位场数据处理的高精度方法研究及应用
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摘要
位场数据处理是利用位场资料进行地质-地球物理综合解释的重要组成部分，伴随着人们对地质目标精细解释的迫切需求，位场数据处理的高精度方法研究已成为地球物理工作者日益重视的一项课题。
目前，位场数据处理大多是在波数域中进行的，然而某些数据转换诸如向下延拓、高阶导数、低纬度化极等计算，由于在波数域中表现为转换因子对某些频率成分的显著放大，导致FFT理论计算结果不稳定。为此，学者们提出了一系列提高计算稳定性和计算精度的改进方法，其中迭代法具有较好的应用效果，在近些年来受到了普遍重视。
笔者以迭代法的思想为前提，针对向下延拓的不适定问题，提出了Taylor级数迭代法。证明了该方法的收敛性，分析了方法的收敛速度，同时指出当迭代通式中所取项数N=0时，与波数域的积分迭代法模式完全一致。模型试验表明，当向下延拓深度较大且项数N取1和0时，如果它们迭代的延拓误差相等，那么N=1时的迭代次数远小于N=0的，且N=1时的迭代结果具有更强的保幅能力。
针对一些位场数据处理方法在计算过程中存在的不稳定性问题，提出了统一的迭代模式—迭代滤波法，给出了一种可以解决迭代法最佳迭代次数的选取方案。在此基础之上，探讨了迭代次数对迭代计算结果的影响机制，并按迭代次数的递增，将迭代结果依次划分为信号压制区、最佳迭代区和局部干扰区等三个计算区域。导数换算、向下延拓和水平磁化化极的含噪模型试验表明，本文的迭代滤波法相对于其他迭代模式具有较好的计算稳定性和较高的计算精度，试验结果也验证了最佳迭代次数选取方案的正确性。
笔者还将迭代法引入到了位场分离、重力归一化总梯度、常密度界面反演等方法中。位场分离的迭代滤波法是针对异常分离不彻底时给出一种改进方案，其方法是：当分离出的局部异常中含有较多区域场成分时，对局部场进行逐次剥离，并将剥离出的成分“返还”给区域场，以此达到分离场的目的。针对重力归一化总梯度，提出了截止圆滑滤波，该滤波算子可以有效地压制高频干扰，保留低频有用信号；模型试验表明：该方法相对于常规计算方法而言，具有参数试算时间少，计算分辨能力高的优势。在密度界面反演中，提出了线性迭代法，该方法是将界面深度变化值与异常值之间建立线性关系，通过逐次迭代实现界面反演；模型检验表明了该算法相对于常规的Parker-Oldenburg法具有计算稳定性强、精度高和对迭代次数依赖弱的优点。
利用位场资料进行地质体边界检测是本文研究的另一个重点。应用位场数据识别地质体边界是地质-地球物理综合解释的一项重要工作。位场异常中包含有场源边界的信息，但边界信息的提取需要进行相关的数据处理。近些年来地球物理工作者们提出了许多基于位场梯度的边界检测方法。然而大多边界识别方法均存在着边界识别模糊和易受高频干扰影响等缺点。针对于此，文中提出了识别地质体边界的归一化均方差比法、归一化差分法、垂向梯度最佳自比值法以及改进型边界识别方法。
归一化均方差法是针对边界点异常具有方向性和均方差可衡量数据波动性提出的，该方法对不同深度的地质体边界都有较好的探测效果；归一化差分法是根据位场异常三个方向的差分算子与构造边界位置对位关系，给出的突出异常梯级带的归一化差分表达式，通过选择不同的差分阶次和差分半径可以识别出不同级别的断裂构造，有利于对断裂构造带平面位置的厘定和盆地内各级构造单元的划分。
垂向梯度最佳自比值法是为了有效消除高阶导数中的干扰成分和提高边界识别能力而提出的。笔者对自比值进行了数值分析，阐述了该算法检测地质体边界的物理机制。最佳自比值法不仅可以进行地质体边界的精细检测，还可以对地质体引起的异常进行有效的圈定。
改进型边界识别方法是针对常规边界识别方法存在识别能力差或识别边界发散等缺点提出的，文中给出了水平总梯度、tilt angle、tilt angle的水平总梯度、Theta map和归一化标准差、归一化均方差比等六种方法的改进型，并通过模型试验验证了改进型边界识别方法可以较好地弥补原方法的不足，有效地提高地质体边界的识别能力和定位精度。
将上述新算法和常规方法同时应用于地质条件较为复杂的鸭绿江盆地位场数据中，处理结果进一步证实了新方法具有较强的计算稳定性和较高的计算精度。根据数据处理计算结果和已知地质资料，对研究区的重、磁场、剩余场以及垂向二阶导数的特征进行了描述；依据多种边界识别方法对重力异常处理的结果，在研究区划分出了32条断裂构造，其中12条断裂被盆地内三条视电阻率断面图所佐证；采用线性迭代界面反演方法对分离出的浅部重力异常进行了低密度地层底界面的反演，预测了两个隐伏凹陷；在此基础上，结合研究区的地质资料，将盆地构造划分成4个一级构造单元和11个二级构造单元。
Potential-field data processing is an important part of potential-field data for geological-geophysicalinterpretation. with the imminence requirement for high resolution data and fine division of geological bodies,to study methods of high-precision in potential-field data processing has become an topic paid more attentionby geophysicists.
Processed data of potential-field is mostly completed in wave number domain. However, the results ofsome calculations such as downward continuation, derivative calculation, reduction to the pole of magneticanomaly and so on, are unstable at times using directly from FFT as their transformation factors cansignificantly amplify some wave number signals. In order to solve this problem, geophysicists proposed aseries of methods to improve computational stability and raise the precision of calculation, and iterativemethod is attached widespread attention because of better results in applications than others.
