Quantitative comparison of the total focusing method, reverse time migration, and full waveform inversion for ultrasonic imaging.

To obtain a physical understanding of gradient-based descent methods in full-waveform inversion (FWI), we find a connection between the FWI gradient and the image provided by reverse time migration (RTM). The gradient uses the residual data as a virtual source, and RTM uses the observed data directly as the boundary condition, so the FWI gradient is similar to a time integration of the RTM image using the residual data, which physically converts the phase of the reflectivity to the phase of the velocity. Therefore, gradient-based FWI can be connected to the classical reflectivity-to-velocity/impedance inversion (RVI). We have developed a new FWI scheme that provides a self-contained and physically intuitive derivation, which naturally establishes a connection among the amplitude-preserved RTM, the Zoeppritz equations (amplitude variation with angle inversion), and RVI, and combines them into a single framework to produce a preconditioned inversion formula. In this scheme, the relative velocity update is a phase-modified and deconvolved RTM image obtained with the residual data. Consistent with the deconvolution, the multiscale approach applies a gradually widening low-pass frequency filter to the deconvolved wavelet at early iterations, and then it uses the unfiltered deconvolved wavelet for the final iterations. Our numerical testing determined that the new method makes a significant improvement to the quality of the inversion result.

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.

ABSTRACTTo obtain a physical understanding of gradient-based descent methods in full-waveform inversion (FWI), we find a connection between the FWI gradient and the image provided by reverse time migration (RTM). The gradient uses the residual data as a virtual source, and RTM uses the observed data directly as the boundary condition, so the FWI gradient is similar to a time integration of the RTM image using the residual data, which physically converts the phase of the reflectivity to the phase of the velocity. Therefore, gradient-based FWI can be connected to the classical reflectivity-to-velocity/impedance inversion (RVI). We have developed a new FWI scheme that provides a self-contained and physically intuitive derivation, which naturally establishes a connection among the amplitude-preserved RTM, the Zoeppritz equations (amplitude variation with angle inversion), and RVI, and combines them into a single framework to produce a preconditioned inversion formula. In this scheme, the relative velocity upd...

In conventional marine seismic surveys, due to the time-delayed reflections from the sea surface on both source and receiver sides, ghosts present in recorded seismograms and lead to both phase and spectrum distortions (especially near certain frequency notches). To achieve a high-quality broad-band image/velocity model with conventional reverse time migration (RTM)/full waveform inversion (FWI) that adopts a synthetic zero-phase source wavelet and absorbing surface condition during wavefield modelling, marine seismic data have to be pre-processed to remove ghost effects. However, seismic deghosting is not a trivial task. Instead of employing an external deghosting process, we propose a strategy to compensate for ghost effects during FWI and RTM, which consists of two parts: first, to address phase distortions due to ghost effects by means of obtaining an accurate source wavelet estimation and adopting an appropriate surface boundary condition in both forward and backward wave propagation to appropriately generate ghosts; secondly, to build a compensation operator in the adjoint state computation to mitigate spectrum distortions caused by dominant ghost effects. To demonstrate the success and robustness of the proposed strategy, we present both synthetic experiments and field examples, which suggest that this strategy can lead to successful applications of FWI/RTM directly on marine seismic data without an extra deghosting process.

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.

After many years of processing seismic streamer data acquired over the Shenzi field in deep-water Gulf of Mexico (GOM) with the best available technology, the workflows have remained highly interpretive, far from robust, often time-consuming, and ultimately proved inadequate for resolving the complexity of the salt and subsalt velocity models. Recent advances in full-waveform inversion (FWI) algorithms combined with a newly acquired, ocean bottom node (OBN) data set have ushered in a fundamental shift in velocity model building and imaging at Shenzi as we move away from mostly interpretation-driven to more data-driven processes. While the velocity model obtained from Time-lag FWI (TLFWI) using the legacy rich-azimuth (RAZ) streamer data provided significant imaging uplift over the best previous processing, an additional step-change improvement in image quality was achieved by running TLFWI with the OBN data. The OBN TLFWI model combined with the long offsets of the OBN data allowed steeply dipping events along the salt feeder to be seen for the first time on the reverse time migration (RTM) image. However, despite these large improvements, the image still suffers in areas of low illumination. Least-squares RTM (LSRTM) showed some good improvement over the RTM but proved less effective where the starting image was too poor. By running TLFWI to a maximum frequency comparable to the RTM, we were able to generate an FWI Image, an estimation of the reflectivity obtained directly from the FWI velocity model, with good S/N, more balanced amplitudes, and improved steep-dip and fault imaging, making it a direct rival to the RTM and LSRTM images.

