that the SSPRS can adapt to all tested scenarios well. Especially, except for the DDS which is extremely sensitive to the nonrepeatable source positions, only the SSPRS can provide meaningful results in the latter two scenarios when compared with others. Furthermore, given that SSPRS through its sharing incurs half of the time cost of seeking stepsizes compared with the PRS and DDS, the total computational cost of SSPRS is less than half of that of the CMS and CDS.

Progressive multitask learning for high-resolution prediction of reservoir elastic parameters

Reservoir elastic parameters play an important role in resource exploration; however, the band-limited characteristics of seismic data and the ill-posed nature of seismic inversion significantly affect inversion accuracy. To alleviate this problem, a high-resolution prediction method for reservoir elastic parameters based on the progressive multitask learning network (PMLN) is proposed. Our network consists of three parts: network 1 for low-frequency extension (LFE), network 2 for reservoir parameter inversion, and network 3 for image superresolution (SR). Taking the seismic frequency band as the link, network 1 is first used to predict the low-frequency information of seismic data. Then, the nonlinear mapping relationship between the high-pass-filtered seismic data (and its envelope) and full-frequency seismic data is established. Second, network 2 directly predicts the reservoir elastic parameters using the seismic data after LFE. Finally, the SR of the inversion results is achieved from the image perspective based on network 3. The three networks have a progressive relationship and can share network features, which is beneficial for improving computing efficiency. As the features extracted by the network represent different contributions to the prediction target, a channel attention mechanism is introduced. Furthermore, the loss function of network 2 is improved using dip constraints to obtain high-precision reservoir parameters. Synthetic and field data analyses find that all three networks are competent for their respective tasks, and the PMLN can obtain high-resolution prediction results of reservoir elastic parameters. Compared with traditional full-waveform inversion, the PMLN effectively improves prediction accuracy. Therefore, the PMLN is expected to become a powerful tool for predicting the elastic parameters of reservoirs.

Distributed iterative reweighted least squares algorithm for high-resolution finite-frequency traveltime velocity inversion using VSP data

Seismic traveltime between a source-receiver pair is a finite-frequency phenomenon. The velocity information at all points inside the first Fresnel zone is contained inside the traveltime. Therefore, finite-frequency traveltime velocity inversion (FFTVI) is able to invert velocity with finer structures than that can be obtained by ray-based tomography. Since FFTVI is a global inversion, its cost is lower than full waveform inversion. The implementation in this paper mainly focuses on the numerical aspects of FFTVI. We analyze the characteristics of FFTVI from the computational point of view. A parallel version, Iterative Reweighted Least Squares (IRLS) is designed for solving a large linear system in the memories of computer clusters. This implementation not only yields the accurate inversion of velocity at arbitrary grids and with an arbitrary acquisition geometry, but also is able to mitigate the impacts of traveltime picks with large uncertainties. The proposed workflow and parallel algorithm are demonstrated on synthetic VSP examples designed from a land project.

Multiparameter 2-D viscoelastic full-waveform inversion of Rayleigh waves: a field experiment at Krauthausen test site

SUMMARYFull-waveform inversion (FWI) has been proven to be an effective tool for high-resolution multiparameter imaging of the shallow subsurface. It has been shown that the Gauss–Newton (GN) optimization method uses the off-diagonal information contained in the Hessian matrix and can increase resolution and mitigate crosstalk in multiparameter viscoelastic FWI. In this work, we demonstrate the advantages of GN viscoelastic FWI over the conventional FWI with a conjugate gradient optimization method by using synthetic examples. We also investigate the potential of shallow seismic-wave 2-D viscoelastic FWI as a method for high-resolution hydrogeological characterization. The GN viscoelastic FWI is applied to two orthogonal profiles acquired at the Krauthausen natural laboratory (Germany). The groundwater table is located at around 2 m, which nicely agrees with an abrupt increase of P-wave velocity in the inverted results. FWI also reveals a low S-wave velocity layer at the depth of 4–6 m with high Poisson’s ratio values close to 0.5, which corresponds to a saturated sand layer known from previous studies. A K-mean cluster analysis is used to further analyse the multiparameter FWI results. By considering the derived Poisson’s ratio, P- and S-wave velocities, we convert the complex relationship between the multivariate data into a lithological meaningful zonation of the shallow subsurface. By comparing the lithological units in the alluvial aquifer with the cone penetration tests clusters, we conclude that the divided facies describe valuable characterization information about the heterogeneity and connectivity of the aquifer. This experiment indicates that the multiparameter models derived by viscoelastic FWI contain useful information for high-resolution aquifer characterization, and the potential of multiparameter FWI combined with cluster analysis in shallow subsurface characterization is encouraging.