Based on the previous research works and the idea of iterative method, firstly, this paper presents Taylorseries iteration for downward continuation of potential-field to solute its intrinsic ill-posed problem. Theconvergence of this method is proved, the convergence speed of the term N=0and N=1is comparativeanalyzed. When Taylor series expansion term equals zero, Taylor series iteration is concordant with theintegral-iteration method in wave number domain. Model tests indicate that the iteration method of N=1hasvery fewer iteration times and better preserved amplitude than N=0when the depth of downward continuationis large and the continuation error of the term N=1equals N=0.
Secondly, In order to improve calculation accuracy of some methods whose calculation is unstable inpotential-field, the paper gives a unified iterated mode called iterative filtering method. And what’s more, ascheme to resolve the problem of choosing the optimal number of iteration, is called the difference of twodifference cross-correlation coefficients. On this basis, I discuss the effect mechanism of calculation resultseffected by using different iterative times. According to the number of iteration increasing, the results can bedivided into three calculation zones including suppression zone, balance zone and interference zone. Modeltests of derivative calculation, downward continuation, and the reduction to the pole, are indicate that resultsof the iterative filtering presented in this paper has stronger stability and higher precision than other proposediterative methods. Meanwhile, the results further test and verify the validity of the method for selecting theoptimal number of iteration.
And then, the iterative method is introduced into potential-field anomaly separation, normalized totalgradient of gravity, and inversion of density interface. Separating potential-field anomaly using the iterativefiltering, is a modified method in allusion to the local field which has a part of component of the regional field. The idea comes from iteration, but its physical mechanism is different from iterative filtering aboved. Modeltest of potential-field separation verifies the validity of using iterative filtering to separate potential-fieldanomaly. Normalized total gradient of gravity can be used to detect oil and gas reservoir. Using cut-offsmoothing method to calculate normalized total gradient of gravity is presented under enlightenment ofiterative method. This method can preserve more low frequency signals and suppress stronger high frequencyinterference than conventional methods, and model tests prove that cut-off smoothing has the advantages ofshorter trial computation and higher resolution than general methods. In order to avoid downwardcontinuation influence on density interface inversion, a new method called linear iterative inversion, has goodpoints about strong stability, high percison and low dependence to the number of iteration, proved by modeltests.
