Full Waveform Inversion of Viscoelastic Media Based on Gradient Preconditioning

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...

The experiences of stress are common to all living things. Noise is one of the most widespread sources of environmental stress. Noise is a pervasive aspect of many modern community and work environments. So, it is important to consider noise when we design human-oriented products. This study investigates the responses of electrocardiogram (ECG) and eye tracker data in order to evaluate the direct effects of low, middle, and high frequency noise on the two main physiological stress axes: the autonomic nervous system, and cognitive responses for a human-oriented product design. A subject was exposed to low (100 Hz), middle (1000 Hz), and high frequency (100000 Hz) noise while awake. ECG and eye tracker data were collected during noise exposure. Sympathetic nervous system (SNS) activity was less in the low and high frequency noise ranges compared to the no sound. On the other hand, parasympathetic nervous system (PNS) activity was greater in the low and high frequency noise ranges than the SNS activity in the no sound. The cognitive responses or latency saccadic eye movement (LSEM), in low or high frequency noise was greater than that in the no sound. And results of EEG and eye movement were statistically significant in low and high frequency noise (r > 0.93, p < 0.05). The findings of this study indicate that the stress induced by low frequency noise is as stressful as the stress induced by high frequency noise. Additionally, utilizing eye tracker data and acquiring the LSEM is useful in the analysis of human stress responses during various stressful situations in addition to the analysis of human stress responses during noise exposure.

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.

Phased array ultrasound is a widely used technique in non-destructive testing. Using piezoelectric elements as both sources and receivers provides a significant gain in information and enables more accurate defect detection. The process is called full matrix capture when all source-receiver combinations are used. The total focusing method (TFM) exploits such datasets and relies on a delay and sum algorithm to sum up the signals on a pixel grid. However, TFM only uses the first arriving p-waves, making it challenging to size complex-shaped defects. By contrast, more advanced methods such as reverse time migration (RTM) and full waveform inversion (FWI) use full waveforms to reconstruct defects. Both methods compare measured signals with ultrasound simulations. While RTM identifies defects by convolving forward and backward wave fields once, FWI iteratively updates material models to reconstruct the actual distributions of material properties. This study compares TFM, RTM, and FWI for six specimens featuring circular defects or Y-shaped notches. The reconstructed results are first evaluated qualitatively by visual assessment, then different defect segmentation approaches are studied, and finally, they are evaluated quantitatively using metrics such as AUPRC, AUROC, and F1-score. The results show that a two-step FWI framework performs best in most of the six samples studied, both qualitatively and quantitatively.

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.

We present a comparative study of high frequency dynamics and low frequency noise in elliptical magnetic tunnel junctions with lateral dimensions under 100 nm presenting current-switching phenomena. The analysis of the high frequency oscillation modes with respect to the current reveals the onset of a steady-state precession regime for negative bias currents above J=107A/cm2, when the magnetic field is applied along the easy axis of magnetization. By the study of low frequency noise for the same samples, we demonstrate the direct link between changes in the oscillation modes with the applied current and the normalised low frequency (1/f) noise as a function of the bias current. These findings prove that low frequency noise studies could be a simple and powerful technique to investigate spin-torque based magnetization dynamics.

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.

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.

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.

