Jinghuai Gao

Beamlet Migration Based On Local Perturbation Theory

Beamlet migration based on local perturbation theory is proposed. The method is formulated with a local bac kground velocity and local perturbations for each window of the wave eld decomposition using GaborDaubechies frame and local cosine basis. The propagators and phase-correction operators are obtained analytically for the G-D tight-frame, and numerically for the local cosine basis. The numerical test using the SEG-EAEG salt model poststac kdata demonstrates the great potential of this approach.

Time-Frequency Analysis of Seismic Data Using Synchrosqueezing Transform

Time-frequency analysis can provide useful information in seismic data processing and interpretation. An accurate time-frequency representation is important in highlighting subtle geologic structures and in detecting anomalies associated with hydrocarbon reservoirs. The popular methods, like short-time Fourier transform and wavelet analysis, have limitations in dealing with fast varying instantaneous frequencies, which is often the characteristic of seismic data. The synchrosqueezing transform (SST) is a promising tool to provide a detailed time-frequency representation. We apply the SST to seismic data and show its potential to seismic signal processing applications.

RTM using effective boundary saving: A staggered grid GPU implementation

Abstract GPU has become a booming technology in reverse time migration (RTM) to perform the intensive computation. Compared with saving forward modeled wavefield on the disk, RTM via wavefield reconstruction using saved boundaries on device is a more efficient method because computation is much faster than CPU–GPU data transfer. In this paper, we introduce the effective boundary saving strategy in backward reconstruction for RTM. The minimum storage requirement for regular and staggered grid finite difference is determined for perfect reconstruction of the source wavefield. Particularly, we implement RTM using GPU programming, combining staggered finite difference scheme with convolutional perfectly matched layer (CPML) boundary condition. We demonstrate the validity of the proposed approach and CUDA codes with numerical example and imaging of benchmark models.

High-Dimensional Waveform Inversion With Cooperative Coevolutionary Differential Evolution Algorithm

In this letter, an improved differential evolution (DE) for high-dimensional waveform inversion is proposed. In conventional evolutionary algorithms, an individual is treated as a whole, and all its variables (genes) are evaluated with a uniform fitness function. This evaluation criterion is not effective for a high-dimensional individual. Therefore, for high-dimensional waveform inversion, we incorporate the decomposition strategy of cooperative coevolution into DE to decompose the individual into some subcomponents. Another novel feature that we introduce is a local fitness function for each subcomponent, and a new mutation operator is designed to guide the mutation direction of each subcomponent with the corresponding local fitness value. Coevolution among different subcomponents is realized in the selection operation with the global fitness function. Many experiments have been carried out to evaluate the performance of this new algorithm. The results clearly show that, for high-dimensional waveform inversion, this algorithm is effective and performs better than some other methods. Finally, the new method has been applied to real seismic data.

A New Highly Efficient Differential Evolution Scheme and Its Application to Waveform Inversion

In this letter, a new differential evolution (DE) algorithm is proposed and applied to waveform inversion. The traditional evolution strategy of this algorithm is not efficient because it treats the individuals in a population equally and evolves all of them in each generation. In order to overcome this shortcoming, we propose a new population evolution strategy (PES) to decrease the population size based on the differences among individuals during an evolution process. We embed the new strategy into the cooperative coevolutionary DE (CCDE) and obtain a new highly efficient DE (HEDE). We apply this new algorithm to waveform inversion experiments of both synthetic and real seismic data to test its performance and demonstrate its validity. The results have clearly shown that, under the same inversion precision, the HEDE can reduce the runtime by about 50% compared with the CCDE.

On analysis-based two-step interpolation methods for randomly sampled seismic data

Interpolating the missing traces of regularly or irregularly sampled seismic record is an exceedingly important issue in the geophysical community. Many modern acquisition and reconstruction methods are designed to exploit the transform domain sparsity of the few randomly recorded but informative seismic data using thresholding techniques. In this paper, to regularize randomly sampled seismic data, we introduce two accelerated, analysis-based two-step interpolation algorithms, the analysis-based FISTA (fast iterative shrinkage-thresholding algorithm) and the FPOCS (fast projection onto convex sets) algorithm from the IST (iterative shrinkage-thresholding) algorithm and the POCS (projection onto convex sets) algorithm. A MATLAB package is developed for the implementation of these thresholding-related interpolation methods. Based on this package, we compare the reconstruction performance of these algorithms, using synthetic and real seismic data. Combined with several thresholding strategies, the accelerated convergence of the proposed methods is also highlighted.

Directional illumination analysis using the local exponential frame

We have developed an efficient method of directional illuminationanalysisinthelocalangledomainusinglocalexponential frame beamlets. The space-domain wavefields with different shot-receiver geometries are decomposed into the local angle domain by using the local exponential beamlets, which form a tight frame with the redundancy ratio two and are implemented by a linear combination of local cosine and localsinetransforms.Becauseofthefastalgorithmsofthelocal cosine/sine transforms, this method is much more efficient than the previously used decomposition methods in directional illumination analysis, such as the local slant-stackingmethodandtheGabor-Daubechiesframemethod.Theresults of directional illumination DI maps and the acquisitiondipresponsesADRforthe2DSEG/EAGEsaltmodel and the 45-shot 3D SEG/EAGE model demonstrated the validity and feasibility of our method. Compared with the illumination results using local slant-stacking decomposition, thenewmethodproducesilluminationmapsofsimilarquality, but it does so a few times faster. Furthermore, because of its high computational efficiency and saving in memory usage, the new method makes the 3D directional illumination analysisreadilyapplicableintheindustry.

Existence results for semilinear fractional differential equations via Kuratowski measure of noncompactness

In this paper, we study the existence of mild solutions for a class of semilinear fractional differential equations with nonlocal conditions in Banach spaces. The results are obtained by using convex-power condensing operator and fixed point theory. An example is presented to illustrate the main result.

Multimutation Differential Evolution Algorithm and Its Application to Seismic Inversion

Seismic inversion problems often involve nonlinear relationships between data and model and usually have many local minima. Linearized inversion methods have been widely used to solve such problems. However, these kinds of methods often strongly depend on the initial model and are easily trapped in a local minimum. Global optimization methods, on the other hand, do not require a very good initial model and can approach a global minimum. However, global optimization methods are exhaustive search techniques that can be very time consuming. When the model dimension or the search space becomes large, these methods can be very slow to converge. In this paper, we propose a new global optimization algorithm by incorporating a new multimutation scheme into a differential evolution algorithm. Because mutation operation with the new multimutation scheme can generate better mutant vectors, the new global optimization algorithm has a very good ability of exploring the search space and can converge very fast. We apply the proposed algorithm to both synthetic and field data to test its performance. The results have clearly indicated that the new global optimization algorithm provides faster convergence and yields better results compared with the conventional global optimization methods in seismic inversion.

Monochromatic Noise Removal via Sparsity-Enabled Signal Decomposition Method

Monochromatic noise always interferes with the interpretation of the seismic signals and degrades the quality of subsurface images obtained by further processes. Conventional methods suffer from several problems in detecting the monochromatic noise automatically, preserving seismic signals, etc. In this letter, we present an algorithm that can remove all major monochromatic noises from the seismic traces in a relatively harmless way. Our separation model is set up upon the assumption that input seismic data are composed of useful seismic signals and single-frequency interferences. Based on their diverse morphologies, two waveform dictionaries are chosen to represent each component sparsely, and the separation process is promoted by the sparsity of both components in their corresponding representing dictionaries. Both synthetic and field-shot data are employed to illustrate the effectiveness of our method.