基于逆散射理论的金属矿地震成像研究
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摘要
金属矿多产出于造山带，通常具有起伏地表的复杂特征，其地震波传播规律要比水平地表和层状介质情形复杂得多。金属矿区往往经历强烈的构造变动和岩浆活动，金属矿具有成矿条件复杂，矿体形状复杂，通常空间尺度不大（在空间尺度上要远远小于油气藏），镜面反射假设通常不成立，陡倾角和直立构造多见等特点，照搬油气资源的传统地震勘探方法来进行金属矿地震勘探，在很多情况下不能取得满意的探测结果。反射地震勘探法大多局限在大尺度的控矿构造预测，对于陡倾角、尺度小于地震波长的复杂金属矿床或地质体还缺乏有效的地震探测手段。井中地震成像技术在一定程度上可解决陡倾角和直立构造的探测问题，但探测范围有限、探测效率较低且不宜推广。反射地震和首波地震层析成像相结合的方法，深部成像依赖反射地震数据，不同深度的构造信息都能得到有效地反映，但对于反射信息严重缺失的小尺度地质体或陡倾角直立构造情况，该方法的效果仍然有限。在散射地震波场方面，目前还只局限于在特定条件下自激自收剖面（叠后剖面）中利用散射地震波场圈定与矿体有关的介质非均匀性。逆散射理论需要先验信息少，对于复杂地表情形下复杂地质体成像具有更大优势，逆散射成像在考虑逆散射序列一阶项的小扰动情形下已经取得显著的应用效果，但大扰动情形下仍有待研究。以上可见，对于复杂地质条件下金属矿的地震成像问题，目前还没有一种切实可行的反演方法可供实际使用。对于散射波地震勘探而言，本质上最终要解决的就是逆散射反演问题。研究复杂介质中散射波传播规律和逆散射反演成像方法将是金属矿地震勘探取得突破的关键。
本文基于奇性反演成像理论和散射序列成像理论，将奇性反演成像方法引入到散射序列成像中。依据Beylkin奇性反演理论，利用小扰动技术在单一散射假定之下将反问题线性化，根据Green函数将线性化的算子方程转化为积分方程形式。引入了一类Fourier积分算子，该算子渐进展开的第一项是一个只含有奇性项的恒等算子。定义了一类因果广义Radon变换，其伴随算子是一个广义反投影算子，而Fourier积分算子等价于散射场的一个积分变换和广义反投影算子的复合运算。
为研究复杂地表情形下，地震波在复杂地质构造中的传播过程，本文建立了起伏地表复杂地质体地震波传播数学模型。提出分段光滑曲线边界法向导数的一种插值算法，解决矩形网格有限差分法处理复杂边界这一长期以来一直困扰人们的难题；采用的波场系列快照技术可以有效地分析和认识起伏地表复杂地质体地震波传播规律，在正演散射序列的计算过程中，给出了利用高维快速卷积计算高维积分的快速算法，提高了计算效率。
进行了起伏地表复杂地质体模型进行了奇性反演成像数值模拟研究。研究了2D炮集地震记录的奇性反演成像算法，研制了相应的成像软件，进行了理论模型的反演成像数值计算，阐述了奇性反演成像算法的一些特点和规律。基于逆散射序列的奇性反演成像算法的计算量要远远大于Beylkin奇性反演方法，逆散射序列的每个子项都是一个高维含参积分，子项的阶数越高积分的维数就越高，通常数值积分的计算速度几乎是无法接受的。本文根据被积函数的特点，将这些高维积分整理成了高维卷积的形式，并利用卷积定理和快速Fourier变换方法计算这些高维含参积分，极大地提高了计算速度。通过理论模型模拟计算，表明本文研究的基于逆散射序列的奇性反演成像算法，可以对复杂地下介质的构造进行有效成像，并具备在成像的过程中同时压制多次波的特点。
开展金属矿地震野外试验，分别进行逆散射成像与常规反射地震数据成像并进行成像结果对比。试验中地震仪采用法国Sercel地震仪，震源采用可控震源。地震数据采集过程中试验两种观测系统，其一是常规反射地震勘探单边激发滚道方式的观测系统，其二是检波器排列固定不动炮点滚动的观测系统。对第一种观测系统采集的地震数据进行常规反射地震数据处理以便与成像结果进行对比。对两种观测系统采集的地震数据都进行了奇性反演成像研究，并取得了较好的成像效果。
Metal mine with orogen prolificly, usually has complex features relief surface,its seismic wave propagation is much more complicated than in layered media andthe level of the surface. Metal mines often experience intense tectonic and magmaticactivity, and metal mine has the characteristic of complex metallogenic conditions,complex ore complex shape, small spatial scale (much smaller than reservoirs in thespatial scale), not applicable specular reflection assumption, usually steep tilt andvertical structure. Metal mine seismic exploration copying traditional seismicexploration of oil and gas resources can not get satisfactory results in many cases.The conventional reflection imaging method is limited to large-scale metal structureprediction and effective seismic exploration method is still lacking in steep angle andscale of deposits seismic or geological body smaller than the wavelength. boreholeseismic imaging technology, to some extent, can resolve the problem of steep tilt andvertical structure, but has problems of limited detection range, low detectionefficiency and difficult to promote. Method combined first wave seismiccomography with seismic reflection method is relied on deep seismic reflectionimaging data, structural information at different depths can be effectively reflection,but is limited to the small-scale geological structure upright or steep dip with aserious lack of information reflecting. Scattering method of seismic wave iscurrently still confined to delineatethe non-uniformity of orebody and related mediaat the certain zero offset section conditions (stacked cross-section). Inverse scatteringtheory requires little priori information, and has a greater advantage for compleximaging complex surface geological circumstances, the inverse scattering imagingcircumstances under small perturbations considering the first order term of inversescattering sequence has made significant application effect, but remains to be studiedin the case of large disturbances. Above that, seismic imaging method for practicaluse at the complicated geological conditions of metal mine is not existed. For thescattered wave seismic exploration, the essence is to ultimately solve the inverse scattering inverse problem. Research on complex medium wave propagation andscattering inverse scattering imaging method will be the key for metal mine seismicexploration.
