本文關(guān)鍵詞：高斯波束-Born散射波模擬實現(xiàn)技術(shù)與基于復(fù)程函方程的地震波復(fù)走時計算　出處：《吉林大學》2017年碩士論文　論文類型：學位論文

  更多相關(guān)文章： 復(fù)走時 復(fù)程函方程 高斯波束 地震波場 等時面疊加

【摘要】：高斯波束-Born理論是基于高斯波束疊加表示格林函數(shù)的高斯波束層析成像、全波形反演以及廣義繞射疊加理論的基礎(chǔ)。其數(shù)學表達式是一種體積分形式,由此而產(chǎn)生的實現(xiàn)方案為對整個散射區(qū)域的所有散射場的逐次疊加。為了解決Born積分中體積分計算量大的問題,本文將高斯波束-Born公式中的體積分變?yōu)槊娣e分,并用一種改進的等時面疊加方案完成計算,這種實現(xiàn)方式的優(yōu)點是能夠提高計算效率。此外,高斯波束-Born方法的基礎(chǔ)是高斯波束計算,對于高斯波束的計算主要包含振幅和相位兩部分,其中,振幅計算是依賴于射線追蹤算法,而相位部分是角頻率和復(fù)走時的乘積。目前,對于復(fù)走時的計算主要是通過給定復(fù)值初值的動力學射線追蹤法。但是,動力學射線追蹤法依賴于傍軸近似,復(fù)走時數(shù)學表達式是以二階Taylor展開為基礎(chǔ),并且該表達式只運用到中心射線上的速度,而沒有顧及射線兩側(cè)的速度變化。因此,當波束傳播到速度強烈不均勻處,特別是中心射線兩側(cè)速度不對稱時,復(fù)走時計算精度收到很大影響,從而限制了高斯波束的適用范圍。一種運用擾動理論建立的高斯牛頓-快速推進法,通過直接對復(fù)程函方程進行求解來計算復(fù)走時能解決上述困難。但是,在應(yīng)用上,該方法具有兩個弱點:1)目前只能運用于簡單的垂直射線計算,而無法計算一般情況下的彎曲射線復(fù)走時和高斯波束;2)在對虛慢度的計算中,由于運用了最優(yōu)化方法,因此計算量較大,計算效率受到影響。為了克服上述弱點,本文將非等距網(wǎng)格差分法引入處理彎曲中心射的彎曲邊界問題,提出了能適用于彎曲射線的基于復(fù)程函方程的復(fù)走時計算方法。同時,將L-BFGS優(yōu)化方法引入到計算等效虛慢度中,該方法在計算過程中避免了多次計算和儲存Hessian矩陣,數(shù)值實例表明,提高了復(fù)走時計算效率。根據(jù)定義,用以描述這種具有衰減特性的波的復(fù)走時必須依附于所考慮的射線,即本文計算的復(fù)走時是一種局部復(fù)走時。具體地,局部復(fù)走時實部和虛部分別為常規(guī)射線走時和傍軸走時。因此,在對單個射線的復(fù)走時計算時,如果不對傍軸區(qū)域加以限制,將計算整個模型的復(fù)走時。為了計算具有一定范圍的局部復(fù)走時,根據(jù)具體應(yīng)用需要,提出了局部算法計算局部復(fù)走時,數(shù)值結(jié)果證明了其適用性。與上述求解各向同性介質(zhì)中復(fù)程函方程不同,各向異性介質(zhì)復(fù)程函方程涉及參數(shù)眾多。因此,對于各向異性介質(zhì)(例如TTI介質(zhì))復(fù)走時計算時,上述方法受到很大限制。為此,本文利用擾動理論思想,提出了將TTI復(fù)程函方法線性化從而計算復(fù)走時。數(shù)值結(jié)果表明,擾動方法對求解TTI復(fù)程函方程是有效的。最后,通過對比發(fā)現(xiàn),根據(jù)上述復(fù)走時計算方法計算的復(fù)走時進一步計算的高斯波束波場相比于動力學射線追蹤方法計算結(jié)果在精度上很大改善。
[Abstract]:Gao Si's beam-Born theory is the basis of Gao Si beam tomography, full waveform inversion and generalized diffraction superposition theory based on the Gao Si beam superposition representation. The mathematical expression of Gao Si beam superposition theory is a form of volume division. The resulting scheme is the successive superposition of all scattering fields in the whole scattering region, in order to solve the problem of large volume integral calculation in Born integral. In this paper, the volume fraction of Gao Si beam Born formula is changed into area fraction, and a modified isochronous superposition scheme is used to complete the calculation. The advantage of this realization is that the calculation efficiency can be improved. Gao Si beam-Born method is based on Gao Si beam calculation. The calculation of Gao Si beam mainly includes two parts: amplitude and phase, in which amplitude calculation is dependent on ray tracing algorithm. The phase part is the product of the angular frequency and the complex travel time. At present, the calculation of the complex travel time is mainly based on the dynamic ray tracing method with given complex initial values. However, the dynamic ray tracing method depends on the paraxial approximation. The mathematical expression of complex walk time is based on the second-order Taylor expansion, and the expression is applied only to the velocity of the central ray, without taking into account the variation of the velocity on both sides of the ray. When the beam propagates to the strong inhomogeneity of velocity, especially when the velocity of the two sides of the central ray is asymmetrical, the calculation accuracy of the complex beam is greatly affected. Thus limiting the scope of application of Gao Si beam. By solving the complex function equation directly to calculate the difficulties mentioned above, a rapid advance method based on the perturbation theory is proposed. However, the above problems can be solved by solving the complex function equation directly. However, this method can be used to solve the problems mentioned above. In application, the method has two weaknesses: 1) at present, it can only be used in simple vertical ray calculation, but can not calculate the bending ray rerun time and Gao Si beam in general. 2) in the calculation of virtual slowness, due to the use of optimization method, the computational complexity is large and the computational efficiency is affected. In this paper, the nonequidistant grid difference method is introduced to deal with the bending boundary problem of bending center ejection, and a complex travel time calculation method based on complex function equation is proposed, which can be applied to bending rays. The L-BFGs optimization method is introduced into the calculation of equivalent virtual slowness. The method avoids calculating and storing the Hessian matrix many times in the process of calculation. According to the definition, the rerun time of this kind of wave with attenuation characteristic must be attached to the ray under consideration, that is, the calculated rerun time in this paper is a kind of local rerun time. The real part and the imaginary part are regular ray travel time and paraxial travel time, respectively. Therefore, if the paraxial region is not restricted in the calculation of the rerun time of a single ray. In order to calculate the local rerun time of the whole model, a local algorithm is proposed to calculate the local rerun time according to the specific application needs. The numerical results prove its applicability. Different from solving the complex equation in isotropic medium, the complex equation of anisotropic medium involves many parameters. For anisotropic media (such as TTI medium), the above method is limited greatly. Therefore, the perturbation theory is used in this paper. The TTI complex function method is linearized to calculate the complex travel time. The numerical results show that the perturbation method is effective for solving the TTI complex function equation. The accuracy of the further calculation of the Gao Si beam wave field based on the above complex travel time calculation method is much better than that of the dynamic ray tracing method.
【學位授予單位】：吉林大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：P631.4

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