LARGE SCALE RANDOMIZED LEARNING GUIDED BY PHYSICAL LAWS WITH APPLICATIONS IN FULL WAVEFORM INVERSION

Full-waveform inversion (FWI) has proved itself as a valuable tool for updating and improving the accuracy of subsurface velocity models. For optimum performance, particularly in complex geological environments such as subsalt targets in the Gulf of Mexico (GOM), FWI requires 3D seismic data containing low frequencies and long offsets. For onshore seismic surveys, it is relatively straightforward and cost-effective to record long-offset data; however, for offshore surveys it can incur the additional cost of ocean-bottom cable (OBC) acquisition or multivessel towed-streamer techniques. The recent introduction of dual-coil-shooting multivessel full-azimuth acquisition has provided a highly efficient method of delivering marine 3D seismic data sets with long offsets. Tests using synthetic data and a real GOM dual-coil acquisition data set with full-azimuth distribution and long (up to 14.3-km) offsets demonstrate significant potential for improving the accuracy of velocity models and the reliability of the resulting depth images. The results indicate that the long offsets and low frequencies provided by the dual-coil acquisition method are of particular benefit in helping FWI to enhance the shallow section of the model. Furthermore, lower frequencies and longer offsets mitigate the sensitivity of the inversion process to the initial velocity model by enabling FWI to update the low-wavenumber component of the velocity model.

Communication-efficient distributed cubic Newton with compressed lazy Hessian

Reflection traveltime information is generally used for producing a kinematically accurate velocity model for seismic imaging. Accurately estimating the traveltime difference between the demigrated and observed data is crucial for data-domain reflection traveltime tomography. To enhance the robustness of signal’s alignment, we propose a new method of segment dynamic image warping (SDIW). It first exploits windowed polynomial fitting for signal processing and then aligns the signals based on point-wise segment-to-segment matching. Compared with the conventional point-to-point matching strategy, our method is more robust and insensitive toward strong random noise. By minimizing the traveltime difference computed by SDIW, data-domain reflection traveltime inversion (DRTI) is then used to find an accurate background velocity model. Synthetic tests show that SDIW provides reliable time shifts between the demigrated and observed data even if the signal-to-noise ratio of input data is rather low. This enables DRTI to automatically reconstruct the deep background velocity model. The subsequent full waveform inversion (FWI) gradually added short-wavelength velocity structures and finally recovers a high-resolution and high-fidelity model. The results demonstrate that the DRTI provides a kinematically accurate background velocity model sufficient for following FWI to fully retrieve the detail of the subsurface structures even when the low frequencies are missing.

SUMMARY Compared to first-arrival traveltime tomography (FATT), first-arrival traveltime and slope tomography (FASTT) integrates both traveltimes and local slopes of first arrivals at sources and/or receivers to construct more accurate subsurface velocity models. Local slopes serve as additional constraints, helping to mitigate the ill-posedness of tomography by better constraining ray directions. This is particularly beneficial in regions with complex topography, where shadow zones arise due to strong velocity contrasts. However, representing complex topography or bathymetry can be less accurate when using classical rectangular grid discretization. To address these complexities with greater versatility and accuracy, we compute traveltimes of locally coherent events using a factored topography-dependent eikonal solver on curvilinear grids. Slopes are then estimated by finite differences in the traveltime maps after a back-and-forth coordinate transform from the curvilinear grid to a rectangular computational grid. Additionally, we solve the inverse problem with the matrix-free approach, where the data misfit gradient is computed with the adjoint-state method. This adjoint-state formulation avoids the explicit construction and storage of large Fréchet derivative matrices and does not require a tedious posterior ray tracing on curvilinear grids. A land synthetic example first illustrates the sensitivity of slopes to topography and the more accurate velocity models with FASTT than with FATT in the presence of topography. We then perform a first application of the topography-dependent FASTT method on a real redatumed ocean-bottom node data set, where the bathymetry exhibits a steep scarp. We show that the topography-dependent FASTT generates a velocity model that matches more closely a legacy reflection tomography model than conventional FATT. We conclude that the topography-dependent FASTT provides a versatile approach for handling complex surfaces during velocity model building in both marine and land environments.

