钻孔γ场理论与核测井分层解释方法研究与应用
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摘要
γ测井是主要的核地球物理技术,是三类核测井的基础方法,很多核测井技术都基于γ测井。例如,自然γ测井是测量地层岩石自身产生的γ射线;γ-γ测井是利用人工γ源照射地层岩石,测量其产生的散射γ射线;中子俘获测井是利用中子照射地层岩石使其俘获低能中子,测量其产生的特征能量γ射线;中子活化测井是利用中子照射地层岩石,测量其产生的活化γ射线。γ测井分为总量型和能谱型两类γ测井,通常将自然γ测井直接简称为γ测井。
γ测井主要探测地层岩石所产生的自然γ射线,研究地层岩石中的铀、钍、钾等放射性元素含量,识别或推断地层的岩性分布范围,寻找富含某些矿产的地层,求解岩石密度等某些地质问题。本文主要研究γ测井涉及的钻孔γ场理论、钻孔γ场计算的正反演技术、以及放射性元素含量定量的分层解释方法。
γ测井分层解释方法建立在钻孔γ场理论基础上,本文通过研究现有钻孔γ场理论和直孔γ场场强计算的表达函数,推导并提出了斜孔γ场场强计算的D函数。借助场源互换原理,推导并给出了非点状探测器接收时的直孔和斜孔γ场井轴任意点的场强计算公式,扩展了现有钻孔γ场场强计算的适用范围。
分层解释理论建立在两类假设基础上,一类是将沿井轴的地层岩石划分为一定厚度的有限个薄层,即单元层,以形态系数描述单元层的钻孔γ场;另一类是将沿井轴的地层岩石划分为无数个无限薄的薄层,即面状辐射体,以地质脉冲函数描述面状辐射体的钻孔γ场。本文从钻孔γ场理论出发,推导了两类钻孔γ场场强计算的分层解释正演方程,基于面状辐射体的正演方程称为第一基本方程,基于单元层的正演方程称为第二基本方程,并建立了它们之间的关系表达式。
为了简化面状辐射体所表达的钻孔γ场场强计算公式,国内外学者采用负指数函数来表示地质脉冲函数,即本文所称的实用地质脉冲函数。本文首先按钻孔γ场理论推导了地质脉冲函数的表达公式,再经理论分析和实验验证,探讨了实用地质脉冲函数的简化依据。通过分析和比较,论证了实用地质脉冲函数的准确性和实用性,并借助分层解释正演计算的两个基本方程之间的表达关系,提出了实用形态系数的概念,并推导了实用形态系数的表达公式。
特征参数α是实用地质脉冲函数和实用形态系数的唯一参数,本文为此进行了较深入的理论探讨和实验探索。因分层解释的正演问题或反演问题必依赖于信号的离散取样,须遵行取样定理,因而它们的数值解将产生截断误差,该截断误差是分层解释负值含量的主要来源。特征参数α的取值取决于地层环境、钻井条件、能谱成分和测量仪器等诸多因素,取值不合适将引起解释含量的严重偏差,甚至产生负值含量。本文论证了不可通过改变特征参数α的取值来人为地消除负值含量,相反可利用微小的负值含量来确定特征参数α的合适取值。
在铀矿勘探的定量铀含量解释中,为摒弃传统的平均含量法,我国通过引进分层解释法而展开了广泛的基础研究和生产实践。本文在研究多种分层解释方法的基础上,提出了多点式反褶积法和数字信号法。
反褶积法通过实用地质脉冲函数来创建分层解释正演方程(第一基本方程),利用连续信号反滤波技术(反褶积)得到了定量核素含量的反演方程,该反演方程的通解是一个微分表达式,三点式反褶积法是按照线性插值方法对该微分表达式求取数值解。本文提出了利用插值多项式对该微分表达式求取数值解的思想,并推导了多点式反褶积法的定量核素含量计算公式,还重点探讨了五点式反褶积法含量计算公式及其截断误差。通过研究模型井的解释结果,提出了基于负值含量确定特征参数α的方法——相对判别因子法,并将其应用于生产实践中。
本文提出的数字信号法是一种离散反褶积法,它采用形态系数创建分层解释正演方程(第二基本方程),利用离散信号反滤波技术(反褶积)求得反演方程及定量核素含量的数值解通式。本文还采用实用形态系数推导了所谓的精确三点式反褶积法及定量核素含量的公式,以及采用由钻孔γ场理论计算(或模型井实测)的形态系数求解核素含量的计算公式,进一步发展了反褶积技术。
通过模型井的大量实验和野外井的生产实践,并与引进的三点式反褶积法、比值迭代法和差值迭代法、逆矩阵法等方法的对比研究,验证了本文提出的多点式反褶积法(特别是五点式反褶积法)和数字信号法(特别是加长算子的数字信号法)所具有参数确定方法简单、解释精度高、分层能力强等优点,可在生产实践中采用这些新分层解释方法,且五点式反褶积法被我国核行业标准采用。
本文还初步探讨了能谱型γ测井的分层解释技术,提出了“等效含量”的概念,并利用该概念简化了能谱型γ测井的剥谱方法,实现了铀、钍、钾等放射性核素的分离解释。对比传统的能谱型γ测井剥谱方法,可通过γ射线特征能量谱创建计数率的测井曲线,采用分层解释技术求取各测点的放射性核素含量。该研究还获得了国家863计划的资助,有望在进一步研究中取得更大成绩。
Theγlogging is a major nuclear geophysical technology,and also a basic method of three types of nuclear logging.Many nuclear logging techniques are based onγlogging.For example,the naturalγlogging is to measure theγ-ray of rock itself;theγ-γlogging is to measure the scatteringγ-ray by a artificialγsource radiation to rock; the neutron capture logging is to measure the characteristic-energyγ-ray from low-energy neutron capture by the neutron irradiation of rock;and the neutron activation logging is to measure the activationγ-ray by the neutron irradiation of rock. Theγlogging is divided into two types,the total and spectrum-γlogging.Usually,the naturalγlogging is referred to asγlogging.
Theγlogging is mainly to measure the naturalγ-ray from rock itself,to study the radioactive element contents such as uranium,thorium and potassium,to inference or identify the distribution of rock formation,to find the mineral-rich strata,and to solve some geological problems such as rock density.This study is to discuss theγfield theory inside borehole duringγlogging,the forward and inversion technology of theγfield in borehole,and the subdivision interpretation methods for quantitative contents of radioactive elements.
