Near-surface velocity estimation using annealing static-constrained early arrival waveform inversion

Early arrival waveform inversion (EWI) is an essential approach to obtaining velocity structures in near-surface. Due to suffering from a cycle‐skipping issue, it is difficult to reach the global minima for conventional EWI with the misfit function of least-squares norm (L2‐norm). Following the optimal transportation theory, we developed an EWI solution with a new objective function based on quadratic‐Wasserstein‐metric (W2-norm) to maintain the geometric characteristics of the distribution and improve the stability and convexity of the inverse problem. First, we gave the continuous form of the adjoint source and the Frechet gradient of the Wasserstein metric for seismic early arrival, which leads to an easy and efficient way to implement in the adjoint-state method. Then, we conducted two synthetic experiments on the target model containing some velocity anomalies and hidden layers to test its effectiveness in mapping accurate and high-resolution near-surface velocity structure. The results show that the W2-normed EWI can mitigate cycle-skipping issues compared with the L2-normed EWI. In addition, it can deal with hidden layers and is robust in terms of noise. The application to a real dataset indicates that this new solution can recover more details in the shallow structure, especially in the aspect of dealing with hidden layers.

plex shallow subsurface. This workflow incorporates dispersion curve inversion, traveltime tomography and full waveform inversion into a single framework to optimize the advantages of each. An accurate near-surface velocity is derived using the dispersion curve inversion technique that overcomes limitations of traditional traveltime tomography. This velocity is then incorporated into layer-stripping full waveform or RMO inversion schemes by “freezing” the ultra-shallow part of the model in order to retrieve the deeper velocity structure. We illustrate the workflow on a test data set from Inner Mongolia, China, whose long-offsets and low-frequency content provide the necessary input for both the dispersion curve and full waveform inversion techniques. Using this data set, we demonstrate the efficacy of the integrated methodology in determining both the macro-velocity model and near-surface velocities in structurally complex geological setting.

Refraction traveltime tomography based on damped wave equation for irregular topographic model

Near-surface seismic imaging often plays a significant role in producing quality data processing results for the deep subsurface in land and shallow marine environments. First-arrival traveltime tomography is a common approach for near-surface imaging due to its high efficiency and simplicity. However, the method faces issues of missing hidden layers and resolving the structures with low resolution. On the other hand, waveform inversion should offer better solutions for dealing with these issues, but it may suffer from the cycle-skipping problem. We intend to use the advantages and reduce the disadvantages of the two methods by developing a new strategy of alternately applying traveltime tomography and waveform inversion through iterations. First-arrival traveltime tomography applies a wavefront raytracer and a nonlinear inversion approach. Waveform inversion is a multiscale approach in which a wavelet transform is applied in the data domain to better handle the cycle-skipping problem. By alternating the two inversions rather than performing a joint inversion, we reduce the memory requirements and avoid nonphysical scaling problems between the two approaches. Using one synthetic and two real data examples, we determine that alternating inversions minimize two separate objective functions at the same time and constrain the near-surface structures fairly well compared with the waveform inversion method alone. For the field examples, the new method avoids generating the obvious artifacts and provides results consistent with the geology analysis of those areas.

The initial model is the crucial to full waveform inversion. First arrival traveltime tomography can provide a more accurate near-surface model, improve the accuracy of the FWI and accelerate convergence. In this paper, the initial model is based on fast marching method (FMM) traveltime tomography to obtain the near-surface velocity model. The second-order FMM is used to solve the Eikonal equation; although our implementation belongs to the family of adjoint-state tomographies, we do not need to compute the adjoint-state variable as an intermediate product for the gradient. The first arrival traveltime tomography based on FMM can provide a more accurate near-surface initial model for FWI, and improve the convergence rate of FWI. On synthetic data examples, we show the advantages of the proposed approach. Moreover, the use of parallel computing improves computational efficiency.

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.

