高精度重力异常数据处理方法、技术研究
摘要
重力资料处理是重力勘探的重要组成部分,是物探工作者致力研究的一项重要课题。随着数据采集精度的提高,高精度重力异常数据处理新方法、新技术的研究显得更为重要。
为了提高重力异常数据处理的精度,本文以组合滤波法和离散Hilbert变换为理论基础,增加了重力归一化总梯度及相位法的可延拓深度,提高了该法的分辨率。以离散余弦变换(DCT)理论为基础,研究了重力位余弦变换谱的基本特征,给出重力位余弦变换谱一般表达式,推导出重力异常垂向、水平各阶导数以及异常向上延拓余弦谱理论公式,初步建立重力位余弦变换谱分析及异常转换理论;探讨并给出了理论模型的重力异常余弦变换谱正反演模式以及影响数据处理精度的主要因素。在此基础上,进一步研究了基于DCT的单密度界面异常正反演、欧拉反褶积反演的理论以及数值实现方法,给出了相应的理论研究模式。
在数值上实现了上述分析研究工作。在模型计算中,分析了重力异常转换谱中深度因子和导数响应因子的影响规律,重力异常余弦变换谱中混叠效应和吉布斯效应在数值计算中的影响规律,给出相应的滤波及补偿方式。模型实验证实:本课题研究的正、反演方法具有较高的分辨率和精度。
在实际应用中,选择黑龙江省虎林盆地平面布格重力异常资料和大庆探区外围盆地DB1线高精度剖面布格重力异常数据,实现了上述方法在实际资料处理中的应用,取得了较好的效果。
Data processing of gravity anomaly is important component part for gravityprospecting, and is a significant topic for operators who engage in geophysicalprospecting. With the developing of gravimeter for high-precision data acquisition, thestudy of new method and technique became great important for high-precision dataprocessing of gravity anomalies.
With the developing and perfecting of signal analysis theory, the method for dataprocessing of gravity anomaly was not any more restricted within the theory of Fouriertransform spectrum analysis. In the past thirty years, the method and technique for dataprocessing of gravity anomaly have permeated into domain of signal analysis, forexample, Hilbert transform, Hartley transform, et al., in which some progress havebeen attained to improve the precision of data processing of gravity anomaly.
There are characteristics in Hilbert transform in which that can use all informationof potential filed and are influenced less by background filed, so the precision of dataprocessing can be improved using the Hilbert transform. Discrete cosine transform(DCT) excel non-sine transform in theoretical and applied value, and it has excellentcapability, so it hold leading status in orthogonal transformation. DCT can avoid pluraloperation to real continuous function, and it has similar capability to Karhunen-Loèvetransform that can remove relativity and reserve superior energy of original signal. At present, wehave not found any correlative literature that used DCT to analyze spectrum of potential filed and toprocess the data of gravity anomaly.