The subdivision interpretation methods ofγlogging are based on theγfield theory of borehole.In this study,the existingγfield theory of borehole,and the expression formula ofγfield strength calculation in straight-hole are used to deduce the D function for the calculation ofγfield strength in slant-hole.According to the principle of exchange of theγfield and source,theγfield strength calculation formulas of any point in the well-axis with non-point detector to receiveγ-ray in straight-hole and slant-hole,are derived and given.Their application is extended beyond the existing calculation formulas ofγfield strength in borehole.
The subdivision interpretation theory is based on two assumptions.One of the assumptions is to divide the rock formation into many thin layers with limited number along the well-axis,i.e.,unit layer.Theγfield of unit-layer is described with its shape-factor.The other assumption is to divide the rock formation into unlimited thin layers along the well-axis,i.e.,surface-radiation-body.Theγfield of surface-radiation-body is described with its geological pulse function.In this study, according to theγfield theory of borehole,the two forward calculation equations ofγ field strength in borehole are derived for the subdivision interpretation,the first basic equation based on surface-radiation-body,and the second one based on unit-layer.And the relationship expressions between two assumptions are established.
In order to simplify the expression formula of strength calculation ofγfield of surface-radiation-body,the geological pulse function is streamlined into a negative exponential function by scholars,the practical geological pulse function.The expression formula of geological pulse function from theγfield theory of borehole is deduced in this study.Then,the simplification of the practical geological pulse function is discussed in terms of theoretical analysis and experimental validation. Through the analysis and comparison,the accuracy and usefulness of practical geological pulse function is proved.Using relationship between the two basic equations of subdivision interpretation,this study proposes the concept of practical shape-factor and the expression formula.
The characteristic parameterαis the only coefficient of the practical geological pulse function and practical shape-factor.It is discussed more theoretically and experimentally.Both forward and inverse problems of subdivision interpretation depend on the discrete signal sampling.So,they are subject to sampling theorem. Therefore,their numerical solution causes a truncation error.It is the major source for the negative content of subdivision interpretation.Theαvalue depends on the environments of rock formation,drilling conditions,compositions of energy spectrum, measuring instruments and others.The inappropriate value forαwill cause a big error for interpreting content,or even a negative content.This study demonstrates that the negative content cannot be artificially eliminated through changingα.On the contrary, the negative content can be used to determineα.