Velocity model building is an essential step in seismic exploration, which runs through the whole process of seismic data acquisition, processing, and interpretation. The velocity information is conventionally obtained by iterative optimization methods such as full-waveform inversion or tomography. These traditional methods are computationally expensive, and they require an initial velocity model and human interactions. To simplify the model building problem, we develop a supervised end-to-end conventional neural network to reconstruct the P-wave velocity models directly from raw seismic data. The network takes in one-shot seismic traces simulated with acoustic wave equations in VSP geometry. To train the network, we create 870 2D synthetic seismic images and corresponding labeled images, which are shown to be sufficient for the network to learn the nonlinear relationship between one-shot seismic data and the corresponding velocity model. The numerical examples show that the trained network is capable of predicting accurate layered velocity models from only one-shot seismic data.

Summary Full-waveform inversion (FWI) can capture high-resolution geophysical properties but tends to fall into local minima. We addressed this problem by reducing the degree of freedom in the optimization problem and estimating an initial velocity model from shot gathers; our method comprises three steps. First, we trained a variational autoencoder using synthetic velocity models and created a low-dimensional latent space that represents realistic velocity models. Second, we prepared another encoder model, which estimates the latent features of the corresponding velocity model from shot gathers. Finally, we implemented latent space optimization (LSO) from the initial guess selected by the encoder. In the experiment, LSO reproduced much more accurate and realistic velocity models than the naive FWI, even when the initial guess was considerably different from the ground truth. This implies that with our method the latent space becomes easier to optimize than the original velocity model space. Furthermore, we verified that LSO using an initial guess selected by the encoder could increase the estimation accuracy. Our method also succeeded in accurately estimating the Marmousi2 model, without using any part of the benchmark dataset to directly train the variational autoencoder.

Velocity model building and depth imaging are known to be complicated endeavors in numerous onshore areas in the Middle East. Despite recent advancements toward denser, wide-azimuth, and low-frequency seismic acquisitions, the application of full-waveform inversion (FWI) remains challenging. The main difficulties arise from complex near-surface geology that creates wave mode conversions (P to S waves but also strong multiples) and very energetic and complex ground roll overlaying reflected waves and dominating low frequencies, with the diving waves being less energetic and noisier. This paper presents recent progress in land FWI toward higher-resolution velocity models, with successful applications to case studies from the Sultanate of Oman. The first example shows an application of land FWI imaging. It shows that we are able to invert jointly diving and reflected waves in acoustic FWI. With proper input data conditioning and initial model preparation, we successfully ran acoustic FWI up to 45 Hz, resulting in a high-resolution velocity model and derived FWI image that significantly improved subsurface imaging and geologic understanding. The inverted high-frequency velocity could also be more reliably used for subsequent reservoir characterization steps. Given the important role of a good-quality near-surface model for stabilizing high-frequency FWI updates, the second example highlights the creation of a detailed shallow velocity model. We propose using elastic FWI of surface waves for characterization of the near surface in complex geologic settings. Here, we demonstrate the effectiveness of this workflow to enhance imaging of the shallow subsurface. Compared to conventional methods such as surface-wave inversion, elastic FWI of surface waves has the advantage of 3D full-wavefield modeling with no requirement for picking. Our workflow also benefits from the ultra-low frequencies recovered by interferometry to obtain a more stable deeper update.

