Semi-blind-trace algorithm for self-supervised attenuation of trace-wise coherent noise

Trace-wise noise is a type of noise often seen in seismic data, which is characterized by vertical coherency and horizontal incoherency. Using self-supervised deep learning to attenuate this type of noise, the conventional blind-trace deep learning trains a network to blindly reconstruct each trace in the data from its surrounding traces; it attenuates isolated trace-wise noise but causes signal leakage in clean and noisy traces and reconstruction errors next to each noisy trace. To reduce signal leakage and improve denoising, we propose a new loss function and masking procedure in semi-blind-trace deep learning. Our hybrid loss function has weighted active zones that cover masked and non-masked traces. Therefore, the network is not blinded to clean traces during their reconstruction. During training, we dynamically change the masks' characteristics. The goal is to train the network to learn the characteristics of the signal instead of noise. The proposed algorithm enables the designed U-net to detect and attenuate trace-wise noise without having prior information about the noise. A new hyperparameter of our method is the relative weight between the masked and non-masked traces' contribution to the loss function. Numerical experiments show that selecting a small value for this parameter is enough to significantly decrease signal leakage. The proposed algorithm is tested on synthetic and real off-shore and land datasets with different noises. The results show the superb ability of the method to attenuate trace-wise noise while preserving other events. An implementation of the proposed algorithm as a Python code is also made available

Semi-blind-trace algorithm for self-supervised attenuation of trace-wise coherent noise

Trace-wise noise is a type of noise often seen in seismic data, which is characterized by vertical coherency and horizontal incoherency. Using self-supervised deep learning to attenuate this type of noise, the conventional blind-trace deep learning trains a network to blindly reconstruct each trace in the data from its surrounding traces; it attenuates isolated trace-wise noise but causes signal leakage in clean and noisy traces and reconstruction errors next to each noisy trace. To reduce signal leakage and improve denoising, we propose a new loss function and masking procedure in a semi-blind-trace deep learning framework. Our hybrid loss function has weighted active zones that cover masked and non-masked traces. Therefore, the network is not blinded to clean traces during their reconstruction. During training, we dynamically change the masks' characteristics. The goal is to train the network to learn the characteristics of the signal instead of noise. The proposed algorithm enables the designed U-net to detect and attenuate trace-wise noise without having prior information about the noise. A new hyperparameter of our method is the relative weight between the masked and non-masked traces' contribution to the loss function. Numerical experiments show that selecting a small value for this parameter is enough to significantly decrease signal leakage. The proposed algorithm is tested on synthetic and real off-shore and land data sets with different noises. The results show the superb ability of the method to attenuate trace-wise noise while preserving other events. An implementation of the proposed algorithm as a Python code is also made available

Robust data driven discovery of a seismic wave equation

Despite the fact that our physical observations can often be described by derived physical laws, such as the wave equation, in many cases, we observe data that do not match the laws or have not been described physically yet. Therefore recently, a branch of machine learning has been devoted to the discovery of physical laws from data. We test such discovery algorithms, with our own flavor of implementation D-WE, in discovering the wave equation from the observed spatial-temporal wavefields. D-WE first pretrains a neural network (NN) in a supervised fashion to establish the mapping between the spatial-temporal locations (x,y,z,t) and the observation displacement wavefield function u(x,y,z,t). The trained NN serves to generate meta-data and provide the time and spatial derivatives of the wavefield (e.g., u_tt and u_xx) by automatic differentiation. Then, a preliminary library of potential terms for the wave equation is optimized from an overcomplete library by using a genetic algorithm. We, then, use a physics-informed information criterion to evaluate the precision and parsimony of potential equations in the preliminary library and determine the best structure of the wave equation. Finally, we train the "physics-informed" neural network to identify the corresponding coefficients of each functional term. Examples in discovering the 2D acoustic wave equation validate the feasibility and effectiveness of D-WE. We also verify the robustness of this method by testing it on noisy and sparsely acquired wavefield data

S2S-WTV: Seismic Data Noise Attenuation Using Weighted Total Variation Regularized Self-Supervised Learning