The Arabian Gulf near-surface geology is complex, with extremely shallow waters and a hard water bottom generating high amplitude short period multiples and thinly bedded high and low velocity layers creating high apparent anisotropy in the bandwidth of seismic surveys. Obtaining an accurate description of the velocity variations in the near-surface and at intermediate depths is a necessity for reliable imaging and positioning of the reservoir layers located underneath. We propose a two-step full-waveform inversion (FWI) of ocean-bottom node (OBN) seismic data from offshore Abu Dhabi. We update a velocity model, using both diving and reflected waves, to reach the required depth of penetration. FWI has become an industry standard for velocity model building. However, due to the oscillatory nature of seismic data, FWI is known to be subject to cycle-skipping, where the inversion process falls into a local minimum. This risk is mitigated by using an accurate enough initial model and the use of low frequencies. In the shallow waters of offshore Abu Dhabi, near-offset data suffer from strong mud-roll and guided-wave energy that are not properly modeled with acoustic FWI. We exclude these offsets from the input data and use diving waves, starting at 3.5Hz, to update the near surface. The diving waves penetration is limited to approximately one kilometer in this area and corresponds to the base of a shallow high velocity layer. To reconcile the kinematics of reflected waves, travelling mostly vertically and used for imaging, and diving waves, travelling mostly horizontally, and used in the velocity update, we need an accurate estimation of the anisotropy. This is obtained using Backus averaging from available well logs. For deeper updates, the data are processed to remove the mud-roll and guided wave energy. This allows for the inclusion of reflections and near offsets. The FWI update is performed to 10Hz and penetrates about 3km into the sub-surface. We applied this FWI workflow to a recent node survey acquired offshore Abu Dhabi. The velocity model obtained follows the main geological structures and accurately describes the velocity variations in the shallow sub-surface. The estimation of anisotropy is important to ensure good convergence of the FWI and for imaging and vertical positioning of the migrated events. The reverse-time migration (RTM) image obtained with the updated model shows improved focusing and simplified depth structures compared to the RTM image obtained with the smooth initial model. To the best of our knowledge, this is the first successful implementation of FWI, here combining diving and reflected waves, on a dataset from offshore Abu Dhabi. It is a step towards resolving buried anomalies such as karst features, that cause imaging distortions at deeper reservoir levels.

Undetected inclusions and porosities in the additive manufactured components are undesirable in industries like aerospace engineering. This paper is focused on imaging of micro inclusions and porosities in numerical models based on the properties of an additive manufactured metal using an advanced imaging technique—full-waveform inversion (FWI) as an ultrasonic non-destructive testing (NDT) technique. We developed three models with—single inclusion of 200µm, multiple inclusions of different sizes (30-200µm) and wave speeds, and multiple porosities (30-100µm). The performance of FWI was analyzed for each model. The reconstructed images of all models from the proposed FWI method gave relatively accurate results about the porosities and inclusions, exhibiting the potential of applying FWI in overcoming challenges in NDT for additively manufactured materials.

Time-lapse seismic analysis plays an essential role in reservoir monitoring. We aim at developing a reservoir monitoring approach using a permanent seismic source “ACROSS” (Accurately Controlled and Routinely Operated Signal System) that can produce repeatable, extremely precise source signature. Both vertical and horizontal single forces are reconstructed by clockwise and counter-clockwise rotations of an asymmetric cylindrical mass. Here, we performed test observation of low-frequency data (3.5-15Hz) at JOGMEC Kashiwazaki test field, Niigata, Japan. We installed the ACROSS source with a horizontal rotation axis that can generate pronounced P-wave energy. With the assumption that one or two ACROSS sources are installed at a CCS (carbon capture and storage) field, we performed 2D simulation study using reverse time migration (RTM) and full waveform inversion (FWI) for delineating temporal change of the P-wave velocity. Since ACROSS precisely controls the sweep source signature, it is possible to discuss application of time-lapse FWI rather than just the first arrival or P-wave reflection traveltime inversion. To simplify the multi-component, multi-parameter problem on elastic FWI, we invert only for P-wave velocity residual using so-called scalar potential of the elastic wavefields. The synthetic FWI result shows sharp delineation of P-wave velocity residual associated with fluid replacement. The superior repeatability of ACROSS and developments of time-lapse imaging methods may bring a breakthrough towards hydrocarbon reservoir monitoring.

