Jianwei Ma

Peking University | PKU · School of Earth and Space Sciences

In seismic processing, one goal is to recover missing traces when the data is sparsely and incom-pletely sampled. We present a method which treats this reconstruction problem from a novel perspective. By utilizing its connection with the general matrix completion (MC) problem, we build a special low rank matrix, which can be reconstructed through s...

Restoration/interpolation of missing traces plays a crucial role in the seismic data processing pipeline. Efficient restoration methods have been proposed based on sparse signal representation in a transform domain such as Fourier, wavelet, curvelet, and shearlet transforms. Most existing methods are based on transforms with a fixed basis. We consi...

Reconstruction of seismic data is routinely used to improve the quality and resolution of seismic data from incomplete acquired seismic recordings. Curvelet‐based Recovery by Sparsity‐promoting Inversion, adapted from the recently‐developed theory of compressive sensing, is one such kind of reconstruction, especially good for recovery of undersampl...

Multiresolution methods are deeply related to image processing, biological and computer vision, and scientific computing. The curvelet transform is a multiscale directional transform that allows an almost optimal nonadaptive sparse representation of objects with edges. It has generated increasing interest in the community of applied mathematics and...

Seismic data interpolation is essential in a seismic data processing workflow, recovering data from sparse sampling. Traditional and deep learning based methods have been widely used in the seismic data interpolation field and have achieved remarkable results. In this paper, we propose a seismic data interpolation method through the novel applicati...

One of the key objectives in geophysics is to characterize the subsurface through the process of analyzing and interpreting geophysical field data that are typically acquired at the surface. Data-driven deep learning methods have enormous potential for accelerating and simplifying the process but also face many challenges, including poor generaliza...

Full‐waveform inversion (FWI) is a powerful geophysical imaging technique that reproduces high‐resolution subsurface physical parameters by iteratively minimizing the misfit between the simulated and observed seismograms. Unfortunately, conventional FWI with a least‐squares loss function suffers from various drawbacks, such as the local‐minima prob...

Starting from an initial model and pre-defined priors, a variational full waveform in- version (VFWI) seeks posterior distributions of model parameters via optimization using Bayesian theorem. VFWI is thus useful in estimating uncertainties in full-waveform inversions (FWIs). However, the resolution of the inverted models from VFWIs is usually not...

The conventional least-squares misfit function compares the synthetic data to the observed data in a point by point style. The Wasserstein distance function, also called optimal transport function, matches patterns. The kinematic information of a seismograms is therefore efficiently extracted. This property makes it more convex than the conventiona...

Frequency-domain simulation of seismic waves plays an important role in seismic inversion, but it remains challenging in large models. The recently proposed physics-informed neural network (PINN), as an effective deep learning method, has achieved successful applications in solving a wide range of partial differential equations (PDEs), and there is...

Seismic samples are generally designed to be placed on perfect Cartesian coordinates, that is, on-the-grid. However, sampling geometry is disturbed by obstacles in field applications. Large obstacles result in missing samples. For small obstacles, geophones or sources are placed at an available off-the-grid location nearest to the designed grid. To...

Secondary microseisms are caused by non-linear interactions between ocean waves of approximately equal wavelengths and opposite propagation directions. This seismic forcing is evaluated using ocean sea-state hindcast data and further modulated by the bathymetric effect. The numerical ocean model provides a global activity representation of the seco...

Seismic data interpolation is an essential procedure in seismic data processing. However, conventional interpolation methods may generate inaccurate results due to the simplicity of assumptions, such as linear events or sparsity. On the contrary, deep learning trains a deep neural network with a large dataset without relying on predefined assumptio...

Full-waveform inversion (FWI) is a powerful technique for building high-quality subsurface geological structures. It is known to suffer from local minima problems when a good starting model is lost. To obtain a desirable solution, regularization constraints are needed to impose suitable priors, in particular for salt models. Recent studies have all...

Multidimensional pre-stack seismic data reconstruction can be viewed as a low-rank tensor completion problem. Recently, the nuclear norm has been widely used as a convex surrogate of the tensor rank function for low-rank tensor recovery and has been successfully applied to 5D seismic data reconstruction. However, solving the nuclear norm-based rela...

