Space and time spectra of stationary stochastic waves, with special reference to microtremors

The Trace transform proposed, a generalization of the Radon transform, consists of tracing an image with straight lines along which certain functionals of the image function are calculated. Different functionals that can be used may be invariant to different transformations of the image. The paper presents the properties the functionals must have in order to be useful in three different applications of the method: construction of invariant features to rotation, translation and scaling of the image, construction of sensitive features to the parameters of rotation, translation and scaling of the image, and construction of features that may correlate well with a certain phenomenon we wish to monitor.

The Trace transform and its applications.

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Fast dictionary learning for noise attenuation of multidimensional seismic data

A practical introduction to signal processing in scientific measurement, for scientists, engineers, researchers, instructors, and students working in academia, industry, environmental, medical, engineering, earth science, space, military, financial, and agriculture. Includes such topics as smoothing, differentiation, peak detection, integration and peak area measurements, harmonic analysis, convolution and deconvolution, Fourier filtering, least-squares curve fitting, multi-component spectroscopy, nonlinear iterative least-squares peak fitting. Provides many demonstrations and real data examples, plus download links to many free Matlab/Octave scripts and functions plus spreadsheet templates which has been widely used and have been cited in over 160 published papers, theses, and patents. Includes an appendix containing case studies, examples, and simulations, plus an alphabetical index.

A Pragmatic Introduction to Signal Processing: with applications in scientific measurement

Random noise elimination acts as an important role in the seismic signal processing. Generally, noise in seismic data can be divided into two categories of coherent and incoherent or random noise. Suppression of wide-band noise which is characterized by random oscillation in seismic data over time is one of the challenging issues in the seismic data processing. This paper describes a new noise suppression algorithm for seismic data denoising. The seismic data, trace-by-trace are transformed into sparse subspace using the synchrosqueezed wavelet transform, then the obtained sparse time-frequency representation is decomposed into semilow-rank and sparse components using the Optshrink algorithm. Finally, the denoised seismic trace can be recovered by back-transforming the semilow-rank component to the time domain using inverse synchrosqueezed wavelet transform. The proposed method is assessed using a single synthetic seismic trace and a synthetic seismic section with two crossover linear and curve events with two discontinuities that are buried in the random noise. We have also evaluated the method using a prestack real seismic data set from an oil field in the southwest of Iran. A comparison is performed between the proposed method and the semisoft GoDec algorithm, classical f-x singular spectrum analysis, and prediction Wiener filter. The results visually and quantitatively confirmed the superiority of the proposed method in contrast to the other well-established noise reduction methods.

Seismic Random Noise Attenuation Using Synchrosqueezed Wavelet Transform and Low-Rank Signal Matrix Approximation

Distributed acoustic sensing (DAS) is a novel technology, which has the advantages of full well coverage, high sampling density, and strong tolerance to harsh environments. However, compared with conventional geophones, the signal-to-noise ratio (SNR) of vertical seismic profile (VSP) data obtained using DAS is low, and there are many types of noise (such as random noise, coupled noise, fading noise, background abnormal interference, horizontal noise, and checkerboard noise). These noises bring great difficulties to the interpretation of seismic data. Existing DAS VSP data denoising methods generally can only suppress one type of noise. Faced with DAS VSP data with many types of noise, the denoising process is extremely complicated. To solve the above problems, we propose a DAS VSP data denoiser based on the convolutional neural network (CNN), which can suppress a variety of common noise at one time, and the denoising process is more convenient and efficient. In addition, since there is currently no publicly available training set for DAS VSP data, we also use field data and synthetic data to construct a training set for the denoiser. The denoising results show that the proposed method can effectively suppress a variety of common noise in DAS VSP data and the effective signal has almost no energy attenuation. Both the shallow layer signal affected by strong noise and the deep layer signal with weak energy are well recovered.

Distributed Acoustic Sensing Vertical Seismic Profile Data Denoiser Based on Convolutional Neural Network

High-quality seismic data are the basis for stratigraphic imaging and interpretation, but the existence of random noise can greatly affect the quality of seismic data. At present, most understanding and processing of random noise still stay at the level of Gaussian white noise. With the reduction of resource, the acquired seismic data have lower signal-to-noise ratio and more complex noise natures. In particular, the random noise in the desert area has the characteristics of low frequency, non-Gaussian, nonstationary, high energy, and serious aliasing between effective signal and random noise in the frequency domain, which has brought great difficulties to the recovery of seismic events by conventional denoising methods. To solve this problem, an improved feed-forward denoising convolution neural network (DnCNN) is proposed to suppress random noise in desert seismic data. DnCNN has the characteristics of automatic feature extraction and blind denoising. According to the characteristics of desert noise, we modify the original DnCNN from the aspects of patch size, convolution kernel size, network depth, and training set to make it suitable for low-frequency and non-Gaussian desert noise suppression. Both simulation and practical experiments prove that the improved DnCNN has obvious advantages in terms of desert noise and surface wave suppression as well as effective signal amplitude preservation. In addition, the improved DnCNN, in contrast to existing methods, has considerable potential to benefit from large data sets. Therefore, we believe that it can open a new direction in the area of seismic data processing.