We present feasibility of applying full-waveform inversion (FWI) to densely sampled node data for better imaging of complex targets being beyond the reach of typical towed-streamer surveys. We attempt to process the SFJ-OBS ultra-long offset data acquired in the Eastern Nankai Trough region by first-arrival traveltime tomography (FATT) and state-of-the-art frequency-domain acoustic FWI in order to obtain high resolution crustal velocity model. Our efforts were focused on mitigating cycle-skipping and developing robust quality control workflow for this extremely challenging dataset. The starting FATT model was built in an iterative mode with first-arrival picks refinement after initial FWI. Subsequently, we develop a hierarchical, multiscale layer-stripping inversion strategy with simultaneous opening of the inverted offset range and relaxation of the damping constants, coupled with tuning of the pre-whitening of the diagonal pseudo-Hessian. As a result, the cycle-skipping is kept under control and the reliability of the final model manifests by a good data fit (quantified by the time shifts between real and synthetic data calculated using Dynamic Image Warping) and very consistent source wavelets. FWI model shows several prominent geological features and ties well with a PSDM image build from towed-streamer data acquired along the same profile.

Traditional iteration-based full-waveform inversion (FWI) methods encounter serious challenges if the initial velocity model is far from the true model or if the observed data are lacking low-frequency content. As such, the optimization algorithm may be trapped in local minima and fail to go to a global optimal model. In addition, the traditional FWI method requires long-offset data to update the deep structure of a velocity model with diving waves. To overcome the disadvantages of traditional FWI under these circumstances, we have developed a reflection intensity waveform inversion method. This method aims to minimize the seismic intensity differences between the modeled reflection data and field data. Our method is less dependent on the starting model, and long-offset data are no longer required. The wave intensity, proportional to the square of the original data amplitude, can have a low-frequency band and a higher frequency band, even for waveforms without initial low-frequency content. Our multiscale intensity inversion starts from the low-frequency information in the intensity data, and it can largely avoid the cycle-skipping problem. Synthetic and field data examples demonstrate that our method is able to overcome cycle skipping in handling data with no low-frequency information.

We introduce an inversion approach to simultaneously invert for both velocity and reflectivity. The core of the inversion workflow is a novel wave-equation that provides the full acoustic wavefield, which is parameterized in terms of velocity and vector reflectivity. A key aspect is the separation of the low- and high-wavenumber components of the gradient based on inverse scattering theory, enabling the sensitivity kernels to update the velocity and the vector reflectivity, respectively. The estimation problem is essentially a multi-parameter inversion where the crosstalk trade-offs between the two parameters are minimized with scale separation. Our adjoint state-based inversion is equivalent to performing Full Waveform Inversion (FWI) and Least-Squares Reverse Time Migration (LS-RTM) using the full acoustic wavefield within the same framework. The final inverted reflectivity is an accurate estimate of the true earth reflectivity, compensated for acquisition and poor illumination effects, and with reduced image crosstalk from multiples. The new approach reduces the turnaround time of imaging projects by combining velocity model building (FWI) and imaging (LS-RTM) into a single inversion process with minimum data preprocessing from an inaccurate initial model. We demonstrate the benefits of our scheme using synthetic and field data examples.

We argue in this paper for a hierarchical approach for Full Waveform Inversion that begins with the establishment of “starting models” with traveltime tomography, proceeds to Acoustic Waveform Tomography, and will eventually lead on to Anisotropic, Visco-Elastic Waveform Tomography inversions. With each step increasingly accurate physical descriptions are invoked, more of the information content of the data is used, and the final results are correspondingly enhanced. The ultimate goal is “Full” Waveform Inversion, in which the full (anisotropic, 3D, visco-elastic) physics of the earth is incorporated and all parts of the waveform are utilized. Within the framework of Acoustic Waveform Tomography itself, we formulate 2 alternative approaches to the Laplace-Fourier domain formulation of waveform inversion: i) A conventional L2 misfit function, and ii) phase-only misfits derived from the logarithmic wavefield residuals. We apply these approaches to two real 2D data examples: Marine OBS data from the Nankai subduction zone, and land surface seismic data from the Canadian Foothills. We find in both data examples that the phase-only misfit outperforms the conventional L2 approach, and we suggest that this is due to increased ability of the phase-only approach to recover the low-wavenumber components of the model. We also find that a logarithmic phase-amplitude approach that provides a marginal improvement over the phase-only approach. Finally, we use point scattering responses and chequerboard tests to demonstrate the artefacts introduced by the use of an acoustic approach.

