A Full-Waveform Inversion Method Based on Structural Tensor Constraints

This study investigates the effectiveness and the applicability of full waveform inversion (FWI) method to estimate underwater sound velocity structures. We use a frequency domain full waveform inversion method in this study. We use an adjoint-state method for the calculation of the gradient in an iterative inversion based on a preconditioned conjugate gradient method. We first apply the FWI method to a synthetic dataset that is simulated for a sound velocity structure. The results of our inversion are then compared with those from a conventional ray-based traveltime inversion (TTI) method to evaluate the effectiveness of the method. The results show that the full waveform inversion method could provide more precise image with higher resolution than the ray-based method. The FWI method is also applied to a field dataset acquired by a vertical-cable-seismic (VCS) data acquisition experiment in Lake Biwa. In spite of very limited raypath condition using only direct arrival wave, the full waveform inversion method could reproduce a horizontally stratified velocity structure whose vertical profile showed the existence of a seasonal thermocline in the lake that was to be confirmed by temperature measurements after the VCS experiment. We conclude that the FWI method could be the key success factor for the higher resolution at estimation of underwater sound velocity structure.

This study investigates the effectiveness and the applicability of the full waveform inversion (FWI) method to estimate underwater sound velocity structures. We use the frequency domain full waveform inversion method in this study. In this study, the FWI is applied to the shallow-acoustic tomography first, and then we show some prospects of application to the long-range ocean acoustic tomography. We used an optimal 9 point finite difference frequency domain method for shallow acoustic tomography and the wide angled parabolic equation method for long-range acoustic tomography. We use an adjoint-state method for the calculation of the gradient in an iterative inversion based on a pre-conditioned conjugate gradient method. We first demonstrate results from a FWI method applied to a VCS experiment field data in Lake Biwa. In spite of very limited path condition using only direct arrival wave, the full waveform inversion method could describe the horizontal velocity structure possibly due to seasonal thermocline in the lake. Then, we applied the FWI method to the synthetic dataset of long-range acoustic propagation. We conclude that the FWI method could be the key success factor for the higher resolution at estimation of underwater sound velocity structure.

The full-waveform inversion (FWI) method relies on an effective numerical solution of the wave equation. The wave equation must be solved numerous times during an inversion run. In the past, to be able to use FWI in practice, it was necessary to assume that the earth's subsurface was a 2D acoustic medium. Recent increases in computational power have made it possible to include more real-world physics in the FWI method, such that the computational subsurface can mimic the real-world subsurface as closely as possible. Going from 2D to 3D is challenging, primarily due to the numerical methods involved in solving the wave equation. Including elastic effects is not straightforward due to the increase in possible models that can explain the data, more complicated wave phenomena involved in the wave propagation, as well as trade-off between the subsurface elastic parameters during the inversion. We discuss some of the challenges and solution strategies for using the FWI method in the time domain using a 3D elastic computational domain.

The main difficulty in seismic full waveform inversion (FWI) is the strong nonlinearity, which is caused by the complexity of seismic wave propagation. Different components of elastic parameters result in different characteristics in seismic data. Meanwhile, different inversion quality is required in different stages of exploration or exploitation. So, there is no need to pursue matching all the seismic information during the inversion. Some problems can be solved by matching part of seismic information and the strong nonlinearity can also be avoided by this way. According to this consideration, a generalized FWI strategy and method based on seismic data subsets is presented. For different seismic data subsets, the gradients of the misfits have the same form and can be calculated by two times of seismic wave forward modeling just as traditional FWI. The only difference in calculating the gradients is the adjoint source. During the waveform inversion based on seismic data subsets, the responses of seismic data to different scales of perturbation on different media parameters should be analyzed intensively. Different seismic data subsets should be used in different stages of full waveform inversion. And then the residual of this seismic data subset is back‐projected along the reasonable sub‐kernels to decide where and which component of the model parameter need to be updated. As examples, envelope and reflection data subsets are used in FWI with synthetic and practical data to prove the validity and effectiveness of our presented FWI strategy and method. Especially, in the absence of low frequency contents, reasonable misfits can be used to recover the background compressional and shear velocity models using these FWI methods.