Low-Frequency Noise Suppression Method Based on Improved DnCNN in Desert Seismic Data

In seismic exploration, random noise suppression is one of the key problems in seismic data processing. For random noise attenuation, the most important thing is the understanding of seismic random noise generation and propagation. Seismic random noise is considered as temporal and spatial random processes, and it can be analyzed only qualitatively for now, due to its high variability. In this paper, we classify seismic random noise sources by their generation factors and simulate the random noise of the desert in West China. According to Green’s function, it can be assumed that seismic random noise sources are point-like sources that are distributed around geophones. A seismic random noise record is taken as the superimposed wave field exited by all the independent sources in a homogeneous isotropy half-infinite surface. Based on the wind vibration theory and preliminary study about ambient vibrations, the noise source functions are determined. We obtain the waveforms of different kinds of noise by solving the inhomogeneous wave equations and analyze the characteristics qualitatively and quantitatively. The seismic synthetic record with a 1.6-s time and 250-m distances is obtained, and the characteristics are compared between the simulated and the real noise record in time domain and space domain, respectively. The comparative results show the same characteristics of the simulated noise and the real noise, which demonstrates the feasibility of the proposed method. According to the noise modeling, it is known that the near-field cultural noise is the main component of the random noise in the desert, on the basis of which complex diffusion filtering is selected. The filtered results by complex diffusion filtering is compared with the results of time–frequency peak filtering, which is a popular filtering method of seismic random noise suppression in recent years. The comparative results show that complex diffusion filtering is more suitable for the noise of the desert in the Tarim Basin. This result proves that seismic random noise modeling can provide the guidance for noise attenuation. It lays a foundation for researching the propagation characteristics and better attenuation of seismic random noise in the future.

Seismic Exploration Random Noise on Land: Modeling and Application to Noise Suppression

Time-frequency peak filtering (TFPF) is a classical filtering method in time-frequency domain. It applies Wigner-Ville distribution to estimate the instantaneous frequency of an analytical signal. There is a pair of contradiction in this method, i.e., selecting a short window length may lead to good preservation for signal amplitude but bad random noise reduction whereas selecting a long window length may lead to serious attenuation for signal amplitude but effective random noise reduction. In order to make a good tradeoff between valid signal amplitude preservation and random noise reduction, we adopt empirical mode decomposition (EMD) to improve the TFPF results. The new idea is to utilize the decomposition characteristic of EMD which decomposes a signal to several modes from high to low frequency and to take advantage of the time-frequency filtering characteristic of TFPF which can recognize the valid signal component in the time-frequency plane in order to achieve effective random noise reduction together with good amplitude preservation. Through some experiments on synthetic seismic models and field seismic records, we show the better performance of the new method compared with the conventional TFPF.

An Amplitude-Preserved Time–Frequency Peak Filtering Based on Empirical Mode Decomposition for Seismic Random Noise Reduction

The time-frequency peak filtering (TFPF) is an effective tool in random-noise attenuation and has been applied to seismic record denoising in recent years. The window length (WL) of the time-frequency distribution (TFD) is the key to the conventional TFPF technology. A fixed WL is not optimal for both the low- and high-frequency components at the same time; an adaptive WL results in serious distortion of the reflected waveform. In this letter, we discuss a modified TFPF along the radial-trace direction and prove its advantage in TFD window selection. Experiments on both synthetic models and field data show that the radial-trace TFPF result is no longer much influenced by the WL as the conventional TFPF. Furthermore, it can provide better performance in both random-noise attenuation and reflected signal preservation with a fixed WL.

Yue Li

Papers

Distributed Acoustic Sensing Vertical Seismic Profile Data Denoiser Based on Convolutional Neural Network

Low-Frequency Noise Suppression Method Based on Improved DnCNN in Desert Seismic Data

Seismic Exploration Random Noise on Land: Modeling and Application to Noise Suppression

An Amplitude-Preserved Time–Frequency Peak Filtering Based on Empirical Mode Decomposition for Seismic Random Noise Reduction

Noise Attenuation for 2-D Seismic Data by Radial-Trace Time-Frequency Peak Filtering