Full-waveform inversion (FWI) has become the centerpiece of velocity model building (VMB) in seismic data processing in recent years. It has proven capable of significantly improving the velocity model and, thus, the migration image for different acquisition types and geologic settings, including complex environments such as salt. With the advent of FWI imaging, the scope of FWI applications has extended further from VMB into the imaging landscape. However, current FWI applications in the industry prevalently employ the acoustic approximation. One common problem of acoustic FWI (A-FWI) is the apparent salt halos at the salt-sediment interface in the resulting FWI velocity and FWI image, the presence of which hinders direct interpretation and imaging focusing around salt bodies. With synthetic and field data examples, we demonstrate that this salt halo is caused mainly by the large mismatch between the elastic recorded data and the acoustic modeled data, particularly at middle to long offsets. To overcome limitations imposed by acoustic assumptions, we developed an elastic FWI (E-FWI) algorithm that combines an elastic modeling engine with the time-lag cost function, which we call elastic time-lag FWI (E-TLFWI). With a more accurate modeling engine, E-TLFWI significantly reduces the salt halo observed in its acoustic counterpart. However, we also observe that the images migrated using the A-FWI and E-FWI velocity models remain similar overall, with some slight improvements around and beneath salt boundaries, particularly near steep salt flanks, as a result of the reduced salt halo. By contrast, FWI images derived from E-TLFWI show considerable benefits over those from acoustic time-lag FWI, such as improved event focusing, better structural continuity, and higher signal-to-noise ratio. The sharpened salt boundaries and enhanced quality of the FWI images reveal the significant value of E-FWI and provide the justification for its greatly increased cost.

Full Waveform Inversion (FWI) is a seismic imaging technique that utilizes the entire content of seismic trace. This method aims to minimizes differences between real and synthetic seismograms. FWI consists of three main steps: forward modelling to simulate synthetic seismograms, adjoint simulation to calculate the gradient misfit, and optimization to obtain an appropriate model perturbation. FWI is an extremely non-linear inversion technique and computationally intensive since it involves many model parameters. In the context of geophysics, finding parameter models that describe the structure of the earth’s subsurface is the main goal. Geophysical measurements in the field only obtain data that is influenced by the parameter model, in this case seismic recording data, therefore mathematical techniques are studied and applied to determine the correct parameter model from the data obtained, also known as the inversion process. In this study, main research area is on optimization step which include mathematical approach to find perturbation model effectively. The Newton method can be used in the optimization step of FWI. However, its implementation is not promising due to high computational cost in calculating Hessian matrix. To reduce computation cost, an identity matrix is chosen to replace the Hessian matrix, as it usually done in the steepest descent method. Since FWI has a high level of non-linearity, steepest descent method requires many iterations to minimize the objective function. Therefore, this study uses a conjugate gradient method to make the data misfit minimized more quickly. Apart from that, the Line search technique is used to find an appropriate step-length at each iteration on both methods. The FWI workflow is applied to the synthetic acoustic velocity model. We conduct FWI using steepest descent and conjugate gradient methods. The results show that the conjugate gradient method requires fewer iterations than the steepest descent method to minimize the objective function. FWI model result using conjugate gradient method is closer with the true model compared to steepest descent method, showed on misfit result and model image. By comparing these methods we can see that conjugate gradient method can be chosen for application on FWI optimization step for better result on seismic imaging. On the industry scale, better results provide less uncertainty on the model parameters that useful for energy exploration or engineering.

An accurate earth model is key to any successful depth imaging effort. Full waveform inversion is an advanced velocity model building process which uses the full two way wave equation. Existing methods use a ray tracing approach to distribute velocity errors within the model. In this presentation, we will show examples of seismic data processed with the latest technology, including earth model building with full waveform inversion. Introduction The industry has moved to using two-way wave equation migrations(commonly known as reverse time migration), especially in areas of complex geology such as the salt bodies in the Gulf of Mexico and offshore Brazil. The velocity model, including velocity anisotropy, is key to any depth migration effort. The natural next step is to use the two-way wave equation for velocity model building. One of the most advanced tools for velocity model building using the two-way wave equation is Full Waveform Inversion(FWI). Full-waveform inversion uses computer intensive forward modeling of the seismic measurement combined with residual wavefield back propagation to iterate to a final velocity model, which can provide greater detail than tomographic ray tracing approaches. Velocity inversion using full waveform inversion has been used on a number of projects around the world including the GOM, Brazil and the North Sea.