Roadways are key components of the modern transportation system. Therefore, assessment of roadway subsidence is critical to the health and safety of the traveling public. Existing seismic refraction and waveform tomography methods can be used for subsidence evaluation; however, the data acquisition time is significant because they require multiple source impacts (shots) along a test line. To mitigate the negative impact caused by closing the traffic flow under seismic testing, a land-streamer seismic testing system and waveform analysis are developed. An existing 2D Gauss-Newton full-waveform inversion (FWI) method is extended for analysis of the land-streamer waveform data. The main advantage of using land-streamer waveform data is that geophones are not coupled to test materials and source-receiver offsets are fixed; thus, the whole test system can be moved along the roadway quickly for data acquisition. To demonstrate the effectiveness of land-streamer waveform data, the FWI method was tested on synthetic and field data sets. The synthetic result reveals that buried voids can be well-characterized by the land-streamer waveform analysis. Field data were collected on asphalt pavement using a 24 channel land streamer and a propelled energy generator to induce seismic wave energy. The test system was towed by a pickup truck along a roadway with an on-going subsidence (repaired sinkhole). The data were collected over 277.5 m distance at a 3 m interval, and the total data acquisition time was approximately 1 h. The field data result indicates that the waveform analysis was able to delineate low-velocity soil zones and laterally variable bedrock. The FWI results are also compared with multichannel analysis of surface wave (MASW) results. The 2D [Formula: see text] profiles from the FWI and MASW methods are consistent; however, the FWI method provides more detailed information ([Formula: see text] of [Formula: see text] cells) of low-velocity anomalies for assessment of roadway subsidence.

Joint inversion of gravity and vertical gradient data based on modified structural similarity index for the structural and petrophysical consistency constraint

Prestack seismic inversion usually suffers from a lower signal-to-noise ratio, which could result in unstable inversion results. The conventional multitrace lateral constrained inversion blurs steeply dipping layers, whereas the simple structural constrained inversion is affected by noise. To solve this issue, an inversion method with multiple constraints is proposed, which include (1) a local smoothing operator is used to suppress the inversion anomalies caused by data noise, (2) a difference operator is used to protect the stratum boundary, and (3) a structural dipping constraint is used to enhance the characterization of the possible dipping stratum. The multiconstraint inversion (MCI) method suppresses the inversion anomalies caused by data noise without blurring the stratum boundary. The effects of different constraints in the inversion process and the influence of noise on the inversion results are analyzed. In MCI, the regularization coefficient of each constraint operator is dynamically changed, thereby controlling the significance of each regularization term in the inversion. The proposed algorithm is tested on synthetic and field data, which demonstrate its effectiveness and improved accuracy on the inversion results.

Seismic velocity plays an important role in imaging and identifying underground geology. Conventional seismic velocity inversion methods, like full waveform inversion, directly update the velocity model based on the misfit between the observed and synthetic data. However, seismic velocity inversion is a highly nonlinear process, and the inversion effect greatly relies on the initial inversion model. In this paper, we propose a novel network‐domain full waveform inversion method. Different from the existing network‐domain full waveform inversion methods, which use random or fixed numbers as network input, we reparameterize the low‐dimensional acoustic velocity model in a high‐dimensional inversion network parameter domain with seismic observed data as the network input. In this way, the physical information within the observed data can be directly encoded into the inversion parameters, leading to a better inversion effect than the current network‐domain full waveform inversion method. Moreover, comparison experiments on the Society of Exploration Geophysicists and the European Association of Geoscientists and Engineers Overthrust model and the Marmousi model show the advantages of the proposed method over conventional full waveform inversion from the aspects of inversion accuracy, robustness to noisy data, and more complex geological structures. These advantages may benefit from the fact that reparameterization within the inversion network domain can empower the inversion process with the regularization ability of denoising and mitigating the cycle‐skipping issue. In the end, the potential of the proposed method in terms of network initialization is further discussed.

