Integrable nonlocal nonlinear Schrödinger equations associated with 𝑠𝑜(3,ℝ)

We construct integrable PT-symmetric nonlocal reductions for an integrable hierarchy associated with the special orthogonal Lie algebra so ⁡ ( 3 , R ) \operatorname {so}(3,\mathbb {R}) . The resulting typical nonlocal integrable equations are integrable PT-symmetric nonlocal reverse-space, reverse-time and reverse-spacetime nonlinear Schrödinger equations associated with so ⁡ ( 3 , R ) \operatorname {so}(3,\mathbb {R}) .

Elastic least-squares reverse time migration of steeply dipping structures using prismatic reflections

The migration of prismatic reflections can be used to delineate steeply dipping structures, which is crucial for oil and gas exploration and production. Elastic least-squares reverse time migration (ELSRTM), which considers the effects of elastic wave propagation, can be used to obtain reasonable subsurface reflectivity estimations and interpret multicomponent seismic data. In most cases, we can only obtain a smooth migration model. Thus, conventional ELSRTM, which is based on the first-order Born approximation, considers only primary reflections and cannot resolve steeply dipping structures. To address this issue, we develop an ELSRTM framework, called Pris-ELSRTM, which can jointly image primary and prismatic reflections in multicomponent seismic data. When Pris-ELSRTM is directly applied to multicomponent records, near-vertical structures can be resolved. However, the application of imaging conditions established for prismatic reflections to primary reflections destabilizes the process and leads to severe contamination of the results. Therefore, we further improve the Pris-ELSRTM framework by separating prismatic reflections from recorded multicomponent data. By removing artificial imaging conditions from the normal equation, primary and prismatic reflections can be imaged based on unique imaging conditions. The results of synthetic tests and field data applications demonstrate that the improved Pris-ELSRTM framework produces high-quality images of steeply dipping P- and S-wave velocity structures. However, it is difficult to delineate steep density structures because of the insensitivity of the density to prismatic reflections.

Deep learning for enhancing multi-source reverse time migration

<p>Reverse time migration (RTM) is a technique used to obtain high-resolution images of underground reflectors; however, this method is computationally intensive when dealing with large amounts of seismic data. Multi-source RTM can significantly reduce the computational cost by processing multiple shots simultaneously. However, multi-source-based methods frequently result in crosstalk artifacts in the migrated images, causing serious interference in the imaging signals. Plane-wave migration, as a mainstream multi-source method, can yield migrated images with plane waves in different angles by implementing phase encoding of the source and receiver wavefields; however, this method frequently requires a trade-off between computational efficiency and imaging quality. We propose a method based on deep learning for removing crosstalk artifacts and enhancing the image quality of plane-wave migration images. We designed a convolutional neural network that accepts an input of seven plane-wave images at different angles and outputs a clear and enhanced image. We built 505 1024×256 velocity models, and employed each of them using plane-wave migration to produce raw images at 0°, ±20°, ±40°, and ±60° as input of the network. Labels are high-resolution images computed from the corresponding reflectivity models by convolving with a Ricker wavelet. Random sub-images with a size of 512×128 were used for training the network. Numerical examples demonstrated the effectiveness of the trained network in crosstalk removal and imaging enhancement. The proposed method is superior to both the conventional RTM and plane-wave RTM (PWRTM) in imaging resolution. Moreover, the proposed method requires only seven migrations, significantly improving the computational efficiency. In the numerical examples, the processing time required by our method was approximately 1.6% and 10% of that required by RTM and PWRTM, respectively.</p>

