發(fā)布時(shí)間：2018-07-10 01:14

  本文選題：重力和重力梯度聯(lián)合反演 + 重力和重力梯度數(shù)據(jù)分析�。� 參考：《吉林大學(xué)》2016年博士論文

【摘要】：重力數(shù)據(jù)的處理和解釋一直是地球物理數(shù)據(jù)處理和解釋中的重要組成部分。近年來,隨著全張量重力梯度測量系統(tǒng)(FTG)的發(fā)展及應(yīng)用,重力梯度數(shù)據(jù)的地位也越來越重要。從理論上說,重力數(shù)據(jù)是重力位在垂直方向上的偏導(dǎo)數(shù),重力梯度數(shù)據(jù)則是重力位在各方向的二次求導(dǎo)。在求導(dǎo)計(jì)算過程中,低頻信號被壓制,高頻信號被增強(qiáng)。所以,在頻率域比較重力數(shù)據(jù)和重力梯度數(shù)據(jù),結(jié)果表明,重力數(shù)據(jù)包含較多的低頻信息,重力梯度數(shù)據(jù)則包含較多的高頻信息。因此,將重力和重力梯度數(shù)據(jù)聯(lián)合,可以實(shí)現(xiàn)信息的互補(bǔ),有效的降低反演中的多解性�；谶@一點(diǎn),本文針對重力和重力梯度數(shù)據(jù)聯(lián)合反演的問題展開討論。首先,對重力和重力梯度數(shù)據(jù)進(jìn)行量化比較分析。通過重力梯度數(shù)據(jù)在頻率域的表達(dá)式,推導(dǎo)重力梯度各分量之間的關(guān)系,發(fā)現(xiàn)在重力梯度各分量中,zzg分量包含的信息更多;隨后,通過對比不同深度模型的zg分量和zzg分量的振幅譜,分析zg分量和zzg分量隨深度的變化;分別對zg和zzg分量進(jìn)行反演計(jì)算,結(jié)果表明,zg反演結(jié)果在深部的分辨率較高,zzg反演在淺部具有較高的分辨率。我們通過再加權(quán)反演的方法將深度加權(quán)函數(shù)結(jié)合到穩(wěn)定函數(shù)部分,在僅考慮深度加權(quán),不加任何其他約束條件的情況下,分別對重力場和重力梯度數(shù)據(jù)各分量進(jìn)行反演計(jì)算,依據(jù)各分量的反演結(jié)果,對各分量在反演計(jì)算中的表現(xiàn)有了一個(gè)直觀的印象,對各分量所包含信息的特點(diǎn)進(jìn)行對比。隨后,我們針對重力和重力梯度聯(lián)合反演問題深入討論。與單一分量反演相比,多分量聯(lián)合反演需要消耗更多的計(jì)算時(shí)間和內(nèi)存。首先,在反演計(jì)算開始前,我們需要計(jì)算并存儲各分量的靈敏度矩陣。因?yàn)榉至糠N類的增加,存儲和計(jì)算靈敏度矩陣所消耗的內(nèi)存空間和計(jì)算時(shí)間也增加。因此,我們提出了一種快速計(jì)算靈敏度矩陣的方法,能夠有效的減少計(jì)算時(shí)間,并基于此提出了一種存儲靈敏度矩陣的策略。之后,我們對反演過程中深度加權(quán)函數(shù)的選擇展開了討論。我們列舉了幾種深度加權(quán)函數(shù),針對其在重力和重力梯度反演中的表現(xiàn)進(jìn)行了對比,最后選擇了基于異常體深度信息的加權(quán)函數(shù)。這種深度加權(quán)函數(shù)依據(jù)異常體的埋深設(shè)置權(quán)值,與數(shù)據(jù)類型無關(guān),因而適用于重力和重力梯度數(shù)據(jù)聯(lián)合反演。我們給出了再加權(quán)光滑反演的計(jì)算流程及相應(yīng)的公式推導(dǎo)。基于再加權(quán)的光滑反演,我們對深度加權(quán)函數(shù)對異常體埋深信息準(zhǔn)確性的要求進(jìn)行了討論,發(fā)現(xiàn)在埋深信息與實(shí)際信息存在一定差異時(shí),采用這種深度加權(quán)函數(shù),仍能獲得合理的反演結(jié)果。之后,我們將其應(yīng)用到反演計(jì)算中,并將這種加權(quán)函數(shù)在反演中的表現(xiàn)與基于靈敏度矩陣的深度加權(quán)函數(shù)進(jìn)行對比。結(jié)果表明,基于異常體深度信息的加權(quán)函數(shù),因?yàn)閷⑸疃刃畔⒔Y(jié)合到了反演計(jì)算中,有效的提高了反演結(jié)果的分辨率。接下來,針對穩(wěn)定函數(shù)的選擇開展了研究,并對本文所采用的優(yōu)化算法展開了討論。針對不同的地質(zhì)體,需要選擇不同的穩(wěn)定函數(shù)。本文中,我們主要針對具有陡峭邊界的地質(zhì)體,因此選擇了最小梯度支撐函數(shù)作為構(gòu)成聯(lián)合反演正則化方程的穩(wěn)定函數(shù)。本文中,我們主要采用非線性共軛梯度算法,這是一種適合解決大規(guī)模反演問題的算法。這種算法在三維電磁反演中有著廣泛的應(yīng)用,在重力和重力梯度反演中的應(yīng)用則較少。通過模型試驗(yàn),我們將非線性共軛梯度算法與BFGS擬牛頓法進(jìn)行對比,發(fā)現(xiàn)與BFGS擬牛頓法相比,雖然非線性共軛梯度算法收斂速度較慢,但是其消耗的時(shí)間更短,對內(nèi)存的要求更低。為了將密度約束結(jié)合到反演計(jì)算中,同時(shí),確保不會對反演過程的穩(wěn)定性造成影響,我們采用了不等式約束條件。我們建立了由多個(gè)不同異常體組成的模型,對重力梯度分量組合反演進(jìn)行對比和討論。結(jié)果表明,多分量組合能夠有效的提高反演結(jié)果的分辨率,但是,當(dāng)數(shù)據(jù)量達(dá)到一定程度后,雖然數(shù)據(jù)能夠更好的擬合,反演結(jié)果收斂程度更好,但是,反演結(jié)果與理論模型的一致性降低,這就需要額外的信息來約束反演過程。綜合考慮反演結(jié)果和反演效率,我們給出了反演結(jié)果和反演效率最佳的分量組合。隨后,我們基于同一模型對重力和重力梯度聯(lián)合反演進(jìn)行了對比和討論。結(jié)果表明:加入重力數(shù)據(jù)后,得到的聯(lián)合反演的結(jié)果與重力梯度分量組合反演結(jié)果大體一致;對于其中的某些異常體,加入重力數(shù)據(jù)后,其反演結(jié)果的分辨率得到了提升。針對具有不同埋深的異常體,我們將空間梯度加權(quán)函數(shù)應(yīng)用到了反演計(jì)算中。這一函數(shù)的應(yīng)用,使得我們能夠?qū)⑶按蔚姆囱萁Y(jié)果中的有效信息作為先驗(yàn)信息結(jié)合到下次的反演計(jì)算中。通過模型試驗(yàn),我們發(fā)現(xiàn),采用這種方法,反演結(jié)果的分辨率得到了提升。最后,我們將本文中的方法應(yīng)用到了在美國路易斯安娜州的文頓鹽丘測得的實(shí)際數(shù)據(jù)。利用重力和重力梯度數(shù)據(jù)進(jìn)行三維反演計(jì)算,進(jìn)而依據(jù)反演結(jié)果推斷鹽蓋的分布。通過對不同分量組合反演結(jié)果對比,我們發(fā)現(xiàn)zg|xyg|xzg|yyg|yzg|zzg反演結(jié)果最好。我們給出了反演結(jié)果的三維分布圖,與該地區(qū)已有的研究成果對比,可以得出,我們的反演結(jié)果是合理的。