To image supercritical water reservoirs, we have proposed to use the distributed acoustic sensing (DAS) in the borehole, surface seismic array, active or passive seismic sources and full-waveform inversion (FWI) method. Through the comparison test of DAS and geophones in a field, we confirmed that the DAS system can be used as an array seismic sensor although it is less sensing the seismic waves perpendicular to the fiber elongation. The sensitivity is almost comparable to the surface seismometers. It can be used as dense seismic array(s). We have also examined the usefulness of full-waveform inversion (FWI) method for imaging of geothermal reservoirs. The FWI result suggests it can be used for geothermal reservoir imaging. To evaluate our approach, we carried out a feasibility study in e Medipolis geothermal field located on Kyushu Island, Japan. We deployed an optical fiber down to a 977 m depth in a borehole. Using distributed temperature sensing (DTS) mode, the measured temperature at the 914 m depth was 264 °C. We obtained four and half days of continuous seismic data via DAS and surface seismometers. The DAS data were obtained every 1 m from a 977 m depth to ground surface. We observed seven natural earthquakes. The DAS sensitivity is comparable to the surface seismometers. This suggest that the optical fiber deployment in the exiting borehole could provide reasonable coupling to the borehole casing. We obtained apparent interval Vp profile along the borehole. There was no distinct seismic attenuation observed, even in the high-temperature zone, and Vp in the high-temperature zone is estimated as 3.0 km/s. The P-to-S converted phase was evident on the surface seismometers, and this could indicate the presence of a conversion zone around the 4 km-depth beneath the Medipolis geothermal field. To image supercritical water reservoirs, we have proposed to use the distributed acoustic sensing (DAS) in the borehole, surface seismic array, active or passive seismic sources and full-waveform inversion (FWI) method. Through the comparison test of DAS and geophones in a field, we confirmed that the sensitivity is almost comparable to the surface seismometers. We have also examined the usefulness of full-waveform inversion (FWI) method for imaging of geothermal reservoirs. We carried out a field study in geothermal field. We deployed an optical fiber down to a 977 m depth in a borehole. Using distributed temperature sensing (DTS) mode, the measured temperature at the 914 m depth was 264 °C. We obtained 4.5 days of continuous seismic data The DAS data were obtained every 1 m from a 977 m depth to ground surface. We confirmed that the optical fiber deployment in the exiting borehole could provide reasonable coupling to the borehole casing. There was no distinct seismic attenuation observed, even in the high-temperature zone, and Vp in the high-temperature zone is estimated as 3.0 km/s. The P-to-S converted phase was evident on the surface seismometers, and this could indicate the presence of a conversion zone around the 4 km-depth.

Traditional full-waveform inversion (FWI) methods only render a “best-fit” model that cannot account for uncertainties of the ill-posed inverse problem. Additionally, local optimization-based FWI methods cannot always converge to a geologically meaningful solution unless the inversion starts with an accurate background model. We seek the solution for FWI in the Bayesian inference framework to address those two issues. In Bayesian inference, the model space is directly probed by sampling methods such that we obtain a reliable uncertainty appraisal, determine optimal models, and avoid entrapment in a small local region of the model space. The solution of such a statistical inverse method is completely described by the posterior distribution, which quantifies the distributions for parameters and inversion uncertainties. To efficiently sample the posterior distribution, we introduce a sampling algorithm in which the proposal distribution is constructed by the local gradient and the diagonal approximate Hessian of the local log posterior. Our algorithm is called the gradient-based Markov chain Monte Carlo (GMCMC) method. The GMCMC FWI method can quantify inversion uncertainties with estimated posterior distribution given sufficiently long Markov chains. By directly sampling the posterior distribution, we obtain a global view of the model space. Theoretically speaking, statistical assessments do not depend on starting models. Our method is applied to the 2D Marmousi model with the frequency-domain FWI setting. Numerical results suggest that our method can be readily applied to 2D cases with affordable computational efforts.