To improve the precision of data processing of gravity anomaly, the paper use the
combinatorial filter and Hilbert transform to discuss the method of improving the depthof continuation and resolution power for calculating the normalized full gradient ofgravity anomaly and its phase and use DCT to study characteristics of cosine transformspectrum of gravity potential, to found theory of cosine transform spectrum analysisand conversion of gravity anomaly and to discuss the pattern of forward modeling andinversion and main factors that influence the precision of data processing for theorymode based on cosine transform of gravity anomaly. We study the theory for forwardmodeling and inversion of density interface and its way of numerical value calculationin order to improve the precision of inversion based on DCT, and we research thelocation problem of theory mode using the Euler's Deconverlution based on DCT topoint out its corresponding theory mode.1. Methods of improving the depth of continuation and resolution powerfor calculating the normalized full gradient of gravity anomaly and itsphase(1) The combinatorial filter techniqueWe introduce the combinatorial filter technique in the method of the normalizedfull gradient of gravity anomaly and its phase, i.e. put forward introducing smoothingfilter operator respectively in the process of downward continuation and derivationabout potential field conversion. This way increased reliability and stability ofcalculation and extended the depth of continuation. By lots of experiments of modeland analysis of data, we confirmed experiential value of exponential parameter aboutsmoothing filter operator in calculating of downward continuation and derivation,pointed out variational rule between the depth of geologic body and theharmonic-number N, in which the lower (deeper) the depth of geologic body is thebigger (lesser) the value of N is. At the same time, we discovered they had similarcharacters of contour GH field between three dimension model of symmetrical densityanticline and of asymmetry oil storage anticline and two dimension model of them andoffered the new thought of calculating center of gravity and researching oil storage
structure. We indicated the inadaptability of maximal value theory of the full gradientof gravity in researching faulted structure. To the boundless outstretched faultedstructure, we should base the trend and the shape of GH field contour and link breakpoints of gravity phase curve to confirm the location of rupture.(2) The Hilbert-transform methodA method of calculating normalized full gradient of gravity anomalies usingHilbert transform was advanced in order to improve the resolution of geophysical dataprocessing. The paper proved the feasibility of the method in theory and pointed outthe calculating way that can be performed in computer. We calculated the GH fieldvalue of model using methods of Fourier series, Fourier transform and Hilberttransform respectively and discussed the resolution power for oil-bearing structureswith the methods. The methods of Fourier series and Fourier transform can'tdistinguish the anomaly of low-density body but the method of Hilbert transform canfairly do when the thickness of oil storage part (low-density body) of 3-Dsphere-coronal (approximate model of 3-D oil storage anticline) is lower than one tenthof it of sphere-coronal. It is shown that there exists higher resolution power ofdiscerning anomaly in computing GH field value using Hilbert transform than other twomethods.The discuss of the combinatorial filter technique and the Hilbert transform methodhave their own important research meaning to improve the precision for calculatingcentroid of geologic bodies, inversing fault points and analyzing oil storage structures,et al.2. The spectrum analysis of gravity potential field and technique ofanomalies conversion based on DCT(1) Characteristic of cosine-transform spectrum of gravity potential fieldWe advanced and proved three theorems and by which deduced the theoreticalformulas of cosine transform spectrum of gravity anomalies of the point mass and thevertical rectangular-cylinder in order to obtain the general equation of gravity anomaly.
So basal characteristics of cosine transform spectrum were analyzed, in which contourlines of 2D cosine transform of point mass present the shape of a quarter of concentriccircles and the number of counter become small along with the increasing of wavenumbers. The spectrum of vertical rectangular-cylinder put up periodic zero counterswhich mark off a × bquadrate areas, the values of counter in each areas alternatelychange between the plus and the minus, and with the increasing of wave number, thevalues of counter present attenuation character alike e exponent.(2) Inversion of regular bodiesThe characteristic and inversion method of gravity anomalies spectrum areproposed using cosine transform. Formulas of inversion and cosine transform spectrumof gravity anomaly of sphere, infinite horizontal cylinder, infinite and finite stretchedstaircase are deduced. The cosine transform spectrum of sphere are about the same asinfinite horizontal cylinder, of infinite stretched staircase are very spiculate, but offinite stretched staircase presented well-regulated leap. In the calculating example ofmodel inverse, the proper sampling interval and ‘trend-band' method were selected andinversed errors of linear density and axes depth of cylinder were 0.25% and 3.8%respectively.(3) Calculating gravity derivative using DCTIn order to improve the accuracy of derivative conversion of gravity anomaliesand reflect anomaly characteristic of geologic body effectively. The paper proposed thenew method of calculating anomaly derivative using cosine transform. Two theoremswere put forward and proved and the common expression of cosine transform spectrumof gravity potential field and formula of every stairs derivative of gravity anomaly werededuced using them. So the theory of cosine-transform-spectrum of potential-field wasfound. In model experiment, we discovered that the deviation of the fist derivativecalculated by Fourier transform are very big compare to theoretical derivative, but fiteffect of the derivative of anomaly calculated by cosine transform is very good. Thecalculating accuracy of data are all very high except that errors of several data ofboundary are bigger because of remains of Gibbus effect induced by finite truncation