Seismic data often undergoes severe noise due to environmental factors, which seriously affects subsequent applications. Traditional hand-crafted denoisers such as filters and regularizations utilize interpretable domain knowledge to design generalizable denoising techniques, while their representation capacities may be inferior to deep learning denoisers, which can learn complex and representative denoising mappings from abundant training pairs. However, due to the scarcity of high-quality training pairs, deep learning denoisers may sustain some generalization issues over various scenarios. In this work, we propose a self-supervised method that combines the capacities of deep denoiser and the generalization abilities of hand-crafted regularization for seismic data random noise attenuation. Specifically, we leverage the Self2Self (S2S) learning framework with a trace-wise masking strategy for seismic data denoising by solely using the observed noisy data. Parallelly, we suggest the weighted total variation (WTV) to further capture the horizontal local smooth structure of seismic data. Our method, dubbed as S2S-WTV, enjoys both high representation abilities brought from the self-supervised deep network and good generalization abilities of the hand-crafted WTV regularizer and the self-supervised nature. Therefore, our method can more effectively and stably remove the random noise and preserve the details and edges of the clean signal. To tackle the S2S-WTV optimization model, we introduce an alternating direction multiplier method (ADMM)-based algorithm. Extensive experiments on synthetic and field noisy seismic data demonstrate the effectiveness of our method as compared with state-of-the-art traditional and deep learning-based seismic data denoising methods

Elastic pre-stack seismic inversion through Discrete Cosine Transform reparameterization and Convolutional Neural Networks

We develop a pre-stack inversion algorithm that combines a Discrete Cosine Transform (DCT) reparameterization of data and model spaces with a Convolutional Neural Network (CNN). The CNN is trained to predict the mapping between the DCT-transformed seismic data and the DCT-transformed 2-D elastic model. A convolutional forward modeling based on the full Zoeppritz equations constitutes the link between the elastic properties and the seismic data. The direct sequential co-simulation algorithm with joint probability distribution is used to generate the training and validation datasets under the assumption of a stationary non-parametric prior and a Gaussian variogram model for the elastic properties. The DCT is an orthogonal transformation that is here used as an additional feature extraction technique that reduces the number of unknown parameters in the inversion and the dimensionality of the input and output of the network. The DCT reparameterization also acts as a regularization operator in the model space and allows for the preservation of the lateral and vertical continuity of the elastic properties in the recovered solution. We also implement a Monte Carlo simulation strategy that propagates onto the estimated elastic model the uncertainties related to both noise contamination and network approximation. We focus on synthetic inversions on a realistic subsurface model that mimics a real gas-saturated reservoir hosted in a turbiditic sequence. We compare the outcomes of the implemented algorithm with those provided by a popular linear inversion approach and we also assess the robustness of the CNN inversion to errors in the estimated source wavelet and to erroneous assumptions about the noise statistic. Our tests confirm the applicability of the proposed approach, opening the possibility to estimate the subsurface elastic parameters and the associated uncertainties in near real-time while satisfactorily preserving the assumed spatial variability and the statistical properties of the elastic parameters

Full waveform inversion based on dynamic data matching of convolutional wavefields

Cycle skipping problem caused by the absent of low frequencies and inaccurate initial model makes full waveform inversion (FWI) deviate from the true model. A novel method is proposed to mitigate cycle skipping phenomenon by dynamic data matching which improves the matching of synthetic and observed events to regulate the updating of initial model in a correct direction. 1-dimentional (1-D) Gaussian convolutional kernels with different lengths are used to extract features of each time sample in each trace which represents the integrated properties of wavefield at different time ranges centered on each time sample. According to the minimum Euclidean distance of the features, the optimally matched pairs of time samples in the observed and synthetic trace can be found. A constraint evaluates the reliability of dynamic matching by attenuating the amplitude of synthetic data according to the values of traveltime differences between each pairs of optimally matched time samples is proposed to improve the accuracy of data matching. In addition, Gaussian kernels have the capability to extract features of time samples contaminated by strong noises accurately to improve the robustness of the propose method further. The selection scheme of optimal parameters is discussed and concluded to ensure the convergence of the proposed method. Numerical tests on Marmousi model verify the feasibility of the propose method. The proposed method provides a new approach to tackle the convergence problem of FWI when using the field seismic data

DIPPAS: A Deep Image Prior PRNU Anonymization Scheme

Source device identification is an important topic in image forensics since it allows to trace back the origin of an image. Its forensics counter-part is source device anonymization, that is, to mask any trace on the image that can be useful for identifying the source device. A typical trace exploited for source device identification is the Photo Response Non-Uniformity (PRNU), a noise pattern left by the device on the acquired images. In this paper, we devise a methodology for suppressing such a trace from natural images without significant impact on image quality. Specifically, we turn PRNU anonymization into an optimization problem in a Deep Image Prior (DIP) framework. In a nutshell, a Convolutional Neural Network (CNN) acts as generator and returns an image that is anonymized with respect to the source PRNU, still maintaining high visual quality. With respect to widely-adopted deep learning paradigms, our proposed CNN is not trained on a set of input-target pairs of images. Instead, it is optimized to reconstruct the PRNU-free image from the original image under analysis itself. This makes the approach particularly suitable in scenarios where large heterogeneous databases are analyzed and prevents any problem due to lack of generalization. Through numerical examples on publicly available datasets, we prove our methodology to be effective compared to state-of-the-art techniques