Seismic full-waveform inversion (FWI) method has been used to estimate subsurface velocity structure. FWI directly utilizes observed waveforms that could include information on the properties of subsurface materials. In seismic time-lapse surveys, we observe the difference between waveforms as a function of time for the change such as fluid alteration. Residual waveforms between the observed before and after a certain time interval are used to estimate the changes in the fluid distribution in terms of seismic velocities in FWI method. In contrast to the previous FWI applications, our research focuses directly on the properties in the hydrocarbon reservoir in order to estimate the fluid distribution and alteration. We simulate the wave propagation based on the Biot theory that includes the effects of fluid in porous media. The simulation model is composed of a block of sandstone saturated with water and gas. We assume a transition zone around the fluid contact, whose vertical profile of the saturation rate varies gradually in time in this zone. The result inspires that the combination of elastic parameters is necessary for estimating the seismic velocity contact in fluid transition zone relating to the fluid-contact movement by FWI.

The travel-time inversion method has been developed using a ray-tracing scheme in the Munk's Ocean Acoustic Tomography (OAT) method. The method has some similarity with seismic exploration both in the theory and data processing methods except for the direct utilization of waveform in seismic exploration. The waveform analysis is a powerful tool to investigate the velocities in the areas of interest, and the importance to use waveform is widely recognized in seismic explorations. However there are few precedent studies dealing with waveform inversion in the application of OAT. This study investigates the effectiveness and applicability of the full waveform inversion method to estimate underwater sound velocity structures. We use an adjoint-state method for the calculation of the gradient in an iterative inversion based on a pre-conditioned conjugate gradient method. We first demonstrate results from a full waveform inversion method applied to a synthetic dataset that reflects the sound velocity structure. The results are then compared with those from a conventional ray-based travel time inversion method to evaluate the effectiveness of the method. The results show that the full waveform inversion method could provide more precise image with higher resolution than the ray-based method. The full waveform inversion method is also applied to a VCS experiment field data in Lake Biwa. In spite of very limited path condition using only direct arrival wave, the full waveform inversion method could describe the horizontal velocity structure possibly due to seasonal thermocline in the lake. We conclude that the FWI method could be the key success factor for the higher resolution at estimation of underwater sound velocity structure.

Summary Full waveform inversion has been successful in building high resolution velocity models for shallow layers. To be successful, it requires refracted waves or low frequencies in the reflection/refraction data. We revisit full waveform inversion theory in hopes of relaxing the dependence on low frequency reflections. We implement an approach allowing the updating of long wavelength components of the velocity model affecting the reflected arrivals even with absence of low frequency in the input data. Our tactic is based on a non-linear iterative relaxation approach where short and long wavelength components of the velocity model are updated alternatively. We study theoretically the associated Frechet derivatives and gradients and discussed how and why such a strategy improves the resolution that we can expect from full waveform inversion. The kernel of our approach is very similar to the algorithm of migration based travel time tomography proposed by Chavent et al. (1994). Finally we present a preliminary 2D application to a 2D Gulf of Mexico conventional streamer dataset.

6. An introduction to full waveform inversion

This work presents the development of a FWI method in time, that uses seismic data acquired using a blended geometry. Blended geometry involves temporal and spatial overlap of multiple shots, randomly located in the same acquisition, whereas the traditional acquisition uses regular spacing of the receivers and one single shot at a time. The FWI method uses the acoustic wave equation with constant density 2D to find the modeled data, and a l 2 -error norm as misfit function between the observed and modeled data. The blended geometry acquisition was designed to obtain synthetically the seismic data at the surface with 5 shots simultaneous, using the Marmousi model of size 3.025 km × 12.425 Km (with a grid of 121 × 497 points) as true subsurface velocity model. The FWI method estimates the velocity using an smoothed version of the Marmousi as initial model, and it updates the velocity model iteratively using a gradient descent method. The FWI method for blended and traditional geometries was implemented and tested on the same computer under controlled conditions, for the same number of shots and iterations. The experimental results of the velocity models obtained using blended and traditional geometries have similar quadratic error norm, and the execution time of the FWI for the blended acquisition is up to 1.88 times faster than the FWI method for the traditional acquisition.