Full-waveform inversion (FWI) is an efficient technique for capturing the subsurface physical features by iteratively minimizing the misfit between simulated and observed seismograms. As such a problem is ill-posed, a significant ingredient for a satisfactory solution is to incorporate desirable priors. Most traditional regularized FWI approaches s...

First arrival enhancement can improve the picking accuracy. Traditional seismic interferometry is based on the correlation calculation of multiple iterations to enhance the first arrival. Besides being sensitive to non-uniform Gaussian noise, the correlated and iterative operations causing seismic wavelet deformation with positive sidelobes are mai...

In seismic exploration, collected traces inevitably appear noise and irregular sampled along the spatial coordinates, which affects seismic inversion and imaging. Seismic data interpolation is modelled by solving an inverse problem with regularization terms in mathematics. But sparse or low-rank priors in model-based methods cannot capture complex...

Current machine learning methods make a positive difference to outlook on data assimilation. In this paper, an efficient assimilation of image sequences that incorporated in a deep neural networks (DNN) framework is put forward. To tackle the motion estimation of fluid, the image model characterizing both the evolution of the tracers and the veloci...

Random noise attenuation is of great importance to obtain high-quality seismic data. Unsupervised deep learning methods have received much attention for various seismic data processing tasks in recent years. Specifically, the self-supervised deep learning method obtains supervisory information from the data itself, showing its promising denoising a...

Data processing has to deal with many practical difficulties. Data is often corrupted by artifacts or noise and acquiring data can be expensive and difficult. Thus, the given data is often incomplete and inaccurate. To overcome these problems, it is often assumed that the data is sparse or low-dimensional in some domain. When multiple measurements are...

Seismic denoising is an essential step for seismic data processing. Conventionally, dictionary learning methods for seismic denoising always assume the representation coefficients to be sparse and the dictionary to be normalized or a tight frame. Current dictionary learning methods need to update the dictionary and the coefficients in an alternatin...

Frequency-domain simulation of seismic waves plays an important role in seismic inversion, but it remains challenging in large models. The recently proposed physics-informed neural network (PINN), as an effective deep learning method, has achieved successful applications in solving a wide range of partial differential equations (PDEs), and there is...

Seismic data can be described in a low-dimensional manifold. Thus, the low dimensionality of the seismic data patch manifold can serve as a good regularizer for seismic data interpolation. However, we have found that having only low-dimensional manifold regularization is not sufficient for interpolating seismic data with large data gaps or spectral...

The dictionary learning method has been successfully applied to denoise and interpolate seismic data. However, this method cannot be used to adequately interpret weak seismic events and structural features. By combining dictionary learning and a convolutional neural network (CNN) denoiser, we constructed a new dictionary learning method regularized...

Data processing has to deal with many practical difficulties. Data is often corrupted by artifacts or noise and acquiring data can be expensive and difficult. Thus, the given data is often incomplete and inaccurate. To overcome these problems, it is often assumed that the data is sparse or low-dimensional in some domain. When multiple measurements...

Migration velocity analysis is a crucial seismic processing step that aims to translate residual moveout in common-image gathers (CIGs) into velocity updates. However, this is often an iterative process that requires migration and significant human effort in each iteration. To derive the residual moveout correction accurately and efficiently, we pr...

Inspired by the complexity and diversity of biological neurons, a quadratic neuron is proposed to replace the inner product in the current neuron with a simplified quadratic function. Employing such a novel type of neurons offers a new perspective on developing deep learning. When analyzing quadratic neurons, we find that there exists a function su...

Random noise attenuation is an important step in seismic data processing. Unfortunately, most conventional denoising methods heavily rely on specific prior knowledge and fine-tuning of the parameters. Therefore, they often fail to suppress random noise. Recent works based on supervised learning techniques for seismic noise suppression show outstand...

Noise present in real gravity data can lead to inaccurate inversion results. Multi-task strategy in deep learning provides a promising method to solve this problem. In this study, a multi-task framework is proposed for simultaneous inversion and denoising of noisy gravity data, in which the denoising task can constrain the inversion task. To extrac...

