The conventional energy flux density vector indicates the propagation direction of mixed P- and S-wave wavefields, which means when a wavefront of P-wave encounters a wavefront of S-wave with different propagation directions, the vectors cannot indicate both directions accurately. To avoid inaccuracies caused by superposition of P- and S-waves in a conventional energy flux density vector, P- and S-wave energy flux density vectors should be calculated separately. Because the conventional energy flux density vector is obtained by multiplying the stress tensor by the particle-velocity vector, the common way to calculate P- and S-wave energy flux density vectors is to decompose the stress tensor and particle-velocity vector into the P- and S-wave parts before multiplication. However, we have found that the P-wave still interfere with the S-wave energy flux density vector calculated by this method. Therefore, we have developed a new method to calculate P- and S-wave energy flux density vectors based on a set of new equations but not velocity-stress equations. First, we decompose elastic wavefield by the set of equations to obtain the P- and S-wave particle-velocity vectors, dilatation scalar, and rotation vector. Then, we calculate the P-wave energy flux density vector by multiplying the P-wave particle-velocity vector by dilatation scalar, and we calculate the S-wave energy flux density vector as a cross product of the S-wave particle-velocity vector and rotation vector. The vectors can indicate accurate propagation directions of P- and S-waves, respectively, without being interfered by the superposition of the two wave modes.
Based on arbitrarily wide-angle wave equations, a reverse-time propagation scheme is developed by substituting the partial derivatives of depth and time with central differences. The partial derivative of horizontal direction is replaced with high order difference. The imaging condition is computed by solving the eikonal equations. On the basis of above techniques, a prestack reverse-time depth migration algorithm is developed. The processing examples of synthetic data show that the method can remove unwanted internal reflections and decrease the migration noise. The method also has the advantage of fidelity and is applicable of dip angle reflector imaging.
The source vessel noise is a very common noise type in offshore seismic surveys. The state‐of‐art deep learning‐based methods provide an end‐to‐end framework for seismic data denoising. The denoising performance of a pretrained network is, however, highly dependent on the completeness of the training set. When training a denoising network with only field data, especially for attenuating erratic noise, it is hard to obtain a noise‐free data as the training target for the network. Transfer learning, by combining the synthetic and field data, is an alternative solution for improving the generalization capabilities of the network, although being able to model such erratic noise represents also a challenge. Although the denoising results by traditional methods are not accurate enough for creating a complete training set, the features in residual noise by subtracting the denoised data from noisy data are enough for the network to learn. Considering the aforementioned factors, we develop a deep learning‐based workflow for the attenuation of the erratic source vessel noise from ocean bottom node 4C data. Instead of using denoising results directly, we use the conventional methods to extract noise and add them to the high signal‐to‐ratio region of the field data. The created noisy dataset is different from the original noisy data in noise regions; thus, the pretrained network can also be used for predicting the same original data. The denoising results of synthetic and field data all show that even the network is trained on a noisy labelled dataset, we still can obtain high signal‐to‐noise ratio denoising result. Besides, when compare with the results by filtering‐based methods, our proposed method can attenuate the vessel noise more effectively and preserve the near offsets reflections.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.