Ground-penetrating radar (GPR) profiling is the primary tool to provide detail information of the internal structure and characteristics inside a sand dune in the desert area. However, with the severe elevation change in a short horizontal distance and on the rugged and complex surface topography of the sand dunes, getting clear imaging of the internal structure of sand dunes from the GPR profiling is still a big challenge. The classic imaging technique such as the Kirchhoff migration has been applied to process GPR data on sand dunes, with limited success. The reverse-time migration (RTM) technique is the most advanced imaging technique that can handles GPR data acquired on rugged surface with severe topographic relief to generate subsurface structural images with high fidelity and has been tried to process GPR data on sand dunes. The results are encouraging, and the imaging quality is significantly improved. The finite-difference time-domain (FDTD) method is the major numerical tool for forward and backward continuations of the wave field during the RTM process. There are two aspects for using FDTD in RTM of GPR data on sand dunes still need improvement: the numerical scattering caused by the staircase approximation of the ground surface by using gridding in the Cartesian coordinate, and the negligence of the possible anisotropy of the electromagnetic material properties due to the calcareous cementation bedding inside a sand dune. In this paper, we develop the RTM algorithm based on the staggered grid FDTD that handles the rugged topographic surface by using the curvilinear coordinate, and the possible anisotropic radar wave velocity of the sand dune media. We first demonstrate the equivalency of the nonuniform, isotropic medium and the uniform, anisotropic medium for justifying using the uniform, anisotropic velocity in the RTM by synthetic modeling. Next, we validate our approach of using the synthetic data with the comparison of using the Cartesian coordinate and the curvilinear coordinate in an isotropic medium. The results indicate that the RTM algorithm using the curvilinear coordinate can efficiently eliminate the adverse effect of the staircase approximated boundary of the topography surface. Finally, we processed the real GPR data collected on a sand dune in the Badain Jaran desert by using the curvilinear coordinate and the uniform, anisotropic velocity in FDTD forward and backward wave field continuation. Comparison of the results indicates that the RTM imaging using the boundary-conforming curvilinear coordinate and anisotropic velocity gains more coherent and higher resolution images for the calcareous cementation layers and the water table.

Full Waveform Inversion (FWI) is a successful and well-established inverse method for reconstructing material models from measured wave signals. In the field of seismic exploration, FWI has proven particularly successful in the reconstruction of smoothly varying material deviations. By contrast, non-destructive testing (NDT) often requires the detection and specification of sharp defects in a specimen. If the contrast between materials is low, FWI can be successfully applied to these problems as well. However, so far, the method is not fully suitable for reconstructing homogeneous Neumann boundaries such as hidden backsides of walls, crack-like defects, or internal voids, which are characterized by an infinite contrast in the material parameters. Inspired by fictitious domain methods, we introduce a dimensionless scaling function γ to model void regions in the forward and inverse scalar wave equation problem. Applying the scaling function γ to the material parameters in different ways results in three distinct formulations for mono-parameter FWI and one for two-parameter FWI. The resulting problems are solved by first-order optimization, where the gradient is computed using the adjoint state method. The corresponding Fréchet kernels are derived for each approach and the associated minimization is performed using an L-BFGS algorithm. A comparison between the different approaches shows that scaling the density with γ is most promising for parametrizing void material in forward and inverse problems. Finally, in order to consider arbitrary complex geometries known a priori, this approach is combined with an immersed boundary method, the finite cell method (FCM).

In viscoelastic media, reverse time migration (RTM) requires accurate Q value for energy compensation and phase correction. Full waveform inversion (FWI) has the potential to provide accurate Q value. In the wide frequency band seismic data, the quality factor Q almost does not change with frequency, which is called constant Q model, but its computational complexity is large. In the narrow frequency band data, when the memory variable order L is assumed to be 1 in the standard linear solid (SLS) model, the attenuation simulation effect of the subsurface Q value is acceptable, and the calculation amount is small. In this paper, we derive the back propagation wave field equation and gradient formula of full waveform inversion of viscoelastic medium based on the SLS model with memory variable order L = 1, and analyzes the effectiveness and feasibility of this method. In viscoelastic medium, low velocity body will produce low frequency noise in seismic record, which will lead to heterogeneous gradient energy. This low frequency noise is similar to the low frequency noise produced near the source of shallow strata. This will reduce the accuracy of the inversion results. The gradient preconditioning method using the pseudo-Hessian operator can make the gradient energy more balanced. Therefore, we introduce the pseudo-Hessian operator in gradient preconditioning and derives the gradient preconditioning formula for the full waveform inversion in viscoelastic media, which solves the problem of the non-uniform gradient energy. Examples show that the method can suppress the non-uniform gradient energy in the full waveform inversion of viscoelastic media.

Discretized tensor-based model of total focusing method: A sparse regularization approach for enhanced ultrasonic phased array imaging

Reverse time migration (RTM) is achieved by a forward and reverse time propagation of source and receiver wavefields respectively, followed by an imaging condition. The quality of the image from any RTM implementation depends directly on the method’s ability to separate the true reflection data from the backscattered correlation noise between the source and receiver wavefields. In this paper we demonstrate the application of an inverse scattering imaging condition that significantly reduces this backscattered correlation noise and results in a much higher quality subsurface image than is achieved by typical RTM imaging conditions.

Numerical implementation of the gradient of the cost function in a gradient-based full waveform inversion (FWI) is a migration operator used in wave equation migration. In FWI, minimizing different data residual norms results in different weighting strategies of data residuals at receiver locations prior to back propagation into the medium. In this paper, we propose different scaling methods to the receiver wavefield and compare their performances. Using time domain reverse time migration (RTM), we show that this type of scaling is able to significantly suppress outliers compared to conventional algorithms. Our tests also show that scaling by its absolute norm produces better results than other approaches.