In the linearized seismic full waveform inversion (FWI), it is well known that a good initial model is needed to avoid cycle-skipping issue, especially when the low-frequency components of data are lacking. To solve the problem, we develop a joint first-arrival traveltime and early arrival envelope inversion method (JTE) to build a good near-surface velocity model with low-wavenumber components. The JTE method combines the robustness of nonlinear traveltime inversion and the low-frequency information embedded in the waveform envelope. In two synthetic experiments, we confirm that traveltime inversion constrains the top near-surface velocity structures tightly, while the envelope inversion recovers the low-wavenumber structures with low-velocity objects or layers. Using the results of JTE as starting models, we find that FWI can produce accurate solutions for complex numerical models. In a real-data example, JTE followed by FWI resolves a near-surface velocity model to improve statics corrections for the subsurface stacking image.

In most full-waveform inversion (FWI) problems, sufficient prior information is available to constrain the velocity of certain parts of the model, e.g., the water column or, in some cases, near-surface velocities. We take advantage of this situation and develop a fast Schur-complement-based forward modeling and inversion approach by partitioning the velocity model into two parts. The first part consists of the constrained zone that does not change during the inversion, whereas the second part is the anomalous zone to be updated during the inversion. For this decomposition, we partially factorize the governing system of linear equations by computing a Schur complement for the anomalous zone. The Schur complement system is then solved to compute the fields in the anomalous zone, which are then back substituted to compute the fields in the constrained region. For each successive modeling steps with new anomalous zone velocities, the corresponding Schur complement is easily computed using simple algebra. Because the anomalous part of the model is comparatively smaller than the whole model, considerable computational savings can be achieved using our Schur approach. Additionally, we showed that the Schur complement method maintains the accuracy of standard frequency-domain finite difference formulations, but this comes at a slightly higher peak memory requirement. Our FWI workflow shows reduced runtime by 15%–57% depending upon the depth of the water column without losing any accuracy compared to the standard method.

Crustal‐scale imaging by the full‐waveform inversion (FWI) of long‐offset seismic data is inherently difficult because the large number of wavelengths propagating through the crust makes the inversion prone to cycle skipping. Therefore, efficient crustal‐scale FWI requires an accurate starting model and a stable workflow minimizing the nonlinearity of the inversion. Here we attempt to reprocess a challenging 2‐D ocean‐bottom seismometer (OBS) data set from the eastern Nankai Trough. The starting model is built by first‐arrival traveltime tomography (FAT), which is FWI assisted for tracking cycle skipping. We iteratively refine the picked traveltimes and then reiterate the FAT until the traveltime residuals remain below the cycle‐skipping limit. Subsequently, we apply Laplace‐Fourier FWI, in which progressive relaxation of time damping is nested within frequency continuation to hierarchically inject more data into the inversion. These two multiscale levels are complemented by a layer‐stripping approach implemented through offset continuation. The reliability of the FWI velocity model is assessed by means of source wavelet estimation, synthetic seismogram modeling, ray tracing modeling, dynamic warping, and checkerboard tests. Although the viscoacoustic approximation is used for wave modeling, the synthetic seismograms reproduce most of the complexity of the data with a high traveltime accuracy. The revised FWI scheme produces a high‐resolution velocity model of the entire crust that can be jointly interpreted with migrated images derived from multichannel seismic data. This study opens a new perspective on the design of OBS crustal‐scale experiments amenable to FWI; however, a further assessment of the optimal OBS spacing is required for reliable FWI.

In arid regions groundwater aquifers are one of the main sources of water and they are recharged only through rain. Efficient use of aquifers for drinking or agriculture is extremely important. To utilize this water in an optimum way we need to characterize the aquifer geology, its depth, thickness, and the rate of recharge. We could also increase the recharge rate by redirecting rain waters to these aquifers and use them as natural reservoirs for future use. In this study we characterized the geology of Wadi Qudaid, 80 Km north of Jeddah, Saudi Arabia (KSA) for use as a potential rainwater aquifer. In this work, we collected seismic, electric, and EM data to find the depth to and thickness of the aquifer and compared our results to observations in a nearby well. Seismic data are interpreted using traveltime tomography and early arrival waveform inversion, while EM data are inverted to find the true subsurface resistivity. Seismic tomograms and EM results show the existence of 3 subsurface layers (1) a surface layer consists of sand-silt-gravel, (2) a layer of consolidated sand with some gravel, and (3) a layer of highly fractured igneous rocks.

Reflection-based traveltime and waveform inversion with second-order optimization