| 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.
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