Summary Full waveform inversion (FWI) is now well-established for velocity model building in areas penetrated by diving waves. While initial industrial successes were shown around year 2009, the technology has been evolving continuously with very significant improvements allowing for more accurate, robust and detailed results. Some difficulties have been identified, such as the problem of producing improved results at frequencies greater than 10 Hz. We address this point here in a case study involving shallow channels and a dense gas cloud anomaly. In this context, we demonstrate that multi-parameter anisotropic non-linear slope tomography can provide a sufficiently accurate initial anisotropic velocity model that enables FWI to improve the results above 10 Hz. We show results obtained on a 3D OBC dataset where high-frequency data are inverted up to 13 Hz, with the benefit of increased resolution in the velocity model, while ensuring structural conformity.

Old abandoned coal working create major hazards in the form of subsidence of the coalfields. To avoid such hazards, there is need to detect these cavities prior to start of deeper seam mining. There are number of geophysical techniques available for detecting subsurface cavity. High-resolution seismic survey is one such technique which provides accurate results as compared to others. Usually, most of the seismic processing and interpretation of these cavity detection was performed based on stacked data only. To understand these signatures more precisely, in our study, an attempt has been made to image these cavities with the help of Reverse Time Migration (RTM) combined with Full Waveform Inversion (FWI). RTM mostly used for hydrocarbon exploration targets with low central frequency as source. Application of this method to shallow subsurface exploration is still in research stage. Like the same way for velocity model updating, FWI gives mostly appropriate optimization results as compare to other techniques, but it also has the limitation to application of low frequency only. In this paper we first develop a 2D realistic Water Filled Cavity (WFC) model with a work flow of RTM combined with FWI in a high-frequency Ricker source wavelet as 100 Hz. In order to provide a velocity model with high accuracy for RTM, we apply FWI to estimate the subsurface velocity by considering an initial smooth velocity model with addition of 30 % Gaussian noise. The conventional RTM fails to image the cavities and yield a large amount of low frequency back scattered noise at shallow depth during the time of cross correlation due to time/space lag. To avoid these situation, we introduced an automatic shift operator at the time of imaging condition that operates automatically both in time or space. It leads to reduce the lag and improve the results by minimizing the noises at shallow subsurface. By comparing both the results it is observed that most of the noises in the migrated section of conventional method were eliminated by the improved form of RTM with the help of FWI velocity model estimation.

High-quality depth images typically require accurate highresolution representations of the earth model. Full-waveform inversion (FWI) has recently justified its value throughout the industry in providing high-resolution velocity models. However, obtaining an accurate FWI velocity model using narrow-azimuth streamer data can still be challenging in complex geologic environments. The uncertainties, often caused by relatively low resolution perpendicular to the shooting direction and weaker illuminations areas, instill less confidence for reservoir delineation and depth mapping. In this case study from offshore Senegal, we present a joint velocity (Vp) and epsilon (ε) multi-azimuth FWI workflow to construct a high-resolution model to overcome severe image distortion. The updated model improved event focusing and gather flatness and demonstrated significant imaging uplifts consistent with our understanding of the geology in the area.

Full waveform inversion using a decomposed single frequency component from a spectrogram

In seismic exploration, establishing a reliable velocity model is crucial for seismic migration imaging and reservoir characterization. Full-waveform inversion (FWI) is used to recover subsurface physical parameters by iteratively minimizing the misfit between the observed and synthetic data, theoretically offering the highest modeling accuracy. FWI is a combination of migration imaging and tomography. However, for reflection data, the update of the tomographic component is notably weaker than the migration component. When the gradient is dominated by the migration component, FWI can easily fall into local minima, which leads to bad inversion results. Hence, it is necessary to extract the tomographic component from the original FWI gradient to build a robust background velocity model when the initial model is inaccurate. In this paper, we develop to use the bidimensional empirical mode decomposition (BEMD) method to separate the original FWI gradient into the tomography and migration component. The BEMD method first adaptively decomposes the gradient into different-scale subcomponents. Then, the small-scale bidimensional intrinsic mode functions are combined into the migration component, and the large-scale residual component is considered to be the tomographic component. At the beginning of FWI, the background velocity is updated using the tomographic component, and with iterations, small-scale components are gradually added to update the velocity model. Numerical experiments show that the BEMD method can effectively separate the two components. The BEMD-based FWI can reconstruct the background velocity model, improving the FWI accuracy.