of gravity anomaly. Errors are 0.09%~5%.(4) Calculating upward continuation of gravity anomalies using DCTCalculating upward continuation of gravity anomalies using cosine transform is anew method. According to the essential properties of cosine transform, the paperdeveloped theoretic formulas of cosine transform spectrum that were upwardcontinuation of gravity anomalies for two and three-dimensional bodies andaccomplished their numerical calculation using the discrete cosine transform. Westudied the characteristics of dominant frequency of infinite horizontal cylinder incompensated factor and given the linear compensation way of two-dimensional bodies.There are higher computing precision in upward continuation of model gravityanomalies after compensation except that errors of several data of boundary are biggerbecause of discrete and finite truncation of gravity anomaly, errors of other data arewithin 1%. The theoretic and computing curve were approximately superposed. It isshown that in numerical calculation the discrete cosine transform had lesser effect bynon-periodical depth factor, and the compensated way was prone to choice comparedto the Fourier transform. It is that the cosine transform is superior to the Fouriertransform.3. Techniques of forward modeling and inversion for gravity anomalies ofdensity interface and Euler's deconverlution(1) Forward modeling and inversion for gravity anomalies of density interfaceWe put forward researching forward modeling and inversion problem aboutgravity anomaly of density interface using cosine transform in allusion to improvingthe processing accuracy of gravity information. We developed the forward formula ofone-and two-dimensional of cosine-transform-spectrum and its inverse formula of thedepth of interface about gravity anomaly from theory. In order to discuss the inverseprecision of this method, depth of even (density) and single interface model wereinversed by Parker-Oldenberg and Cosine-transform method respectively, at the sametime, errors were analyzed. The biggest error and quadratic deviations of interfacedepth calculated by Parker-Oldenberg method in relation to interface depth of model
were 0.148km and 0.013km, but their inversed by Cosine-transform method were0.041km and 0.003km. the biggest error and quadratic deviations of the latter deducedwere 0.107km and 0.010km. These testified that inverse accuracy of Cosine-transformmethod was higher than Parker-Oldenberg method. Its accuracy increased three times.(2) The DCT method of identifying faulted structuresThe paper proposes an inversion method that determines locations of faultedstructures using the Euler deconvolution (Euler method) based on discrete cosinetransform (DCT) to improve the inversion precision of Euler's method. We give theEuler's homogeneity equation based DCT and point out that the calculating accuracyof gravity anomalies derivatives is significant question which influence the inversionprecision of Euler method. Experiments of step models show that the maximum errorand standard deviation of vertical first derivative calculated by DCT are 0.460×10-9/s2and 0.189×10-9/s2 respectively, and that of horizontal first derivative are 0.182×10-9/s2 and 0.028×10-9/s2. It is demonstrated that the accuracy of gravity anomaliesderivatives calculated by DCT is excellent to compare with DFT. Through computingfor forward models, we determine that the locations inversed by Euler method based onDCT are center of fractured surface of steps, in which the points is consistent withtheoretical locations. It is shown in the experiment of inversion models that theprecisions inversed by DCT method are very high, and validated in the practicalapplication that the method is feasible, practicable and veracious.Because we are empty of the data of protogenic oildom section, the method ofcalculating normalized full gradient of gravity anomalies using Hilbert transform can'tbe applied in practice. But other techniques in the paper were applied in planar gravityanomaly data of Heilongjiang Hulin basin and section date of DB1 line in ‘Peripheryprospect area in Daqing', and we achieved preferable outcome in date processing andexplaining.It is significant to study data processing of gravity anomaly and its correlativetheory of forward modeling, calculating technique of inversion and method of
explanation based on Hilbert transform and cosine transform. In theory, existing dataprocessing theory and explaining technique of gravity anomaly can be developed andperfected, in which they can afford theory mode that approach the real geologic bodiesand establish groundwork for inversion of data processing. In practice, they canimprove the precision of data processing of gravity anomaly, shorten the differencebetween the theory of data processing with practical question, and made our studyaccomplish important effect in domain of geophysical exploration.
