本文選題：波動(dòng)方程 + 正演建模　； 參考：《成都理工大學(xué)》2015年碩士論文

【摘要】：隨著計(jì)算機(jī)技術(shù)的發(fā)展,使得波動(dòng)方程正演由理論研究應(yīng)用到實(shí)際地震勘探中成為了可能,同時(shí)在這發(fā)展過(guò)程中,計(jì)算機(jī)硬件的發(fā)展更加使得波動(dòng)方程在GPU上正演模型計(jì)算變得更加高效。而波動(dòng)方程有限差分技術(shù)作為地震波場(chǎng)模擬技術(shù)中的一種關(guān)鍵技術(shù),被廣泛應(yīng)用到正演計(jì)算的波形正演中。地震波場(chǎng)的數(shù)值模擬技術(shù)是在已知地下介質(zhì)結(jié)構(gòu)和參數(shù)的情況下,利用理論計(jì)算的方法研究地震波在地下介質(zhì)中的傳播規(guī)律,從而合成地震記錄的一種技術(shù)方法。有限差分法是最常用的一種正演模擬方法,它的基本原理是將波動(dòng)方程中波場(chǎng)函數(shù)關(guān)于空間和時(shí)間的導(dǎo)數(shù)用相應(yīng)差分來(lái)代替,也正是由于這種離散近似,不可避免地降低了數(shù)值模擬結(jié)果分辨率。為了有效減小數(shù)值頻散造成的影響,常用的方法即是提高模型的剖分精度。但是當(dāng)模型精度提高、網(wǎng)格規(guī)模增大時(shí),有限差分方法的計(jì)算時(shí)間也會(huì)大幅度提高,若能用并行計(jì)算的方法提高求解效率不失為解決該問(wèn)題的有效方法。英偉達(dá)公司開(kāi)發(fā)的基于GPU硬件的統(tǒng)一計(jì)算架構(gòu)平臺(tái)CUDA,融合了GPU通用計(jì)算特性和類(lèi)C語(yǔ)言編程接口,以計(jì)算高效性和開(kāi)發(fā)友好性成為當(dāng)前高性能計(jì)算的研究熱點(diǎn)。由于基于時(shí)域的有限差分正交網(wǎng)格在計(jì)算時(shí),各個(gè)節(jié)點(diǎn)下一時(shí)刻的數(shù)值計(jì)算與周?chē)?jié)點(diǎn)的計(jì)算無(wú)關(guān),這就使得差分算法在計(jì)算上有著巨大的空間并行性,能非常好地適應(yīng)GPU多線(xiàn)程分配的并行算法設(shè)計(jì)思想。本論文正是針對(duì)基于GPU的波動(dòng)方程正演技術(shù)及方法展開(kāi)研究,以CUDA為應(yīng)用開(kāi)發(fā)平臺(tái)。主要研究?jī)?nèi)容如下：(1)從基于GPU的角度出發(fā)研究二維波動(dòng)方程模型建立,并給出其相應(yīng)的波動(dòng)方程數(shù)學(xué)物理公式進(jìn)行推導(dǎo),導(dǎo)出波動(dòng)方程兩種不同規(guī)格的有限差分公式。(2)同樣是從GPU的角度出發(fā),研究三維波動(dòng)方程模型建立,給出相應(yīng)的波動(dòng)方程數(shù)學(xué)物理公式進(jìn)行推導(dǎo),導(dǎo)出波動(dòng)方程采用不同網(wǎng)格進(jìn)行差分的有限差分公式。(3)針對(duì)波動(dòng)方程有限差分地震正演建模中遇到的震源、穩(wěn)定性、邊界條件等問(wèn)題進(jìn)行研究,并且詳細(xì)討論了震源加載方式,二維及三維聲波波動(dòng)方程的穩(wěn)定性條件,以及兩種邊界吸收條件的特點(diǎn)等。(4)針對(duì)GPU的研究,完成了在CUDA應(yīng)用平臺(tái)上的有限差分運(yùn)算。并在上述情況下,分別給出了二維以及三維的正演模擬效果,最后論證本論文在GPU上實(shí)現(xiàn)波動(dòng)方程正演的有效性。
[Abstract]:With the development of computer technology, it is possible to apply wave equation forward modeling from theoretical research to practical seismic exploration. With the development of computer hardware, the forward model calculation of wave equation on GPU becomes more efficient. As a key technique in seismic wave field simulation, wave equation finite difference technique is widely used in forward calculation waveform forward modeling. The numerical simulation technique of seismic wave field is a technical method to study the propagation law of seismic wave in underground medium by using the method of theoretical calculation when the structure and parameters of underground medium are known. The finite difference method is one of the most commonly used forward modeling methods. Its basic principle is to replace the derivative of wave field function on space and time with the corresponding difference in wave equation, which is precisely due to the discrete approximation. The resolution of the numerical simulation results is inevitably reduced. In order to reduce the influence of numerical dispersion, the commonly used method is to improve the accuracy of the model. However, when the precision of the model is improved and the mesh size increases, the computational time of the finite difference method will also be greatly increased. If the parallel computing method can be used to improve the efficiency of the solution, it is an effective method to solve the problem. The unified computing architecture platform CUDA-based on GPU developed by Nvidia integrates the general computing characteristics of GPU and C-like programming interface, which becomes the research hotspot of high performance computing in order to compute high efficiency and develop friendliness. Because the computation of the finite-difference orthogonal grid based on time domain is independent of the computation of the surrounding nodes at the next moment, the difference algorithm has great spatial parallelism. It can adapt to the parallel algorithm design idea of GPU multi-thread allocation very well. In this paper, the forward modeling technology and method of wave equation based on GPU are studied, and CUDA is used as the development platform. The main contents are as follows: (1) from the perspective of GPU, the establishment of two-dimensional wave equation model is studied, and the corresponding mathematical and physical formulas of wave equation are derived. Two finite difference equations of wave equation with different specifications are derived. (2) from the point of view of GPU, the establishment of three-dimensional wave equation model is studied, and the corresponding mathematical and physical formulas of wave equation are derived. The finite difference formula of wave equation is derived by using different meshes. (3) the source, stability and boundary conditions encountered in forward modeling of wave equation finite difference earthquake are studied, and the source loading mode is discussed in detail. The stability conditions of two-dimensional and three-dimensional acoustic wave equations, as well as the characteristics of two boundary absorbing conditions, etc. (4) the finite difference operation on the CUDA platform is completed for the study of GPU. In the above cases, the forward simulation results of two and three dimensions are given, and the validity of the forward modeling of wave equation on GPU is demonstrated.
【學(xué)位授予單位】：成都理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：P631.4

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 皮紅梅;蔣先藝;劉財(cái);王成祥;姜紹輝;;波動(dòng)方程數(shù)值模擬的三種方法及對(duì)比[J];地球物理學(xué)進(jìn)展;2009年02期

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本文編號(hào)：2115852