[Abstract]:The processing and interpretation of gravity data has always been an important part of geophysical data processing and interpretation. In recent years, with the development and application of the full tensor gravity gradient measurement system (FTG), the status of gravity gradient data is becoming more and more important. In theory, gravity data is the partial derivative of gravity position in the vertical direction and the gravity gradient. The data is the two derivation of the gravity position in all directions. In the course of the calculation, the low frequency signal is suppressed and the high frequency signal is enhanced. Therefore, the gravity data and the gravity gradient data are compared in the frequency domain. The results show that the gravity data contains more low frequency information and the gravity gradient data contains more high frequency information. Therefore, gravity and the gravity data are included in the gravity data. The combination of gravity gradient data can achieve complementary information and effectively reduce the multiple solvability in the inversion. Based on this, this paper discusses the problem of joint inversion of gravity and gravity gradient data. First, the gravity and gravity gradient data are quantified and compared. The gravity gradient data in the frequency domain expression, deduce the weight of gravity and gravity gradient data. It is found that the zzg component contains more information in each component of the gravity gradient, and then, by comparing the ZG component and the amplitude spectrum of the zzg component of the different depth models, the ZG component and the zzg component are analyzed with the depth, and the ZG and zzg components are back calculated respectively. The results show that the ZG inversion results are in the deep part. The resolution is high, and the zzg inversion has a high resolution in the shallow part. We combine the depth weighted function with the stable function part by the method of the re weighted inversion. In the case of only considering the depth weighting and without any other constraints, we invert the gravity field and the gravity gradient data respectively, according to each component. The inversion results have an intuitive impression on the performance of each component in the inversion calculation, and compare the characteristics of the information contained in each component. Then, we discuss the joint inversion problem of gravity and gravity gradient. Compared with the single component inversion, the Multicomponent Joint back performance needs to consume more time and memory. First, Before the inversion is started, we need to calculate and store the sensitivity matrix of each component. Because of the increase of the component, the memory space and calculation time consumed by the storage and calculation sensitivity matrix also increase. Therefore, we propose a square method to quickly calculate the sensitivity matrix, which can effectively reduce the calculation time and based on this method. A strategy of storage sensitivity matrix is proposed. After that, we discuss the selection of depth weighted functions in the inversion process. We enumerate several depth weighted functions, compare their performance in gravity and gravity gradient inversion, and finally choose the weighted function based on the depth information of abnormal body. The weighted function is based on the depth of the buried depth of the abnormal body, which is independent of the data type, so it is applicable to the joint inversion of gravity and gravity gradient data. We give the calculation process of the reweighted smooth inversion and the derivation of the corresponding formula. It is found that when there is a certain difference between the buried depth information and the actual information, a reasonable inversion result can still be obtained by using this depth weighted function. After that, we apply it to the inversion calculation and compare the performance of this weighted function with the depth weighted function based on the sensitivity matrix. The weighted function based on the depth information of the abnormal body is based on the