为了提高重力异常数据处理的精度,本文以组合滤波法和离散Hilbert变换为理论基础,增加了重力归一化总梯度及相位法的可延拓深度,提高了该法的分辨率。以离散余弦变换(DCT)理论为基础,研究了重力位余弦变换谱的基本特征,给出重力位余弦变换谱一般表达式,推导出重力异常垂向、水平各阶导数以及异常向上延拓余弦谱理论公式,初步建立重力位余弦变换谱分析及异常转换理论;探讨并给出了理论模型的重力异常余弦变换谱正反演模式以及影响数据处理精度的主要因素。在此基础上,进一步研究了基于DCT的单密度界面异常正反演、欧拉反褶积反演的理论以及数值实现方法,给出了相应的理论研究模式。
在数值上实现了上述分析研究工作。在模型计算中,分析了重力异常转换谱中深度因子和导数响应因子的影响规律,重力异常余弦变换谱中混叠效应和吉布斯效应在数值计算中的影响规律,给出相应的滤波及补偿方式。模型实验证实:本课题研究的正、反演方法具有较高的分辨率和精度。
在实际应用中,选择黑龙江省虎林盆地平面布格重力异常资料和大庆探区外围盆地DB1线高精度剖面布格重力异常数据,实现了上述方法在实际资料处理中的应用,取得了较好的效果。
Data processing of gravity anomaly is important component part for gravityprospecting, and is a significant topic for operators who engage in geophysicalprospecting. With the developing of gravimeter for high-precision data acquisition, thestudy of new method and technique became great important for high-precision dataprocessing of gravity anomalies.
With the developing and perfecting of signal analysis theory, the method for dataprocessing of gravity anomaly was not any more restricted within the theory of Fouriertransform spectrum analysis. In the past thirty years, the method and technique for dataprocessing of gravity anomaly have permeated into domain of signal analysis, forexample, Hilbert transform, Hartley transform, et al., in which some progress havebeen attained to improve the precision of data processing of gravity anomaly.
There are characteristics in Hilbert transform in which that can use all informationof potential filed and are influenced less by background filed, so the precision of dataprocessing can be improved using the Hilbert transform. Discrete cosine transform(DCT) excel non-sine transform in theoretical and applied value, and it has excellentcapability, so it hold leading status in orthogonal transformation. DCT can avoid pluraloperation to real continuous function, and it has similar capability to Karhunen-Loèvetransform that can remove relativity and reserve superior energy of original signal. At present, wehave not found any correlative literature that used DCT to analyze spectrum of potential filed and toprocess the data of gravity anomaly.
To improve the precision of data processing of gravity anomaly, the paper use the
combinatorial filter and Hilbert transform to discuss the method of improving the depthof continuation and resolution power for calculating the normalized full gradient ofgravity anomaly and its phase and use DCT to study characteristics of cosine transformspectrum of gravity potential, to found theory of cosine transform spectrum analysisand conversion of gravity anomaly and to discuss the pattern of forward modeling andinversion and main factors that influence the precision of data processing for theorymode based on cosine transform of gravity anomaly. We study the theory for forwardmodeling and inversion of density interface and its way of numerical value calculationin order to improve the precision of inversion based on DCT, and we research thelocation problem of theory mode using the Euler's Deconverlution based on DCT topoint out its corresponding theory mode.1. Methods of improving the depth of continuation and resolution powerfor calculating the normalized full gradient of gravity anomaly and itsphase(1) The combinatorial filter techniqueWe introduce the combinatorial filter technique in the method of the normalizedfull gradient of gravity anomaly and its phase, i.e. put forward introducing smoothingfilter operator respectively in the process of downward continuation and derivationabout potential field conversion. This way increased reliability and stability ofcalculation and extended the depth of continuation. By lots of experiments of modeland analysis of data, we confirmed experiential value of exponential parameter aboutsmoothing filter operator in calculating of downward continuation and derivation,pointed out variational rule between the depth of geologic body and theharmonic-number N, in which the lower (deeper) the depth of geologic body is thebigger (lesser) the value of N is. At the same time, we discovered they had similarcharacters of contour GH field between three dimension model of symmetrical densityanticline and of asymmetry oil storage anticline and two dimension model of them andoffered the new thought of calculating center of gravity and researching oil storage