P- and S-wave decomposition is essential for imaging multi-component seismic data in elastic media. A data-driven workflow is proposed to obtain a set of spatial filters that are highly accurate and artifact-free in decomposing the P- and S-waves in 2D isotropic elastic wavefields. The filters are formulated initially by inverse Fourier transforms...

In elastostatics, the scale effect is a phenomenon in which the elastic parameters of a medium vary with specimen size when the specimen is sufficiently small. Linear elasticity cannot explain the scale effect because it assumes that the medium is a continuum and does not consider microscopic rotational interactions within the medium. In elastodyna...

Seismic full waveform inversion (FWI) is a powerful geophysical imaging technique that produces high-resolution subsurface models by iteratively minimizing the misfit between the simulated and observed seismograms. Unfortunately, conventional FWI with least-squares function suffers from many drawbacks such as the local-minima problem and computatio...

In this work, we propose a structure sparsity regularization strategy in the framework of 4-D variational data assimilation (4-D Var). In meteorology and oceanography, the number of unknown model variables is far fewer than that of image observations, often leading to solve an underdetermined nonlinear inverse problem. In recent years, the ℓ¹-norm-...

Traditional physical models are no longer the only foundational tools for processing geophysical data; "big data" help to reveal the laws of geophysics from new angles with exciting results so far.

Quantitative phase imaging (QPI) is an emerging label-free technique that produces images containing morphological and dynamical information without contrast agents. Unfortunately, the phase is wrapped in most imaging system. Phase unwrapping is the computational process that recovers a more informative image. It is particularly challenging with th...

We implement multiparameter full waveform inversions in the framework of recurrent neural networks in elastic isotropic and transversely isotropic media. A staggered-grid velocity-stress scheme is used to solve the first-order elastodynamic equations for forward modeling. The gradients of loss with respect to model parameters are obtained by automa...

Recently deep learning (DL), as a new data-driven technique compared to conventional approaches, has attracted increasing attention in geophysical community, resulting in many opportunities and challenges. DL was proven to have the potential to predict complex system states accurately and relieve the “curse of dimensionality” in large temporal and...

The precise estimation of associated parameters for microseismic and earthquake signals is a challenging task due to the presence of background noise. Important parameters to analyze earthquake signals such as peak ground acceleration, velocity, displacement, and P, S-wave arrival time are affected by noise. In this study, we propose a seismic data...

The physical basis, parameterization, and assumptions involved in root-mean-square (RMS) velocity estimation have not significantly changed since they were first developed. However, all three of these aspects are good targets for novel application of the recent emergence of Machine Learning (ML). So it is useful at this time to provide a tutorial o...

The ability to calculate the seismogram of an earthquake at a local or regional scale is critical but challenging for many seismological studies because detailed knowledge about the 3D heterogeneities in the Earth’s subsurface, although essential, is often insufficient. Here, we present an application of compressed sensing technology that can help...

Quantitative phase imaging (QPI) is an emerging label-free technique that produces images containing morphological and dynamical information without contrast agents. Unfortunately, the phase is wrapped in most imaging system. Phase unwrapping is the computational process that recovers a more informative image. It is particularly challenging with th...

Blind sparse-spike deconvolution is a widely used method to estimate seismic wavelets and sparse reflectivity in the shape of spikes based on the convolution model. To increase the vertical resolution and lateral continuity of the estimated reflectivity, we further improve the sparse-spike deconvolution by introducing the atomic norm minimization a...

Understanding the principles of geophysical phenomena is an essential and challenging task. Model-driven approaches have supported the development of geophysics for a long time; however, such methods suffer from the curse of dimensionality and may inaccurately model the subsurface. Data-driven techniques may overcome these issues with increasingly...

Optical diffraction tomography is an effective tool to estimate the refractive indices of unknown objects. It proceeds by solving an ill-posed inverse problem for which the wave equation governs the scattering events. The solution has traditionally been derived by the minimization of an objective function in which the data-fidelity term encourages...

We propose an interpolation method based on the denoising convolutional neural network (CNN) for seismic data. It provides a simple and efficient way to break though the problem of scarcity of geophysical training labels that are often required by deep learning methods. This new method consists of two steps: (1) training a set of CNN denoisers to l...