In this work a discussion on the estimated volume trap densities (NT) compared to surface traps densities (Neff) related to identified traps in the Si fin of Si/SiGe superlattice I/O n-channel FinFETs using low frequency noise spectroscopy is made. The investigated devices present a fin width of 10 nm, a fin height of 10 nm and four fins in parallel, leading to an equivalent channel width of 120 nm. The equivalent oxide thickness (EOT) is 5.6 nm. More details on the device fabrication and experimental setup may be found in [1,2]. The noise spectra and the estimated surface traps densities are provided in [3]. In this work, focus is only on the identified T4 trap, for which using the linear dependence that should exist between A0i and t0i related to the same trap, without any other assumption, a surface trap density of 2.8∙1012cm-2 is obtained [3]. It should be noted that from the 1/f flat-band noise level an interface trap density value of about 1.9∙1018 eV-1cm-3 is obtained at 300 K.However, as the traps in the Si film are related to a volume phenomenon, two methodologies to estimate the volume trap densities are employed: one using the relationship between the surface trap density and volume trap densitiy [4], where B is a coefficient estimated to be 1/3 [4,5]; and a second one from the temperature (T) evolution at fixed frequency of the Lorentzian plateau level associated to the same trap (from equation 34 in [4]). Using the first method leads to a volume trap density of T4 of about 1.7∙1019 cm-3.The second method consists to use the maximum of the measured Svg_Lor(f 0,T) dependence with temperature. Indeed, the Svg_Lor(f 0,T) of Lorentzians associated to the same trap are proportional with ti(T)/{1 + [2pf 0ti(T)]2}. For a given frequency f 0, if 2pf 0ti(T) ≫ 1, SVg_Lor(f 0,T) ∝ ti(T)]-1, and SVg_Lor(f 0,T) increases with increasing temperature because ti decreases. If 2pf 0ti(T) ≪ 1, then SVg_Lor(f 0,T) ∝ ti(T) and SVg_Lor(f 0,T) decreases with increasing temperature, as explained in detail in [4]. The evolution of the Svg_Lor(f 0,T)∙f 0 in a temperature range where T4 traps are active is illustrated in Figure 1 and presents a bell-shaped behavior, as expected. Using this method, volume trap densities of about 1.25∙1018 cm-3 for f 0 = 10 kHz and of about 1.1∙1018 cm-3 for f 0 = 14 kHz are obtained. It may be observed that the estimated volume trap densities of the T4 defect are about one decade lower than when using the first method. This overestimation by the first method is related to the fact that the theoretical B coefficient was determined for conventional planar devices with one gate [4,5]. Moreover, it may be noticed that the second method is dependent on the fixed f 0 selected.The paper will present a discussion with more details, considering all identified traps in [1] and considering additional new low frequency noise spectroscopy results.References :[1] Hellings, H. Mertens, A. Subirats, E. Simoen, T. Schram, L.-A. Ragnarsson et al., “Si/SiGe superlattice I/O finFETs in a vertically-stacked Gate-All-Around horizontal Nanowire Technology”, in Tech. Dig. Symp. on VLSI Technology, The IEEE New York, 2018, p.p. 85-86, DOI: 10.1109/VLSIT.2018.8510654.[2] Boudier, B. Cretu, E. Simoen, R. Carin, A. Veloso, N. Collaert, and A. Thean, “Low frequency noise assessment in n- and p-channel sub-10 nm triple-gate FinFETs: Part I: Theory and methodology,” Solid State Electron., vol. 128, pp. 102-108, 2017, DOI: 10.1016/j.sse.2016.10.012.[3] Boudier, B. Cretu, E. Simoen, G. Hellings, T. Schram, H. Mertens and D. Linten, “Low frequency noise analysis on Si/SiGe superlattice I/O n-channel FinFETs”, In Proceedings of EUROSOI-ULIS’2019.[4] Lukyanchikova, “Noise and Fluctuations Control in Electronic Device”, edited by A. Balandin, American Scientific, Riverside, CA, 2002, pp. 201-233.[5] Yau and C-T. Sah, “Theory and experiments of low-frequency generation-recombination noise in MOS transistors”, IEEE Trans. Electron Dev., 1969, vol.16, pp. 170-177.Figure 1 : SVg_Lor(f 0,T)·f 0 versus temperature for the T4 trap identified in [3]; on the secondary Oy axis the characteristic frequency f 0i of the Lorentzians is displayed in function of temperature. Figure 1

In viscoelastic full waveform inversion, there is interference between the gradients of the P- and S- wave velocities, leading to the degradation of the inversion accuracy. Therefore, the interference problem in viscoelastic media needs to be solved beforehand. Even though the P-S separation method has been demonstrated to be effective in reducing the crosstalk in elastic media, little attention has been paid to its efficacy in viscoelastic media. We incorporate the P-S separation method in the full waveform inversion of viscoelastic media (QEFWI) and derive a gradient formula for the QEFWI. Numerical tests on the QEFWI demonstrate that the proposed method can successfully reduce the interference problem between the gradients of P- and S- wave velocities, resulting in significant improvement of the viscoelastic full waveform inversion.

Full waveform inversion (FWI) suffers from the cycle skipping problem, because the observed data usually lack low-frequency components or due to errors in the wavelet estimation. In addition, the strong low-frequency non-zero-mean noise can have a large impact on FWI results. Thus, we propose a local waveform traveltime correction scheme to solve the situations when the observed data lack low-frequency components or when the estimation for the wavelet is incorrect. We use a sliding time window, which is used to decrease the traveltime differences between the calculated and observed data to increase the cross-correlation between them. Besides, we propose a zero-mean normalized cross-correlation misfit function to reduce the interference of the low-frequency non-zero-mean noise. Therefore, we propose new approaches to improve FWI results whether the observed data lack low-frequency components or the observed data are contaminated by the non-zero-mean low-frequency noise. Numerical examples on Marmousi model show the feasibility of a FWI based on the zero-mean normalized cross-correlation misfit function and a FWI based on the local traveltime correction method.

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.