Moreover, edge detection is also an important research content in this paper. Edge detection ofpotential-field is commonly used in recognizing edges of geological bodies. Potential-field anomalies have theinformation of field sources’ edges, but the information extraction relies on data processing. At present, thereare many methods can used to recognize edges, but almost of these existent methods have the disadvantagesthat the detected edges are blurred and the results are susceptible to interference. In this situation, The paperproposes normalized mean square error ratio, normalized differential, optimal auto-ratio of vertical gradient,and modified edge-detection methods.
Normalized mean square error ratio based on the directionality of boundary anomaly and the datavolatility evaluated by mean square error, and it can display the edges of geological bodies on different deepsimultaneously.
Normalized differential is according to the relationship between three-directional difference and thecharacter of potential-field anomaly in position of structured edges, and faulted structures with differentgrades can be recognized by using different radius and different order.
The optimal auto-ratio of vertical gradient is used to clear interference and improve the ability of edgerecognition. Mathematical implication of the auto-ration is elaborated and physical meaning of this method isexplained. The optimal auto-ratio method can not only finely detect edges of field sources, but also candelineate different kinds of anomaly from geological bodies.
The paper gives six modified edge-recognition methods including the total horizontal gradient, tilt angle,the total horizontal gradient of tilt angle, Theta map, normalized standard deviations, and normalized meansquare error ratio. Model tests indicate that modified methods can improve the ability of edge recognitionrelative to the original methods.
At last, new methods presented in this paper and the conventional methods are applied to gravity andmagnetic anomalies of Yalujiang basin whose geological conditions are very complex, the data processingresults further confirmed that new methods can improve the precision of data processing. And according to theabove results, geological data, and electric data,32faulted structures including12faults can proved by three two-dimensional resistivity inversion section is detected and the basin is divided into four first-order tectonicunits and11second-order tectonic units including2concealed depressions.
目前，位场数据处理大多是在波数域中进行的，然而某些数据转换诸如向下延拓、高阶导数、低纬度化极等计算，由于在波数域中表现为转换因子对某些频率成分的显著放大，导致FFT理论计算结果不稳定。为此，学者们提出了一系列提高计算稳定性和计算精度的改进方法，其中迭代法具有较好的应用效果，在近些年来受到了普遍重视。