The singularity inversion imaging method is introduced to scatter imagingsequence based on the singularity theory and scattering imaging sequence inversionimaging theory.The inverse is linearized by using the small perturbation in singlescattering assumption based on Beylkin’s singular inversion method, according tothe Green function the linearization operator equation is transformed into integralequation. A class of Fourier integral operator is induced, the operator asymptoticexpansion of the first is a singular item containing only the identity operator. A classof causal generalized Radon transform is defined, its adjoint operator is a generalizedback projection operator, and Fourier integral operator is equivalent to the compoundoperation of an integral transformation in the scattering field and generalized backprojection operator.
To study the circumstances of seismic wave propagation under complex surfacein complex geological structure, the paper will establish the undulating surfaceseismic wave propagation in complex geological mathematical model.Thetopography of the complex geological seismic wave propagation mathematicalmodel is established, an interpolation method is given for computing normalderivative at the rectangular grid point on the boundary to solve a rectangular gridfinite difference method deal with complex boundary, which is a difficult problemand has been troubled people long; and propagation laws in the relief surface andcomplex media are revealed using the technique of a series of wave field snapshots.
A rugged topography and complicated geological model was conducted forsingular inversion imaging numerical simulation.The algorithm of singular inversionimaging for2-D shot seismic record is studied, and the relevant computer imagingsoftware is developed as well. Numerical calculation of inverse imaging of its theorymodel is did, some characteristics and rules of the singularity inversion imagingalgorithm is described. the amount of calculation of the singularity inversion imagingalgorithm of inverse scattering sequence is much larger than the Beylkin singularity inversion method, each item in inverse scattering sequence is a high dimensionalparametric integral, more integral higher of item, and more dimension order, so,usually computing speed of numerical integral is almost unacceptable. According tothe features of the integrand, these high-dimensional integrals are arranged with thehigh dimensional convolution form, and we calculate the high dimensional parametricintegral convolution theorem and the fast Fourier transform method, which greatlyimproves the computational speed. The theoretical model calculation results show thatthe singularity inversion imaging algorithm based on inverse scattering series canconstruct the complex underground medium for effective imaging, and at the sametime suppress the multiple waves in the process of imaging.
The mineral seismic field test will be done and both the singularity inversionimaging results and the conventional reflection imaging results will be get andcompared. The mineral seismic field test will be done using French Sercel seismicinstrument and the vibroseis as the source. Two kinds of observation system are testedin seismic data acquisition in the experiments, one is the conventional reflectionseismic observation system of unilateral excitation raceway mode, the other is theobservation system of detector array fixed and shot rolling. The conventionalreflection seismic data of the first kind of observation system are processed to becompared with the imaging results. The singularity inversion imaging of seismicacquisition data containing all two observation system are studied, and good imagingresults are obtained.