Different from the surface survey, the vertical seismic profile (VSP) survey deploys the sources on the surface and the geophones in a well. VSP provides higher-resolution information of subsurface structures. The faults that cannot be imaged with surface seismic data may be detected with VSP data, and detailed analysis of fracture zones can be ach...

We develop an artificial neural network to estimate P-wave velocity models directly from prestack common-source gathers.The proposed network is composed of a fully connected layer set and a modified fully convolutional layer set. The parameters in the network are tuned through supervised learning to map multi-shot common-source gathers to velocity...

The data-driven tight frame (DDTF) method is a dictionary learning method which has been used widely in the adaptive sparse representation and the seismic random noise attenuation. In the DDTF method, the thresholding operator setting plays a significant role on balancing the noise removal and preservation of detail information with high frequency....

Weak signal preservation is critical in the application of seismic data denoising, especially in deep seismic exploration. It is hard to separate those weak signals in seismic data from random noise, as it is less compressible or sparsifiable, though they are usually important for seismic data analysis. Conventional sparse coding models exploit the...

We introduced a structure learning-type sparsity regularization in the framework of 4D-Var for 2D velocity reconstruction. The result shows promising performance, such as fast convergence and more consistency with the observation.

China ranks second and third in global oil and natural gas consumption, and fifth and sixth in global oil and natural gas production, respectively (U.S. EIA, 2018). In the past 25 years, China's oil consumption has increased 3.5 times, and natural gas consumption is rising rapidly as well. China is increasing its investment in the petroleum industr...

Compared with traditional seismic noise attenuation algorithms that depend on signal models and their corresponding prior assumptions, removing noise with a deep neural network is trained based on a large training set, where the inputs are the raw datasets and the corresponding outputs are the desired clean data. After the completion of training, t...

Earthquake acceleration time chronicles records are important sources of information in the field of tremor engineering and engineering seismology. High frequency noise could considerably reduce P phase picking accuracy and the time. Accurate detection of P phase and onset time arrival picking is very important for the earthquake signal analysis an...

Seismic velocity is one of the most important parameters used in seismic exploration. Accurate velocity models are the key prerequisites for reverse time migration and other high-resolution seismic imaging techniques. Such velocity information has traditionally been derived by tomography or full-waveform inversion (FWI), which are time consuming an...

We propose a convolutional neural network (CNN) denoising based method for seismic data interpolation. It provides a simple and efficient way to break though the lack problem of geophysical training labels that are often required by deep learning methods. The new method consists of two steps: (1) Train a set of CNN denoisers from natural image clea...

Seismic velocity is one of the most important parameters used in seismic exploration. Accurate velocity models are key prerequisites for reverse-time migration and other high-resolution seismic imaging techniques. Such velocity information has traditionally been derived by tomography or full-waveform inversion (FWI), which are time consuming and co...

Seismic wavelet estimation and deconvolution are essential for high-resolution seismic processing. Because of the influence of absorption and scattering, the frequency and phase of the seismic wavelet change with time during wave propagation, leading to a time-varying seismic wavelet. To obtain reflectivity coefficients with more accurate relative...

We propose a novel method for robust estimation of multiple local dips in seismic data via signal decomposition. The decomposition is achieved by regularizing each separated component to have a single dip. The single-dip regularization is built based on the fact that piecewise constant dips indicate that local gradient vectors lie on the same direc...

We herein introduce deep learning to seismic noise attenuation. Compared with traditional seismic noise attenuation algorithms that depend on signal models and their corresponding prior assumptions, a deep neural network is trained based on a large training set, where the inputs are the raw datasets and the corresponding outputs are the desired cle...

This work combines a level-set approach and the optimal transport-based Wasserstein distance in a data assimilation framework. The primary motivation of this work is to reduce assimilation artifacts resulting from the position and observation error in the tracking and forecast of pollutants present on the surface of oceans or lakes. Both errors lea...

In most convolution neural networks (CNNs), downsampling hidden layers is adopted for increasing computation efficiency and the receptive field size. Such operation is commonly so-called pooling. Maximation and averaging over sliding windows (max/average pooling), and plain downsampling in the form of strided convolution are popular pooling methods...