structure. We indicated the inadaptability of maximal value theory of the full gradientof gravity in researching faulted structure. To the boundless outstretched faultedstructure, we should base the trend and the shape of GH field contour and link breakpoints of gravity phase curve to confirm the location of rupture.(2) The Hilbert-transform methodA method of calculating normalized full gradient of gravity anomalies usingHilbert transform was advanced in order to improve the resolution of geophysical dataprocessing. The paper proved the feasibility of the method in theory and pointed outthe calculating way that can be performed in computer. We calculated the GH fieldvalue of model using methods of Fourier series, Fourier transform and Hilberttransform respectively and discussed the resolution power for oil-bearing structureswith the methods. The methods of Fourier series and Fourier transform can'tdistinguish the anomaly of low-density body but the method of Hilbert transform canfairly do when the thickness of oil storage part (low-density body) of 3-Dsphere-coronal (approximate model of 3-D oil storage anticline) is lower than one tenthof it of sphere-coronal. It is shown that there exists higher resolution power ofdiscerning anomaly in computing GH field value using Hilbert transform than other twomethods.The discuss of the combinatorial filter technique and the Hilbert transform methodhave their own important research meaning to improve the precision for calculatingcentroid of geologic bodies, inversing fault points and analyzing oil storage structures,et al.2. The spectrum analysis of gravity potential field and technique ofanomalies conversion based on DCT(1) Characteristic of cosine-transform spectrum of gravity potential fieldWe advanced and proved three theorems and by which deduced the theoreticalformulas of cosine transform spectrum of gravity anomalies of the point mass and thevertical rectangular-cylinder in order to obtain the general equation of gravity anomaly.
So basal characteristics of cosine transform spectrum were analyzed, in which contourlines of 2D cosine transform of point mass present the shape of a quarter of concentriccircles and the number of counter become small along with the increasing of wavenumbers. The spectrum of vertical rectangular-cylinder put up periodic zero counterswhich mark off a × bquadrate areas, the values of counter in each areas alternatelychange between the plus and the minus, and with the increasing of wave number, thevalues of counter present attenuation character alike e exponent.(2) Inversion of regular bodiesThe characteristic and inversion method of gravity anomalies spectrum areproposed using cosine transform. Formulas of inversion and cosine transform spectrumof gravity anomaly of sphere, infinite horizontal cylinder, infinite and finite stretchedstaircase are deduced. The cosine transform spectrum of sphere are about the same asinfinite horizontal cylinder, of infinite stretched staircase are very spiculate, but offinite stretched staircase presented well-regulated leap. In the calculating example ofmodel inverse, the proper sampling interval and ‘trend-band' method were selected andinversed errors of linear density and axes depth of cylinder were 0.25% and 3.8%respectively.(3) Calculating gravity derivative using DCTIn order to improve the accuracy of derivative conversion of gravity anomaliesand reflect anomaly characteristic of geologic body effectively. The paper proposed thenew method of calculating anomaly derivative using cosine transform. Two theoremswere put forward and proved and the common expression of cosine transform spectrumof gravity potential field and formula of every stairs derivative of gravity anomaly werededuced using them. So the theory of cosine-transform-spectrum of potential-field wasfound. In model experiment, we discovered that the deviation of the fist derivativecalculated by Fourier transform are very big compare to theoretical derivative, but fiteffect of the derivative of anomaly calculated by cosine transform is very good. Thecalculating accuracy of data are all very high except that errors of several data ofboundary are bigger because of remains of Gibbus effect induced by finite truncation