combination of the depth information into the inversion calculation, which effectively improves the resolution of the inversion results. Next, the selection of the stable function is studied, and the optimization algorithms used in this paper are discussed. Different stability functions need to be selected for different geological bodies. In this paper, we mainly aim at a geological body with steep boundary, so we choose the minimum gradient support function as a stable function to form a joint inversion regularization equation. In this paper, we mainly use the nonlinear conjugate gradient algorithm, which is a suitable algorithm for solving large-scale inversion problems. This algorithm is in three-dimensional electromagnetic inverse. It has a wide range of applications and less applications in gravity and gravity gradient inversion. Through the model test, we compare the nonlinear conjugate gradient algorithm with the BFGS quasi Newton method, and find that compared with the BFGS quasi Newton method, the nonlinear conjugate gradient algorithm has a slower convergence rate, but its consumption time is shorter and the memory needs to be improved. In order to combine the density constraints into the inversion calculation and to ensure that the stability of the inversion process will not be affected, we have adopted the inequality constraints. We have established a model composed of several different abnormal bodies, and compared and discussed the combination inversion of the gravity gradient component. The results show that the multicomponent combination can be used. It can improve the resolution of the inversion results, but when the amount of data is reached to a certain degree, although the data can be better fitted, the convergence of the inversion results is better, but the consistency of the inversion results and the theoretical model is reduced. This requires additional information to restrain the inversion process. We give a comprehensive consideration of the inversion results and the efficiency of inversion. We give a comprehensive consideration of the inversion results and the efficiency of inversion. Then, we compare and discuss the joint inversion of gravity and gravity gradient based on the same model. The results show that the results of joint inversion obtained from the gravity data are in general agreement with the results of the combined inversion of gravity gradient components. After the gravity data, the resolution of the inversion results has been improved. For the abnormal body with different buried depth, we apply the spatial gradient weighting function to the inversion calculation. The application of this function enables us to combine the effective information in the previous inversion results as the first test information to the next inversion calculation. In the model test, we found that the resolution of the inversion results has been improved by this method. Finally, we applied the method in this paper to the actual data measured in the Lewis Anna salt dunes in the United States. The gravity and gravity gradient data were used to calculate the three-dimensional inversion, and then the distribution of the salt cover was deduced from the inversion results. By comparing the inversion results of different component combinations, we find that the zg|xyg|xzg|yyg|yzg|zzg inversion results are the best. We have given the three-dimensional distribution map of the inversion results, and compared with the existing research results in this area, we can conclude that our inversion results are reasonable.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：P631.1

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