A note on Marchenko-linearised full waveform inversion for imaging

SUMMARY Full waveform inversion and least-squares reverse time migration are the leading technologies for imaging with seismic waves. Both of them usually rely (in one way or another) on a single-scattering approximation, i.e. the Born approximation, to compute gradients and obtain an updated model. This approximation linearises the relation between modelled data and model by ignoring multiple scattering. We propose to use the Marchenko integral, an equation originating from inverse scattering theory, to obtain an alternative linear equation. Using the Marchenko method we can retrieve Green’s functions, including all orders of scattering, for virtual sources anywhere within the volume of interest – without prior knowledge of the high-wavelength model variations that induce scattering. Plugging these estimated Green’s functions into the Lippmann–Schwinger integral delivers a Marchenko-linearised relation between the full waveform data and the model. We present this new linearisation strategy and illustrate its advantages and disadvantages by comparing numerical results for different inversion kernels. Our new linearisation is exact, i.e. it does not exclude any orders of scattering, however, it relies on the quality of the Marchenko-derived Green’s functions. These Marchenko-based Green’s functions require an estimate of the first arrivals of the Green’s functions – commonly obtained by modelling in a background medium. Although these first arrival estimates strongly bias our results for inaccurate background models, we find the Marchenko-linearisation to deliver overall slightly better inverted models than the single-scattering approximation.

3-D Bayesian variational full waveform inversion

SUMMARYSeismic full-waveform inversion (FWI) provides high resolution images of the subsurface by exploiting information in the recorded seismic waveforms. This is achieved by solving a highly non-linear and non-unique inverse problem. Bayesian inference is therefore used to quantify uncertainties in the solution. Variational inference is a method that provides probabilistic, Bayesian solutions efficiently using optimization. The method has been applied to 2-D FWI problems to produce full Bayesian posterior distributions. However, due to higher dimensionality and more expensive computational cost, the performance of the method in 3-D FWI problems remains unknown. We apply three variational inference methods to 3-D FWI and analyse their performance. Specifically, we apply automatic differential variational inference (ADVI), Stein variational gradient descent (SVGD) and stochastic SVGD (sSVGD), to a 3-D FWI problem and compare their results and computational cost. The results show that ADVI is the most computationally efficient method but systematically underestimates the uncertainty. The method can therefore be used to provide relatively rapid but approximate insights into the subsurface together with a lower bound estimate of the uncertainty. SVGD demands the highest computational cost, and still produces biased results. In contrast, by including a randomized term in the SVGD dynamics, sSVGD becomes a Markov chain Monte Carlo method and provides the most accurate results at intermediate computational cost. We thus conclude that 3-D variational FWI is practically applicable, at least in small problems, and can be used to image the Earth’s interior and to provide reasonable uncertainty estimates on those images.

Application of full waveform inversion algorithm in Laplace–Fourier domain for high-contrast ultrasonic bone quantitative imaging

Background and objectivesFull waveform inversion (FWI) has been widely applied for the reconstruction of underground medium parameters in seismic communities and has made a great success. It is also a promising way to image hard tissues such as bones by ultrasonic FWI algorithm. However, the ultrasonic FWI methods for bone parameters imaging reported in literature so far are limited to the time domain and/or Fourier domain, and can only achieve quantitative imaging with acoustic velocity of bone less than 3000 m/s. Because the acoustic velocity of actual cortical bones can be as high as 4200 m/s, it is still a challenge for FWI to achieve higher parameter contrast bone imaging. MethodsHere, we proposed an ultrasonic FWI algorithm in Laplace–Fourier domain (LFDFWI) for high-contrast bone quantitative imaging. Compared to Time domain and Fourier domain, the LFDFWI algorithm is more appropriate for dealing with the presence of high contrast between bone tissues, reducing the possibility of inversion falling into a local minimum, and obtaining better inversion results. We adapted the seismic FWI algorithm to make it suitable for high-frequency ultrasonic sources and small-sized bone parameter imaging. ResultsWe conducted a series of bone models to evaluate the effectiveness of the proposed algorithm, including four kinds of bone model derived from micro computed tomography (Micro-CT) image of rat. We evaluated the experimental results based on visual analysis, error analysis and structural similarity (SSIM). The numerical simulation results showed that, when acoustic approximation is used, the proposed method can obtain accurate high-contrast images of the velocity and density parameters of bone structure, the mean relative error (MRE) in the region of interest (ROI) were all less than 2%, and the SSIM is up to 98%; when the viscoelastic approximation is used, this method can also obtain the desired high-contrast bone parameter distribution, with MRE less than 4% and SSIM higher than 74%, both of which are better than FDFWI in Fourier domain (FDFWI). ConclusionThe results demonstrated that the proposed FWI algorithm can obtain high resolution bone parameter models close to the Micro-CT image, which proves its clinical application potential.