Deep learning for enhancing multi-source reverse time migration

<p>Reverse time migration (RTM) is a technique used to obtain high-resolution images of underground reflectors; however, this method is computationally intensive when dealing with large amounts of seismic data. Multi-source RTM can significantly reduce the computational cost by processing multiple shots simultaneously. However, multi-source-based methods frequently result in crosstalk artifacts in the migrated images, causing serious interference in the imaging signals. Plane-wave migration, as a mainstream multi-source method, can yield migrated images with plane waves in different angles by implementing phase encoding of the source and receiver wavefields; however, this method frequently requires a trade-off between computational efficiency and imaging quality. We propose a method based on deep learning for removing crosstalk artifacts and enhancing the image quality of plane-wave migration images. We designed a convolutional neural network that accepts an input of seven plane-wave images at different angles and outputs a clear and enhanced image. We built 505 1024×256 velocity models, and employed each of them using plane-wave migration to produce raw images at 0°, ±20°, ±40°, and ±60° as input of the network. Labels are high-resolution images computed from the corresponding reflectivity models by convolving with a Ricker wavelet. Random sub-images with a size of 512×128 were used for training the network. Numerical examples demonstrated the effectiveness of the trained network in crosstalk removal and imaging enhancement. The proposed method is superior to both the conventional RTM and plane-wave RTM (PWRTM) in imaging resolution. Moreover, the proposed method requires only seven migrations, significantly improving the computational efficiency. In the numerical examples, the processing time required by our method was approximately 1.6% and 10% of that required by RTM and PWRTM, respectively.</p>

Reverse time migration of phase encoded all-order multiples

Multiples follow long paths and carry more information on the subsurface than primary reflections, making them particularly useful for imaging. However, seismic migration using multiples can generate crosstalk artifacts in the resulting images because multiples of different orders interfere with each others, and crosstalk artifacts greatly degrade the quality of an image. We propose to form a supergather by applying phase-encoding functions to image multiples and stacking several encoded controlled-order multiples. The multiples are separated into different orders using multiple decomposition strategies. The method is referred to as the phase-encoded migration of all-order multiples (PEM). The new migration can be performed by applying only two finite-difference solutions to the wave equation. The solutions include backward-extrapolating the blended virtual receiver data and forward-propagating the summed virtual source data. The proposed approach can significantly attenuate crosstalk artifacts and also significantly reduce computational costs. Numerical examples demonstrate that the PEM can remove relatively strong crosstalk artifacts generated by multiples and is a promising approach for imaging subsurface targets.

Near-Borehole Imaging Using Full-Waveform Sonic Data

This work presents a full waveform sonic (FWS) dataset processing to generate high-resolution images of the near-borehole area. The dataset was acquired in a nearly horizontal well over a distance of 5400 feet. Multiple formation boundaries can be identified on the final image and tracked at up to 200 feet deep, along the wellbore's trajectory. We first present a new preprocessing sequence to prepare the sonic data for imaging. This sequence leverages denoising algorithms used in conventional surface seismic data processing to remove unwanted components of the recorded data that could harm the imaging results. We then apply a reverse time migration algorithm to the data at different processing stages to assess the impact of the main processing steps on the final image.

Reverse time migration with an exact two way illumination compensation

Reverse time migration (RTM) has been widely used for imaging complex subsurface structures in oil and gas exploration. However, because only the adjoint of the forward Born modeling operator is applied to the seismic data in RTM, the output migration profile is biased in terms of the amplitude. To help partially balance the amplitude performance, the RTM image can be preconditioned with the inverse of the diagonal of the Hessian operator. Yet, existing preconditioning methods do not correctly consider the receiver-side effects, assuming that the receiver coverage is infinite or the velocity model is constant. We therefore provide a comparative study aiming to give a clearer understanding on the importance of incorporating the receiver-side effects by developing a frequency-domain scattering-integral reverse time migration (SI-RTM). In the proposed SI-RTM, the diagonal of the Hessian operator is explicitly computed in its exact formulation, and the source-side wavefield and receiver-side Green’s functions are obtained by solving the two-way wave equation. The computational cost is relatively affordable when compared with the more expensive least-squares RTM. In the comparative counterpart, the diagonal of the Hessian operator is approximated by the source-side illumination. We perform two synthetic numerical examples using an overthrust model and a complex reservoir model; the final migration images were significantly improved when the receiver-side effects were accurately considered. A third application of SI-RTM on one field data set acquired from the East China Sea further demonstrates the importance of incorporating the receiver-side effects in normalizing the RTM image. Findings of this study are expected to provide a theoretical basis for improving the ability of RTM imaging of subsurface structures, thereby critically advancing the application of geophysical techniques for imaging complex environments.