本文選題：數(shù)值模擬 + 波動(dòng)方程�。� 參考：《成都理工大學(xué)》2017年碩士論文

【摘要】：正演模擬和偏移成像一直是地震勘探領(lǐng)域中重要的研究?jī)?nèi)容,地震波正演模擬是研究地震波傳播特征的重要手段,雙程波逆時(shí)偏移是在時(shí)間方向上實(shí)現(xiàn)外推,不受成像傾角限制,對(duì)橫縱向速度變化大的復(fù)雜模型也能有較好的成像效果。本文主要對(duì)彈性波波動(dòng)方程正演模擬與逆時(shí)偏移成像技術(shù)進(jìn)行了研究。本文在研究了波動(dòng)方程的理論之后,從本構(gòu)方程、幾何方程和運(yùn)動(dòng)微分方程出發(fā),系統(tǒng)的推算了各向同性介質(zhì)、VTI介質(zhì)、Kelvin黏彈性介質(zhì)及Biot雙相介質(zhì)中的一階應(yīng)力-速度彈性波方程,然后給出了它們?cè)跁r(shí)間上2階空間上2N階的交錯(cuò)網(wǎng)格差分格式。接著對(duì)正演模擬中的的幾個(gè)難點(diǎn)如震源加載方式、邊界問(wèn)題、穩(wěn)定性問(wèn)題以及數(shù)值頻散做了系統(tǒng)的討論。然后,推導(dǎo)了交錯(cuò)網(wǎng)格下聲波方程的高階有限差分格式,并構(gòu)建了均勻二層模型和臺(tái)階模型對(duì)其進(jìn)行模擬試算,在驗(yàn)證了這種算法的可靠性之后,分別對(duì)上述幾種介質(zhì)進(jìn)行了地震波數(shù)值模擬,并分析了不同介質(zhì)中地震波的傳播規(guī)律以及波場(chǎng)特征。最后,對(duì)逆時(shí)偏移的理論進(jìn)行了分析,使用聲波方程的交錯(cuò)網(wǎng)格高階差分格式完成了疊后逆時(shí)偏移,通過(guò)對(duì)常見(jiàn)的地塹模型、張性斷層模型與侵蝕潛山模型進(jìn)行逆時(shí)偏移成像試算,偏移成像結(jié)果驗(yàn)證了該算法的正確性與實(shí)用性。
[Abstract]:Forward modeling and migration imaging are always important research contents in the field of seismic exploration. Seismic wave forward modeling is an important means to study the characteristics of seismic wave propagation. Two-way inverse time migration is extrapolated in time direction. Without the restriction of imaging inclination, the complex model with large velocity variation in horizontal and longitudinal direction can also have good imaging effect. In this paper, forward modeling of elastic wave equation and inverse time migration imaging technique are studied. After studying the theory of wave equation, this paper starts with constitutive equation, geometric equation and differential equation of motion. The first order stress-velocity elastic wave equations in the Kelvin viscoelastic medium and Biot biphase medium are systematically calculated, and their staggered grid difference schemes are given for the second order space in time. Then, some difficulties in forward modeling such as source loading mode, boundary problem, stability problem and numerical dispersion are discussed systematically. Then, the high-order finite-difference scheme of acoustic wave equation in staggered grid is deduced, and the uniform two-layer model and step model are constructed to simulate it. The reliability of the algorithm is verified. The numerical simulation of the seismic waves in the above mentioned media is carried out, and the propagation law and wave field characteristics of the seismic waves in different media are analyzed. Finally, the theory of inverse time migration is analyzed, and the post-stack inverse time migration is completed by using the staggered grid higher-order difference scheme of acoustic wave equation. The inverse time migration imaging of tensile fault model and buried hill model is calculated. The results of migration imaging verify the correctness and practicability of the algorithm.
【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】：2017
【分類(lèi)號(hào)】：P631.4

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