Toward high-fidelity imaging: Dynamic matching FWI and its applications

Full-waveform inversion (FWI) is firmly established within our industry as a powerful velocity model building tool. FWI carries significant theoretical advantages over conventional velocity model building methods such as refraction and reflection tomography. Specifically, by solving a nonlinear inverse problem through the wave equation, FWI is able to recover a broadband velocity model containing both high and low spatial wavenumbers, thus extending the approximation of residual moveout correction inherent in traditional velocity model building approaches. Moreover, FWI is capable of inverting information from the entire wavefield (i.e., early arrivals, reflections, refractions, and multiple energy) rather than from a subset as in conventional approaches (i.e., first break and primary reflections), thereby availing itself of more information to better constrain its model estimate. However, these theoretical benefits cannot be realized easily in practice because various complexities of real seismic data often conspire to violate algorithmic assumptions, leading to unsatisfactory results. Dynamic matching FWI (DMFWI) is a newly developed algorithm that solves an inversion problem that maximizes the cross correlation of two dynamically matched data sets — one recorded and the other synthetic. Dynamic matching of the two data sets de-emphasizes the amplitude impact, which allows the algorithm to focus on minimizing their kinematic differences rather than amplitude in the data-fitting process. The multichannel correlation makes the algorithm robust for data with low signal-to-noise ratio. Applications of DMFWI across different types of acquisition and geologic settings demonstrate that this novel FWI approach can resolve complex velocity errors and provide high-quality migrated images that exhibit a high degree of geologic plausibility. Additionally, reflectivity images can be obtained in a straightforward manner as natural byproducts through computation of the directional derivative of the inverted FWI velocity models.

Frequency-domain elastic full-waveform inversion based on Green functions

In this paper, the elastic full-waveform inversion in the frequency domain based on Green functions is investigated. The method allows to image media velocities of compressional wave and shear wave by using vertical and horizontal components. The forward problem is solved by the finite difference scheme with the perfectly matched layer in the frequency domain. The inversion is an optimization iterative process to minimize the residual between the synthetic data and the observed data on the surface. A gradient method is used to find the optimization direction, preconditioned with the diagonal part of the inverse Hessian matrix. The gradient is constructed based on Green functions, which serves to compute the gradient of the objective function with respect to model parameters effectively. The inversion is completed from low frequency to high frequency so that smaller wavelengths are progressively introduced in inversion. Numerical computations for the benchmark Overthrust model demonstrate the full-waveform inversion method in this paper can inverse media velocities of complex structures accurately.

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.

Average QP and QS estimation in marine sediments using a dense receiver array

A new spectral ratio method has been used to compute average P- and S-wave quality factors, [Formula: see text] and [Formula: see text], for the sedimentary sequence below the “V”-shaped Oseberg permanent reservoir monitoring (PRM) system. Quality factors are important for a more accurate characterization of the subsurface and to obtain additional information on the physical processes within the earth, such as fluid content and partial melt. However, few methods compute the average Q-value in sediments for P and S waves in a region, which can be used as a constraint for attenuation models in more sophisticated inversion techniques such as full-waveform inversion or attenuation tomography. To address this, a spectral ratio method using two receiving stations, one installed on sediment and one installed on bedrock, has been developed. This has resulted in quality factor estimations ranging from approximately 64 to 137 for P waves and 29 to 123 for S waves using a subset of the 172 ocean-bottom nodes in the Oseberg PRM system and a seismometer in Bergen, Norway. The [Formula: see text] values are more scattered and hence more uncertain than the [Formula: see text] values due to the P-wave signal being close to the background noise level. In the study area, local earthquakes of magnitude as low as [Formula: see text] 2.4 can be used to obtain [Formula: see text] values and earthquakes of magnitude lower than 2.1 to find [Formula: see text] values, with the possibility of using lower magnitude events if the epicentral distances to the receivers are similar and smaller. Using this method, the average quality factor in sediment packages, for a variety of regions, can be estimated using appropriate raypath configurations connecting source and receiver.