For quantitative uranium content interpretation,the subdivision interpretation methods are introduced and a wide range of basic research and production practice is launched in order to abandon the traditional average method in China.Based on various subdivision interpretation methods,the multi-point deconvolution and digital signal methods are developed in this study.
The practical geological pulse function is used for the deconvolution to create the forward equation of subdivision interpretation(the first basic equation) and to get the inversion equation of quantitative radionuclide content by continuous signal anti-filtering technology(deconvolution).The General solution of the inversion equation is a differential expression.The three-point deconvolution is based on the linear interpolation to strike a numerical solution of differential expression.This study proposes using polynomial interpolation to strike the numerical solution of differential expression,and deduces the calculation formula for the multi-point deconvolution method for quantitative content,especially discusses the five-point deconvolution method and its truncation error.Based on the interpretation for the logging models,αcan be determined by negative content,i.e.,relative discrimination factor method. This method has found use in production practice.
The digital signal method is a discrete deconvolution technology.It uses the shape-factor to create the forward equation of subdivision interpretation(the second basic equation),and the discrete signal anti-filtering technology(deconvolution) to get the inversion equation and the general formula for numerical solution of quantitative radionuclide content.The so-called accurate three-point deconvolution method and calculating formula of quantitative radionuclide content have also been deduced by the practical shape-factor.And the calculating formula is derived by using the shape-factor from theγfield theory of borehole(or the measuringγfield of logging models) for quantitative radionuclide content.The deconvolution technique has further been developed.
Through many tests of model wells and production practice of field wells,and the comparison with the three-point deconvolution method,the ratio and the margin iteration method,the inverse matrix method and other methods.The multi-point deconvolution method(in particular the five-point deconvolution method) and digital signal method(in particular the longer digital signal operator) have been verified to be simple to determine parameter,high in interpretation accuracy,and strong in subdivision of rock formation.These methods can be used for production,and the five-point deconvolution method has been used as a nuclear industry standard in China.
The study also discusses the subdivision interpretation technology for energy spectrumγ-logging.The "equivalent content" concept has been brought up to simplify the stripping spectrum method ofγ-spectrum logging,and to separate uranium,thorium, potassium and other radionuclides.Compared with the traditional stripping spectrum method ofγlogging,according the characteristic energy to create the logging curve of count rates,the quantitative radionuclide content of every measuring point can be realized by subdivision interpretation.The study also won the national 863 project fund. The new achievements are expected in the future study.
γ测井主要探测地层岩石所产生的自然γ射线,研究地层岩石中的铀、钍、钾等放射性元素含量,识别或推断地层的岩性分布范围,寻找富含某些矿产的地层,求解岩石密度等某些地质问题。本文主要研究γ测井涉及的钻孔γ场理论、钻孔γ场计算的正反演技术、以及放射性元素含量定量的分层解释方法。