Sparse coding method has been used for seismic denoising, as the data can be sparsely represented by the sparse transform and dictionary learning (DL) methods. DL methods have attracted wide attention because the learned dictionary is adaptive. However, for seismic denoising, the dictionary learned from the noise data is a mix of atoms representing...

Low rank approximation has been extensively studied in the past. It is most suitable to reproduce rectangular like structures in the data. In this work we introduce a generalization using shifted rank-1 matrices to approximate $A\in\mathbb{C}^{M\times N}$. These matrices are of the form $S_{\lambda}(uv^*)$ where $u\in\mathbb{C}^M$, $v\in\mathbb{C}^...

Prestack seismic data denoising is an important step in seismic processing due to the development of prestack time migration. Reduced-rank filtering is a state-of-the-art method for prestack seismic denoising that uses predictability between neighbor traces for each single frequency. Different from the original way of embedding low-rank matrix base...

We propose a new decomposition algorithm for seismic data based on a band-limited a priori knowledge on the Fourier or Radon spectrum. This decomposition is called geometric mode decomposition (GMD), as it decomposes a 2D signal into components consisting of linear or parabolic features. Rather than using a predefined frame, GMD adaptively obtains...

Random noise attenuation, preserving the events and weak features by improving signal‐to‐noise ratio and resolution of seismic data are the most important issues in geophysics. To achieve this objective, we proposed a novel seismic random noise attenuation method by building a compound algorithm. The proposed method combines sparsity prior regulari...

We propose a novel method for seismic ground rolls attenuation by employing the dips differences between ground rolls and reflective signals. The dips differences are modeled by gradient-direction differences, and the overall gradient directions are termed gradient flow. Typically, there are frequency overlap between the ground rolls and reflective...

In the field of seismic exploration, ground roll seriously affects the deep effective reflections from subsurface deep structures. Traditional curvelet transform cannot provide an adaptive basis function to achieve a suboptimal denoised result. In this paper, we propose a method based on empirical curvelet transform (ECT) for ground roll attenuatio...

We have developed a new regularization method for the sparse representation and denoising of seismic data. Our approach is based on two components: a sparse data representation in a learned dictionary and a similarity measure for image patches that is evaluated using the Laplacian matrix of a graph. Dictionary-learning (DL) methods aim to find a da...

Acquisition technology advances, as well as the exploration of geologically complex areas, are pushing the quantity of data to be analyzed into the "big-data" era. In our related work, we found that a machine-learning method based on support vector regression (SVR) for seismic data intelligent interpolation can fully use large data as training data...

We have introduced a new decomposition method for seismic data, termed complex variational mode decomposition (VMD), and we have also designed a new filtering technique for random noise attenuation in seismic data by applying the VMD on constant-frequency slices in the frequency-offset (f-x) domain. The motivation behind this paper is to overcome t...

In this paper, we present a novel method for assimilating geometric information from observed images. Image assimilation technology fully utilizes structural information from the dynamics of the images to retrieve the state of a system and thus to better predict its evolution. Level-set method describing the evolution of the geometry shapes of a gi...

Reducing the cost of seismic exploration is a long-standing problem. Compressive sensing (CS) provides a new routine for recovering signals when the seismic acquisition is under the criteria of Nyquist theory. The basic assumptions of CS are: (1) the signal is sparse under a certain transform, and (2) the acquisition or measurement is random in a c...

In seismic data processing, attenuation of random noise from the observed data is the basic step which improves the signal-to-noise ratio (SNR) of seismic data. In this paper, we proposed an anisotropic total bounded variation regularization approach to attenuate noise. An improved constraint convex optimization model is formulated for this approac...

Seismic data interpolation and denoising plays a key role in seismic data processing. These problems can be understood as sparse inverse problems, where the desired data are assumed to be sparsely representable within a suitable dictionary. In this paper, we present a new method based on a data-driven tight frame (DDTF) of Kronecker type (KronTF) t...

We show seismic data can be described in a low dimensional manifold, and then propose using a low dimensional manifold model (LDMM) method for extremely strong noise attenuation. The LDMM supposes the dimension of the patch manifold of seismic data should be low. In other words, the degree of freedom of the patches should be low. Under the linear e...