笔者以迭代法的思想为前提，针对向下延拓的不适定问题，提出了Taylor级数迭代法。证明了该方法的收敛性，分析了方法的收敛速度，同时指出当迭代通式中所取项数N=0时，与波数域的积分迭代法模式完全一致。模型试验表明，当向下延拓深度较大且项数N取1和0时，如果它们迭代的延拓误差相等，那么N=1时的迭代次数远小于N=0的，且N=1时的迭代结果具有更强的保幅能力。
针对一些位场数据处理方法在计算过程中存在的不稳定性问题，提出了统一的迭代模式—迭代滤波法，给出了一种可以解决迭代法最佳迭代次数的选取方案。在此基础之上，探讨了迭代次数对迭代计算结果的影响机制，并按迭代次数的递增，将迭代结果依次划分为信号压制区、最佳迭代区和局部干扰区等三个计算区域。导数换算、向下延拓和水平磁化化极的含噪模型试验表明，本文的迭代滤波法相对于其他迭代模式具有较好的计算稳定性和较高的计算精度，试验结果也验证了最佳迭代次数选取方案的正确性。
笔者还将迭代法引入到了位场分离、重力归一化总梯度、常密度界面反演等方法中。位场分离的迭代滤波法是针对异常分离不彻底时给出一种改进方案，其方法是：当分离出的局部异常中含有较多区域场成分时，对局部场进行逐次剥离，并将剥离出的成分“返还”给区域场，以此达到分离场的目的。针对重力归一化总梯度，提出了截止圆滑滤波，该滤波算子可以有效地压制高频干扰，保留低频有用信号；模型试验表明：该方法相对于常规计算方法而言，具有参数试算时间少，计算分辨能力高的优势。在密度界面反演中，提出了线性迭代法，该方法是将界面深度变化值与异常值之间建立线性关系，通过逐次迭代实现界面反演；模型检验表明了该算法相对于常规的Parker-Oldenburg法具有计算稳定性强、精度高和对迭代次数依赖弱的优点。
利用位场资料进行地质体边界检测是本文研究的另一个重点。应用位场数据识别地质体边界是地质-地球物理综合解释的一项重要工作。位场异常中包含有场源边界的信息，但边界信息的提取需要进行相关的数据处理。近些年来地球物理工作者们提出了许多基于位场梯度的边界检测方法。然而大多边界识别方法均存在着边界识别模糊和易受高频干扰影响等缺点。针对于此，文中提出了识别地质体边界的归一化均方差比法、归一化差分法、垂向梯度最佳自比值法以及改进型边界识别方法。
归一化均方差法是针对边界点异常具有方向性和均方差可衡量数据波动性提出的，该方法对不同深度的地质体边界都有较好的探测效果；归一化差分法是根据位场异常三个方向的差分算子与构造边界位置对位关系，给出的突出异常梯级带的归一化差分表达式，通过选择不同的差分阶次和差分半径可以识别出不同级别的断裂构造，有利于对断裂构造带平面位置的厘定和盆地内各级构造单元的划分。
垂向梯度最佳自比值法是为了有效消除高阶导数中的干扰成分和提高边界识别能力而提出的。笔者对自比值进行了数值分析，阐述了该算法检测地质体边界的物理机制。最佳自比值法不仅可以进行地质体边界的精细检测，还可以对地质体引起的异常进行有效的圈定。
改进型边界识别方法是针对常规边界识别方法存在识别能力差或识别边界发散等缺点提出的，文中给出了水平总梯度、tilt angle、tilt angle的水平总梯度、Theta map和归一化标准差、归一化均方差比等六种方法的改进型，并通过模型试验验证了改进型边界识别方法可以较好地弥补原方法的不足，有效地提高地质体边界的识别能力和定位精度。
将上述新算法和常规方法同时应用于地质条件较为复杂的鸭绿江盆地位场数据中，处理结果进一步证实了新方法具有较强的计算稳定性和较高的计算精度。根据数据处理计算结果和已知地质资料，对研究区的重、磁场、剩余场以及垂向二阶导数的特征进行了描述；依据多种边界识别方法对重力异常处理的结果，在研究区划分出了32条断裂构造，其中12条断裂被盆地内三条视电阻率断面图所佐证；采用线性迭代界面反演方法对分离出的浅部重力异常进行了低密度地层底界面的反演，预测了两个隐伏凹陷；在此基础上，结合研究区的地质资料，将盆地构造划分成4个一级构造单元和11个二级构造单元。
Potential-field data processing is an important part of potential-field data for geological-geophysicalinterpretation. with the imminence requirement for high resolution data and fine division of geological bodies,to study methods of high-precision in potential-field data processing has become an topic paid more attentionby geophysicists.
Processed data of potential-field is mostly completed in wave number domain. However, the results ofsome calculations such as downward continuation, derivative calculation, reduction to the pole of magneticanomaly and so on, are unstable at times using directly from FFT as their transformation factors cansignificantly amplify some wave number signals. In order to solve this problem, geophysicists proposed aseries of methods to improve computational stability and raise the precision of calculation, and iterativemethod is attached widespread attention because of better results in applications than others.
