Accelerating True-amplitude RTM of Deepwater Data Using Analytic Redatuming

Reverse-time migration (RTM) using the crosscorrelation imaging condition requires that the forward-propagated source wavefield and the backward-propagated receiver wavefield be accessible within the imaging domain at the same time step. There are two categories of methods to balance the computer memory requirement and the computational complexity of RTM: checkpointing methods and source-wavefield reconstruction methods. We have developed a new source-wavefield reconstruction method to improve the balance between the computer memory requirement and the computational complexity of RTM. During the forward simulation of the source wavefield, we stored boundary wavefields only at one or two layers of spatial grid points and reconstructed the back-propagated source wavefield at the same time step as that of the back-propagated receiver wavefield, using a high-order wave-equation extrapolation scheme. One conventional RTM method uses boundary wavefields stored at multiple layers of spatial grid points and a high-order finite-difference (FD) scheme to reconstruct the back-propagated source wavefield. For an FD scheme with the eighth or sixteenth order of accuracy in space, our new method used only 37.5% of the computer memory required by this conventional method to store the boundary wavefields. This reduction of computer memory usage is significant because storing the boundary wavefields consumes most of the computer memory required for 3D migration using reconstructed source wavefields. Moreover, our method maintained the spatial order of accuracy of the FD scheme for the entire imaging domain, whereas some conventional methods reduce the spatial-order accuracy of the FD scheme near the boundaries to back-propagate the source wavefield to decrease the computer memory requirement. We validated our method using synthetic seismic data. Our method produced 2D and 3D migration images of complex subsurface structures as accurate as those yielded using an RTM method without reducing the spatial order of accuracy near the boundaries.

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.

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 over 500 1024×256 velocity models, and employed each of them using plane-wave migration to produce raw images at 0°, ±10°, ±20°, and ±30° 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.

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 quality of seismic images obtained by reverse time migration (RTM) strongly depends on the imaging condition. We propose a new imaging condition that is motivated by stationary phase analysis of the classical crosscorrelation imaging condition. Its implementation requires the Poynting vector of the source and receiver wavefields at the imaging point. An obliquity correction is added to compensate for the reflector dip effect on amplitudes of RTM. Numerical experiments show that using an imaging condition with obliquity compensation improves reverse time migration by reducing backscattering artifacts and improving illumination compensation.

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.

Using compact representations of Green’s functions we derive a common framework for reverse time migration (RTM) and Kirchhoff migration. These compact Green’s functions (CGFs) are 3D volumes containing traveltimes and amplitudes for the N most representative events in the upcoming/downgoing decomposed 4D wavefields originating from a point source. Within this framework, we implement an RTM algorithm using a multivalued excitation time/amplitude imaging condition. This new approach produces four complementary imaging volumes (different combinations of source and receiver decomposed wavefields) and angle/azimuth gathers with computational effort less than 15% greater than that of plain (one image and no gathers) RTM algorithms. The advantages of separating the image volume into four complementary volumes are well established in the literature (low-frequency noise separation and turning wave imaging); however, its use has been limited by the computational cost. Despite using two source propagations to decompose the source wavefield, we reduce the computations to less than 20% of a single source propagation by performing finite-difference propagation with half the frequency limit used in the receiver wavefield propagation. The combination of CGF and an excitation time/amplitude imaging condition allows receiver wavefield decomposition with only one wavefield propagation. Our RTM algorithm constructs angle/azimuth gathers using a postmigration computation of the source and receiver wavefield’s propagation directions. To compute the propagation directions after migration, we use a new concept: the cumulative wavefield volumes, which are 3D, imaging-condition-guided compressions, of the 4D source and receiver wavefields. We also use CGF to implement a Kirchhoff migration algorithm that produces four complementary image volumes with RTM-like quality. Furthermore, we present synthetic and field data examples to clarify the new concepts and illustrate the results obtained using these methods.

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.

ABSTRACTNumerical implementation of the gradient of the cost function in a gradient‐based full‐ waveform inversion (FWI) is essentially 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 compared to conventional algorithms, this type of scaling is able to significantly suppress non‐Gaussian noise, i.e., outliers. Our tests also show that scaling by its absolute norm produces better results than other approaches.

Full-waveform inversion (FWI) is capable of handling various wave types, e.g., primary reflections, direct waves, diving waves, and multiple reflections. However, FWI often encounters high nonlinearity when the starting velocity model significantly deviates from the true velocity, and the existence of multiples can further worsen this situation. As a result, the objective function may be trapped in a local minimum, causing the inversion process to fail to converge to the global minimum. Constructing an objective function by decomposing multiples into different controlled orders and performing the FWI on multiples with consecutive orders can expedite convergence. However, conducting the FWI using multiples in an order-by-order way may result in high computational cost. In this study, we address this challenge by creating virtual sources and supergathers. These supergathers phase-encode many orders of multiples and integrate them into one for FWI, requiring only one FWI for all orders of multiples. By employing such a random phase-encoding scheme, crosstalk artifacts arising from interferences between mismatched multiple orders in the source and receiver wavefields can be largely mitigated. The proposed method is validated through numerical experiments with a synthetic dataset, as well as using marine field data from Madagascar. The results demonstrate that FWI employing phase-encoded multiples significantly improves convergence while maintaining computational efficiency.

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...

Vector-based excitation amplitude imaging condition for elastic RTM

3D reverse time migration using a wavefield domain dynamic approach

It is important to apply certain intrinsic properties (e.g., the wave propagation directions and particle motion information) in reconstructed wavefields in order to solve the image problems exhibited in elastic reverse time migration (RTM). This paper presents a procedure to decompose the source and receiver wavefields into local plane waves as well as to separate them into pure P and S modes. We generate the partial PP and PS images by crosscorrelation of these plane waves along different directions, and then formulate an imaging condition as a product of an angle-domain operator and the partial images. The new angle-domain imaging condition substantially reduces the artifacts in the PP image and produces the PS image with correct polarizations. However, the imaging procedure involves intensive computations. A numerical algorithm, which can greatly reduce the calculation, is proposed to improve the efficiency.