本文選題：地震波動(dòng)方程　切入點(diǎn)：有限元法　出處：《中國(guó)石油大學(xué)(華東)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：波動(dòng)方程正演模擬在地震資料采集、處理和解釋等環(huán)節(jié)起著十分重要的作用。要想精確地模擬地震波在地下介質(zhì)中的傳播,不僅要求建立的地球物理模型與實(shí)際地層相一致,而且還需要采用計(jì)算精度較高的數(shù)值模擬方法。有限差分法(FDM)和有限元法(FEM)是波動(dòng)方程正演模擬中非常重要的兩種方法。有限差分法具有編程簡(jiǎn)單,計(jì)算效率高等特點(diǎn),因此在地震波數(shù)值模擬中得到廣泛的研究和應(yīng)用,但不能精確地模擬地震波在復(fù)雜介質(zhì)中的傳播,在精細(xì)地震勘探中已是捉襟見(jiàn)肘;而有限元法具有多種網(wǎng)格剖分方式,因此能夠?qū)θ我鈴?fù)雜的邊界進(jìn)行有效剖分,能夠較為精確地模擬地震波在復(fù)雜介質(zhì)中的傳播,多種插值函數(shù)可以提供精度不同的數(shù)值模擬結(jié)果。本文針對(duì)有限元法進(jìn)行了一系列的研究,首先闡述了有限元法求解波動(dòng)方程的基本理論,研究了地震波在線性插值三角網(wǎng)格、線性插值矩形網(wǎng)格、線性插值任意四邊形網(wǎng)格以及雙二次插值矩形網(wǎng)格中的傳播特征;接著采用“緊湊存儲(chǔ)格式”存儲(chǔ)結(jié)構(gòu)剛度矩陣,使計(jì)算效率和內(nèi)存的占用在可接受的范圍內(nèi);最后重點(diǎn)研究了地震波在矩形網(wǎng)格、三角網(wǎng)格中的頻散特性與穩(wěn)定性條件,為質(zhì)量矩陣、單元網(wǎng)格以及參數(shù)的選擇提供理論基礎(chǔ)。本文還分別就井震資料尺度匹配時(shí)可能會(huì)丟失測(cè)井?dāng)?shù)據(jù)局部信息的缺點(diǎn)以及基于褶積模型合成的地震記錄與井旁地震道一致性不高的問(wèn)題進(jìn)行了研究。在前一問(wèn)題上,采用最小速度差以及最小厚度原理在深時(shí)轉(zhuǎn)換前對(duì)測(cè)井?dāng)?shù)據(jù)進(jìn)行精細(xì)分層處理,分層參數(shù)最小速度差由目的層的具體情況決定,最小厚度則由地震采樣間隔以及最小單層雙程旅行時(shí)決定。在后一問(wèn)題上,采用波動(dòng)方程理論制作合成地震記錄,考慮了地震波場(chǎng)形成的機(jī)理以及地震資料處理對(duì)同相軸的影響。最后通過(guò)實(shí)際資料測(cè)試表明,以上兩種方法分別在保留測(cè)井資料局部信息和提高井震資料一致性方面具有較好的效果。
[Abstract]:Wave equation forward modeling plays an important role in seismic data acquisition, processing and interpretation. The finite difference method (FDM) and the finite element method (FEMM) are two very important methods for forward modeling of wave equation. The finite difference method is characterized by simple programming and high computational efficiency. Therefore, it has been widely studied and applied in numerical simulation of seismic wave, but it can not accurately simulate the propagation of seismic wave in complex medium, so it is already overstretched in fine seismic exploration, and the finite element method has many kinds of mesh generation methods. Therefore, it is possible to partition any complex boundary effectively and simulate the propagation of seismic waves in complex media more accurately. Many kinds of interpolation functions can provide numerical simulation results with different precision. In this paper, a series of research on finite element method is carried out. Firstly, the basic theory of solving wave equation by finite element method is expounded, and the seismic wave in linear interpolated triangular grid is studied. The propagation characteristics of linear interpolated rectangular mesh, linear interpolated quadrilateral mesh and biquadratic interpolation rectangular grid are obtained, and then the structural stiffness matrix is stored in a compact storage format. Finally, the dispersion and stability conditions of seismic waves in rectangular and triangular grids are studied as mass matrix. The cell grid and the selection of parameters provide the theoretical basis. This paper also discusses the shortcomings of the local information of logging data which may be lost when well seismic data scale matching, and the seismic records and seismic traces beside wells based on convolution model synthesis. The problem of low consistency was studied. In the former case, Using the principle of minimum velocity difference and minimum thickness, the logging data are processed by fine stratification before deep time conversion. The minimum velocity difference of stratification parameters is determined by the specific conditions of the target layer. The minimum thickness is determined by the seismic sampling interval and the minimum single-layer two-way travel time. In the latter case, the synthetic seismic records are made by using the wave equation theory. The formation mechanism of seismic wave field and the effect of seismic data processing on the cophase axis are considered. The above two methods have good effect in preserving local information of logging data and improving the consistency of well seismic data.
【學(xué)位授予單位】：中國(guó)石油大學(xué)(華東)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：P631.4

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