Based on the previous research works and the idea of iterative method, firstly, this paper presents Taylorseries iteration for downward continuation of potential-field to solute its intrinsic ill-posed problem. Theconvergence of this method is proved, the convergence speed of the term N=0and N=1is comparativeanalyzed. When Taylor series expansion term equals zero, Taylor series iteration is concordant with theintegral-iteration method in wave number domain. Model tests indicate that the iteration method of N=1hasvery fewer iteration times and better preserved amplitude than N=0when the depth of downward continuationis large and the continuation error of the term N=1equals N=0.
Secondly, In order to improve calculation accuracy of some methods whose calculation is unstable inpotential-field, the paper gives a unified iterated mode called iterative filtering method. And what’s more, ascheme to resolve the problem of choosing the optimal number of iteration, is called the difference of twodifference cross-correlation coefficients. On this basis, I discuss the effect mechanism of calculation resultseffected by using different iterative times. According to the number of iteration increasing, the results can bedivided into three calculation zones including suppression zone, balance zone and interference zone. Modeltests of derivative calculation, downward continuation, and the reduction to the pole, are indicate that resultsof the iterative filtering presented in this paper has stronger stability and higher precision than other proposediterative methods. Meanwhile, the results further test and verify the validity of the method for selecting theoptimal number of iteration.
And then, the iterative method is introduced into potential-field anomaly separation, normalized totalgradient of gravity, and inversion of density interface. Separating potential-field anomaly using the iterativefiltering, is a modified method in allusion to the local field which has a part of component of the regional field. The idea comes from iteration, but its physical mechanism is different from iterative filtering aboved. Modeltest of potential-field separation verifies the validity of using iterative filtering to separate potential-fieldanomaly. Normalized total gradient of gravity can be used to detect oil and gas reservoir. Using cut-offsmoothing method to calculate normalized total gradient of gravity is presented under enlightenment ofiterative method. This method can preserve more low frequency signals and suppress stronger high frequencyinterference than conventional methods, and model tests prove that cut-off smoothing has the advantages ofshorter trial computation and higher resolution than general methods. In order to avoid downwardcontinuation influence on density interface inversion, a new method called linear iterative inversion, has goodpoints about strong stability, high percison and low dependence to the number of iteration, proved by modeltests.
Moreover, edge detection is also an important research content in this paper. Edge detection ofpotential-field is commonly used in recognizing edges of geological bodies. Potential-field anomalies have theinformation of field sources’ edges, but the information extraction relies on data processing. At present, thereare many methods can used to recognize edges, but almost of these existent methods have the disadvantagesthat the detected edges are blurred and the results are susceptible to interference. In this situation, The paperproposes normalized mean square error ratio, normalized differential, optimal auto-ratio of vertical gradient,and modified edge-detection methods.
Normalized mean square error ratio based on the directionality of boundary anomaly and the datavolatility evaluated by mean square error, and it can display the edges of geological bodies on different deepsimultaneously.
Normalized differential is according to the relationship between three-directional difference and thecharacter of potential-field anomaly in position of structured edges, and faulted structures with differentgrades can be recognized by using different radius and different order.
The optimal auto-ratio of vertical gradient is used to clear interference and improve the ability of edgerecognition. Mathematical implication of the auto-ration is elaborated and physical meaning of this method isexplained. The optimal auto-ratio method can not only finely detect edges of field sources, but also candelineate different kinds of anomaly from geological bodies.
The paper gives six modified edge-recognition methods including the total horizontal gradient, tilt angle,the total horizontal gradient of tilt angle, Theta map, normalized standard deviations, and normalized meansquare error ratio. Model tests indicate that modified methods can improve the ability of edge recognitionrelative to the original methods.
At last, new methods presented in this paper and the conventional methods are applied to gravity andmagnetic anomalies of Yalujiang basin whose geological conditions are very complex, the data processingresults further confirmed that new methods can improve the precision of data processing. And according to theabove results, geological data, and electric data,32faulted structures including12faults can proved by three two-dimensional resistivity inversion section is detected and the basin is divided into four first-order tectonicunits and11second-order tectonic units including2concealed depressions.
引文
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