of gravity anomaly. Errors are 0.09%~5%.(4) Calculating upward continuation of gravity anomalies using DCTCalculating upward continuation of gravity anomalies using cosine transform is anew method. According to the essential properties of cosine transform, the paperdeveloped theoretic formulas of cosine transform spectrum that were upwardcontinuation of gravity anomalies for two and three-dimensional bodies andaccomplished their numerical calculation using the discrete cosine transform. Westudied the characteristics of dominant frequency of infinite horizontal cylinder incompensated factor and given the linear compensation way of two-dimensional bodies.There are higher computing precision in upward continuation of model gravityanomalies after compensation except that errors of several data of boundary are biggerbecause of discrete and finite truncation of gravity anomaly, errors of other data arewithin 1%. The theoretic and computing curve were approximately superposed. It isshown that in numerical calculation the discrete cosine transform had lesser effect bynon-periodical depth factor, and the compensated way was prone to choice comparedto the Fourier transform. It is that the cosine transform is superior to the Fouriertransform.3. Techniques of forward modeling and inversion for gravity anomalies ofdensity interface and Euler's deconverlution(1) Forward modeling and inversion for gravity anomalies of density interfaceWe put forward researching forward modeling and inversion problem aboutgravity anomaly of density interface using cosine transform in allusion to improvingthe processing accuracy of gravity information. We developed the forward formula ofone-and two-dimensional of cosine-transform-spectrum and its inverse formula of thedepth of interface about gravity anomaly from theory. In order to discuss the inverseprecision of this method, depth of even (density) and single interface model wereinversed by Parker-Oldenberg and Cosine-transform method respectively, at the sametime, errors were analyzed. The biggest error and quadratic deviations of interfacedepth calculated by Parker-Oldenberg method in relation to interface depth of model
were 0.148km and 0.013km, but their inversed by Cosine-transform method were0.041km and 0.003km. the biggest error and quadratic deviations of the latter deducedwere 0.107km and 0.010km. These testified that inverse accuracy of Cosine-transformmethod was higher than Parker-Oldenberg method. Its accuracy increased three times.(2) The DCT method of identifying faulted structuresThe paper proposes an inversion method that determines locations of faultedstructures using the Euler deconvolution (Euler method) based on discrete cosinetransform (DCT) to improve the inversion precision of Euler's method. We give theEuler's homogeneity equation based DCT and point out that the calculating accuracyof gravity anomalies derivatives is significant question which influence the inversionprecision of Euler method. Experiments of step models show that the maximum errorand standard deviation of vertical first derivative calculated by DCT are 0.460×10-9/s2and 0.189×10-9/s2 respectively, and that of horizontal first derivative are 0.182×10-9/s2 and 0.028×10-9/s2. It is demonstrated that the accuracy of gravity anomaliesderivatives calculated by DCT is excellent to compare with DFT. Through computingfor forward models, we determine that the locations inversed by Euler method based onDCT are center of fractured surface of steps, in which the points is consistent withtheoretical locations. It is shown in the experiment of inversion models that theprecisions inversed by DCT method are very high, and validated in the practicalapplication that the method is feasible, practicable and veracious.Because we are empty of the data of protogenic oildom section, the method ofcalculating normalized full gradient of gravity anomalies using Hilbert transform can'tbe applied in practice. But other techniques in the paper were applied in planar gravityanomaly data of Heilongjiang Hulin basin and section date of DB1 line in ‘Peripheryprospect area in Daqing', and we achieved preferable outcome in date processing andexplaining.It is significant to study data processing of gravity anomaly and its correlativetheory of forward modeling, calculating technique of inversion and method of
explanation based on Hilbert transform and cosine transform. In theory, existing dataprocessing theory and explaining technique of gravity anomaly can be developed andperfected, in which they can afford theory mode that approach the real geologic bodiesand establish groundwork for inversion of data processing. In practice, they canimprove the precision of data processing of gravity anomaly, shorten the differencebetween the theory of data processing with practical question, and made our studyaccomplish important effect in domain of geophysical exploration.
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