Fast hyperbolic Radon transform represented as convolutions in log-polar coordinates

The hyperbolic Radon transform is a commonly used tool in seismic processing, for instance in seismic velocity analysis, data interpolation and for multiple removal. A direct implementation by summation of traces with different moveouts is computationally expensive for large data sets. In this paper we present a new method for fast computation of the hyperbolic Radon transforms. It is based on using a log-polar sampling with which the main computational parts reduce to computing convolutions. This allows for fast implementations by means of FFT. In addition to the FFT operations, interpolation procedures are required for switching between coordinates in the time-offset; Radon; and log-polar domains. Graphical Processor Units (GPUs) are suitable to use as a computational platform for this purpose, due to the hardware supported interpolation routines as well as optimized routines for FFT. Performance tests show large speed-ups of the proposed algorithm. Hence, it is suitable to use in iterative methods, and we provide examples for data interpolation and multiple removal using this approach.Comment: 21 pages, 10 figures, 2 table

Hybrid Kinematic-Dynamic Approach to Seismic Wave-Equation Modeling, Imaging, and Tomography

Estimation of the structure response to seismic motion is an important part of structural analysis related to mitigation of seismic risk caused by earthquakes. Many methods of computing structure response require knowledge of mechanical properties of the ground which could be derived from near-surface seismic studies. In this paper we address computationally efficient implementation of the wave-equation tomography. This method allows inverting first-arrival seismic waveforms for updating seismic velocity model which can be further used for estimating mechanical properties. We present computationally efficient hybrid kinematic-dynamic method for finite-difference (FD) modeling of the first-arrival seismic waveforms. At every time step the FD computations are performed only in a moving narrowband following the first-arrival wavefront. In terms of computations we get two advantages from this approach: computation speedup and memory savings when storing computed first-arrival waveforms (it is not necessary to make calculations or store the complete numerical grid). Proposed approach appears to be specifically useful for constructing the so-called sensitivity kernels widely used for tomographic velocity update from seismic data. We then apply the proposed approach for efficient implementation of the wave-equation tomography of the first-arrival seismic waveforms

Extended structure tensors for multiple directionality estimation

Standard structure tensors provide a robust way of directionality estimation of waves (or edges) but only for the case when they do not intersect. In this work, a structure tensor extension using a one-way wave equation is proposed as a tool for estimating directionality in seismic data and images in the presence of conflicting dips. Detection of two intersecting waves is possible in a two-dimensional case. In three dimensions both two and three intersecting waves can be detected. Moreover, a method for directionality filtering using the estimated directions is proposed. This method makes use of the ideas of a one-way wave equation but can be applied to generic images not related to wave propagation

Sparse wave-packet representations and seismic imaging

In this paper we introduce a new algorithm for seismic imaging based on the flow out of Gaussian wave packets. We follow the standard strategy of decomposing data into wave packets and flowing them out along rays to approximate the downward wavefield extrapolation, and finally applying an imaging condition. We revisit each computational step to gain efficiency. Furthermore, we develop procedure for seismic data decomposition in order to obtain highly sparse representations with Gaussian wave packets. As a result we get fast algorithm heavily exploiting sparse data representation and analytic description of Gaussian wave packets. We tests our algorithm on synthetic example of migrating common-shot gather

A hybrid machine-learning approach for analysis of methane hydrate formation dynamics in porous media with synchrotron CT imaging

Fast multi-phase processes in methane hydrate bearing samples pose a challenge for quantitative micro-computed tomography study and experiment steering due to complex tomographic data analysis involving time-consuming segmentation procedures. This is because of the sample's multi-scale structure, which changes over time, low contrast between solid and fluid materials, and the large amount of data acquired during dynamic processes. Here, a hybrid approach is proposed for the automatic segmentation of tomographic data from time-resolved imaging of methane gas-hydrate formation in sandy granular media, which includes a deep-learning 3D U-Net model. To prepare a training dataset for the 3D U-Net, a technique to automate data labeling based on sample-specific information about the mineral matrix immobility and occasional fluid movement in pores is proposed. Automatic segmentation allowed for studying properties of the hydrate growth in pores, as well as dynamic processes such as incremental flow and redistribution of pore brine. Results of the quantitative analysis showed that for typical gas-hydrate stability parameters (100 bar methane pressure, 7°C temperature) the rate of formation is slow (less than 1% per hour), after which the surface area of contact between brine and gas increases, resulting in faster formation (2.5% per hour). Hydrate growth reaches the saturation point after 11 h of the experiment. Finally, the efficacy of the proposed segmentation scheme in on-the-fly automatic data analysis and experiment steering with zooming to regions of interest is demonstrated

Multi-scale structured imaging using wave packets and prolate spheroidal wave functions

Imaging and inverse scattering of seismic reflection data can be formulated in terms of a certain class of Fourier integral operators. We present an approximation and discretization of such operators following a multiscale approach, based on wave packets as the quanta for representing seismic data. One of the key ingredients in our approach is the coupling of dyadic parabolic decomposition and prolate spheroidal wave functions. As an example, we detail our method for parametrices of evolution equations, and obtain a onestep algorithm wave- equation for imaging and inverse scattering, time and depth extrapolation, velocity continuation, and extended imagin