γ测井分层解释方法建立在钻孔γ场理论基础上,本文通过研究现有钻孔γ场理论和直孔γ场场强计算的表达函数,推导并提出了斜孔γ场场强计算的D函数。借助场源互换原理,推导并给出了非点状探测器接收时的直孔和斜孔γ场井轴任意点的场强计算公式,扩展了现有钻孔γ场场强计算的适用范围。
分层解释理论建立在两类假设基础上,一类是将沿井轴的地层岩石划分为一定厚度的有限个薄层,即单元层,以形态系数描述单元层的钻孔γ场;另一类是将沿井轴的地层岩石划分为无数个无限薄的薄层,即面状辐射体,以地质脉冲函数描述面状辐射体的钻孔γ场。本文从钻孔γ场理论出发,推导了两类钻孔γ场场强计算的分层解释正演方程,基于面状辐射体的正演方程称为第一基本方程,基于单元层的正演方程称为第二基本方程,并建立了它们之间的关系表达式。
为了简化面状辐射体所表达的钻孔γ场场强计算公式,国内外学者采用负指数函数来表示地质脉冲函数,即本文所称的实用地质脉冲函数。本文首先按钻孔γ场理论推导了地质脉冲函数的表达公式,再经理论分析和实验验证,探讨了实用地质脉冲函数的简化依据。通过分析和比较,论证了实用地质脉冲函数的准确性和实用性,并借助分层解释正演计算的两个基本方程之间的表达关系,提出了实用形态系数的概念,并推导了实用形态系数的表达公式。
特征参数α是实用地质脉冲函数和实用形态系数的唯一参数,本文为此进行了较深入的理论探讨和实验探索。因分层解释的正演问题或反演问题必依赖于信号的离散取样,须遵行取样定理,因而它们的数值解将产生截断误差,该截断误差是分层解释负值含量的主要来源。特征参数α的取值取决于地层环境、钻井条件、能谱成分和测量仪器等诸多因素,取值不合适将引起解释含量的严重偏差,甚至产生负值含量。本文论证了不可通过改变特征参数α的取值来人为地消除负值含量,相反可利用微小的负值含量来确定特征参数α的合适取值。
在铀矿勘探的定量铀含量解释中,为摒弃传统的平均含量法,我国通过引进分层解释法而展开了广泛的基础研究和生产实践。本文在研究多种分层解释方法的基础上,提出了多点式反褶积法和数字信号法。
反褶积法通过实用地质脉冲函数来创建分层解释正演方程(第一基本方程),利用连续信号反滤波技术(反褶积)得到了定量核素含量的反演方程,该反演方程的通解是一个微分表达式,三点式反褶积法是按照线性插值方法对该微分表达式求取数值解。本文提出了利用插值多项式对该微分表达式求取数值解的思想,并推导了多点式反褶积法的定量核素含量计算公式,还重点探讨了五点式反褶积法含量计算公式及其截断误差。通过研究模型井的解释结果,提出了基于负值含量确定特征参数α的方法——相对判别因子法,并将其应用于生产实践中。
本文提出的数字信号法是一种离散反褶积法,它采用形态系数创建分层解释正演方程(第二基本方程),利用离散信号反滤波技术(反褶积)求得反演方程及定量核素含量的数值解通式。本文还采用实用形态系数推导了所谓的精确三点式反褶积法及定量核素含量的公式,以及采用由钻孔γ场理论计算(或模型井实测)的形态系数求解核素含量的计算公式,进一步发展了反褶积技术。
通过模型井的大量实验和野外井的生产实践,并与引进的三点式反褶积法、比值迭代法和差值迭代法、逆矩阵法等方法的对比研究,验证了本文提出的多点式反褶积法(特别是五点式反褶积法)和数字信号法(特别是加长算子的数字信号法)所具有参数确定方法简单、解释精度高、分层能力强等优点,可在生产实践中采用这些新分层解释方法,且五点式反褶积法被我国核行业标准采用。
本文还初步探讨了能谱型γ测井的分层解释技术,提出了“等效含量”的概念,并利用该概念简化了能谱型γ测井的剥谱方法,实现了铀、钍、钾等放射性核素的分离解释。对比传统的能谱型γ测井剥谱方法,可通过γ射线特征能量谱创建计数率的测井曲线,采用分层解释技术求取各测点的放射性核素含量。该研究还获得了国家863计划的资助,有望在进一步研究中取得更大成绩。
Theγlogging is a major nuclear geophysical technology,and also a basic method of three types of nuclear logging.Many nuclear logging techniques are based onγlogging.For example,the naturalγlogging is to measure theγ-ray of rock itself;theγ-γlogging is to measure the scatteringγ-ray by a artificialγsource radiation to rock; the neutron capture logging is to measure the characteristic-energyγ-ray from low-energy neutron capture by the neutron irradiation of rock;and the neutron activation logging is to measure the activationγ-ray by the neutron irradiation of rock. Theγlogging is divided into two types,the total and spectrum-γlogging.Usually,the naturalγlogging is referred to asγlogging.
Theγlogging is mainly to measure the naturalγ-ray from rock itself,to study the radioactive element contents such as uranium,thorium and potassium,to inference or identify the distribution of rock formation,to find the mineral-rich strata,and to solve some geological problems such as rock density.This study is to discuss theγfield theory inside borehole duringγlogging,the forward and inversion technology of theγfield in borehole,and the subdivision interpretation methods for quantitative contents of radioactive elements.
The subdivision interpretation methods ofγlogging are based on theγfield theory of borehole.In this study,the existingγfield theory of borehole,and the expression formula ofγfield strength calculation in straight-hole are used to deduce the D function for the calculation ofγfield strength in slant-hole.According to the principle of exchange of theγfield and source,theγfield strength calculation formulas of any point in the well-axis with non-point detector to receiveγ-ray in straight-hole and slant-hole,are derived and given.Their application is extended beyond the existing calculation formulas ofγfield strength in borehole.
The subdivision interpretation theory is based on two assumptions.One of the assumptions is to divide the rock formation into many thin layers with limited number along the well-axis,i.e.,unit layer.Theγfield of unit-layer is described with its shape-factor.The other assumption is to divide the rock formation into unlimited thin layers along the well-axis,i.e.,surface-radiation-body.Theγfield of surface-radiation-body is described with its geological pulse function.In this study, according to theγfield theory of borehole,the two forward calculation equations ofγ field strength in borehole are derived for the subdivision interpretation,the first basic equation based on surface-radiation-body,and the second one based on unit-layer.And the relationship expressions between two assumptions are established.
In order to simplify the expression formula of strength calculation ofγfield of surface-radiation-body,the geological pulse function is streamlined into a negative exponential function by scholars,the practical geological pulse function.The expression formula of geological pulse function from theγfield theory of borehole is deduced in this study.Then,the simplification of the practical geological pulse function is discussed in terms of theoretical analysis and experimental validation. Through the analysis and comparison,the accuracy and usefulness of practical geological pulse function is proved.Using relationship between the two basic equations of subdivision interpretation,this study proposes the concept of practical shape-factor and the expression formula.
The characteristic parameterαis the only coefficient of the practical geological pulse function and practical shape-factor.It is discussed more theoretically and experimentally.Both forward and inverse problems of subdivision interpretation depend on the discrete signal sampling.So,they are subject to sampling theorem. Therefore,their numerical solution causes a truncation error.It is the major source for the negative content of subdivision interpretation.Theαvalue depends on the environments of rock formation,drilling conditions,compositions of energy spectrum, measuring instruments and others.The inappropriate value forαwill cause a big error for interpreting content,or even a negative content.This study demonstrates that the negative content cannot be artificially eliminated through changingα.On the contrary, the negative content can be used to determineα.
For quantitative uranium content interpretation,the subdivision interpretation methods are introduced and a wide range of basic research and production practice is launched in order to abandon the traditional average method in China.Based on various subdivision interpretation methods,the multi-point deconvolution and digital signal methods are developed in this study.
The practical geological pulse function is used for the deconvolution to create the forward equation of subdivision interpretation(the first basic equation) and to get the inversion equation of quantitative radionuclide content by continuous signal anti-filtering technology(deconvolution).The General solution of the inversion equation is a differential expression.The three-point deconvolution is based on the linear interpolation to strike a numerical solution of differential expression.This study proposes using polynomial interpolation to strike the numerical solution of differential expression,and deduces the calculation formula for the multi-point deconvolution method for quantitative content,especially discusses the five-point deconvolution method and its truncation error.Based on the interpretation for the logging models,αcan be determined by negative content,i.e.,relative discrimination factor method. This method has found use in production practice.
The digital signal method is a discrete deconvolution technology.It uses the shape-factor to create the forward equation of subdivision interpretation(the second basic equation),and the discrete signal anti-filtering technology(deconvolution) to get the inversion equation and the general formula for numerical solution of quantitative radionuclide content.The so-called accurate three-point deconvolution method and calculating formula of quantitative radionuclide content have also been deduced by the practical shape-factor.And the calculating formula is derived by using the shape-factor from theγfield theory of borehole(or the measuringγfield of logging models) for quantitative radionuclide content.The deconvolution technique has further been developed.
Through many tests of model wells and production practice of field wells,and the comparison with the three-point deconvolution method,the ratio and the margin iteration method,the inverse matrix method and other methods.The multi-point deconvolution method(in particular the five-point deconvolution method) and digital signal method(in particular the longer digital signal operator) have been verified to be simple to determine parameter,high in interpretation accuracy,and strong in subdivision of rock formation.These methods can be used for production,and the five-point deconvolution method has been used as a nuclear industry standard in China.
The study also discusses the subdivision interpretation technology for energy spectrumγ-logging.The "equivalent content" concept has been brought up to simplify the stripping spectrum method ofγ-spectrum logging,and to separate uranium,thorium, potassium and other radionuclides.Compared with the traditional stripping spectrum method ofγlogging,according the characteristic energy to create the logging curve of count rates,the quantitative radionuclide content of every measuring point can be realized by subdivision interpretation.The study also won the national 863 project fund. The new achievements are expected in the future study.
引文
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