本文基于奇性反演成像理论和散射序列成像理论，将奇性反演成像方法引入到散射序列成像中。依据Beylkin奇性反演理论，利用小扰动技术在单一散射假定之下将反问题线性化，根据Green函数将线性化的算子方程转化为积分方程形式。引入了一类Fourier积分算子，该算子渐进展开的第一项是一个只含有奇性项的恒等算子。定义了一类因果广义Radon变换，其伴随算子是一个广义反投影算子，而Fourier积分算子等价于散射场的一个积分变换和广义反投影算子的复合运算。
为研究复杂地表情形下，地震波在复杂地质构造中的传播过程，本文建立了起伏地表复杂地质体地震波传播数学模型。提出分段光滑曲线边界法向导数的一种插值算法，解决矩形网格有限差分法处理复杂边界这一长期以来一直困扰人们的难题；采用的波场系列快照技术可以有效地分析和认识起伏地表复杂地质体地震波传播规律，在正演散射序列的计算过程中，给出了利用高维快速卷积计算高维积分的快速算法，提高了计算效率。
进行了起伏地表复杂地质体模型进行了奇性反演成像数值模拟研究。研究了2D炮集地震记录的奇性反演成像算法，研制了相应的成像软件，进行了理论模型的反演成像数值计算，阐述了奇性反演成像算法的一些特点和规律。基于逆散射序列的奇性反演成像算法的计算量要远远大于Beylkin奇性反演方法，逆散射序列的每个子项都是一个高维含参积分，子项的阶数越高积分的维数就越高，通常数值积分的计算速度几乎是无法接受的。本文根据被积函数的特点，将这些高维积分整理成了高维卷积的形式，并利用卷积定理和快速Fourier变换方法计算这些高维含参积分，极大地提高了计算速度。通过理论模型模拟计算，表明本文研究的基于逆散射序列的奇性反演成像算法，可以对复杂地下介质的构造进行有效成像，并具备在成像的过程中同时压制多次波的特点。
开展金属矿地震野外试验，分别进行逆散射成像与常规反射地震数据成像并进行成像结果对比。试验中地震仪采用法国Sercel地震仪，震源采用可控震源。地震数据采集过程中试验两种观测系统，其一是常规反射地震勘探单边激发滚道方式的观测系统，其二是检波器排列固定不动炮点滚动的观测系统。对第一种观测系统采集的地震数据进行常规反射地震数据处理以便与成像结果进行对比。对两种观测系统采集的地震数据都进行了奇性反演成像研究，并取得了较好的成像效果。
Metal mine with orogen prolificly, usually has complex features relief surface,its seismic wave propagation is much more complicated than in layered media andthe level of the surface. Metal mines often experience intense tectonic and magmaticactivity, and metal mine has the characteristic of complex metallogenic conditions,complex ore complex shape, small spatial scale (much smaller than reservoirs in thespatial scale), not applicable specular reflection assumption, usually steep tilt andvertical structure. Metal mine seismic exploration copying traditional seismicexploration of oil and gas resources can not get satisfactory results in many cases.The conventional reflection imaging method is limited to large-scale metal structureprediction and effective seismic exploration method is still lacking in steep angle andscale of deposits seismic or geological body smaller than the wavelength. boreholeseismic imaging technology, to some extent, can resolve the problem of steep tilt andvertical structure, but has problems of limited detection range, low detectionefficiency and difficult to promote. Method combined first wave seismiccomography with seismic reflection method is relied on deep seismic reflectionimaging data, structural information at different depths can be effectively reflection,but is limited to the small-scale geological structure upright or steep dip with aserious lack of information reflecting. Scattering method of seismic wave iscurrently still confined to delineatethe non-uniformity of orebody and related mediaat the certain zero offset section conditions (stacked cross-section). Inverse scatteringtheory requires little priori information, and has a greater advantage for compleximaging complex surface geological circumstances, the inverse scattering imagingcircumstances under small perturbations considering the first order term of inversescattering sequence has made significant application effect, but remains to be studiedin the case of large disturbances. Above that, seismic imaging method for practicaluse at the complicated geological conditions of metal mine is not existed. For thescattered wave seismic exploration, the essence is to ultimately solve the inverse scattering inverse problem. Research on complex medium wave propagation andscattering inverse scattering imaging method will be the key for metal mine seismicexploration.
The singularity inversion imaging method is introduced to scatter imagingsequence based on the singularity theory and scattering imaging sequence inversionimaging theory.The inverse is linearized by using the small perturbation in singlescattering assumption based on Beylkin’s singular inversion method, according tothe Green function the linearization operator equation is transformed into integralequation. A class of Fourier integral operator is induced, the operator asymptoticexpansion of the first is a singular item containing only the identity operator. A classof causal generalized Radon transform is defined, its adjoint operator is a generalizedback projection operator, and Fourier integral operator is equivalent to the compoundoperation of an integral transformation in the scattering field and generalized backprojection operator.
To study the circumstances of seismic wave propagation under complex surfacein complex geological structure, the paper will establish the undulating surfaceseismic wave propagation in complex geological mathematical model.Thetopography of the complex geological seismic wave propagation mathematicalmodel is established, an interpolation method is given for computing normalderivative at the rectangular grid point on the boundary to solve a rectangular gridfinite difference method deal with complex boundary, which is a difficult problemand has been troubled people long; and propagation laws in the relief surface andcomplex media are revealed using the technique of a series of wave field snapshots.
A rugged topography and complicated geological model was conducted forsingular inversion imaging numerical simulation.The algorithm of singular inversionimaging for2-D shot seismic record is studied, and the relevant computer imagingsoftware is developed as well. Numerical calculation of inverse imaging of its theorymodel is did, some characteristics and rules of the singularity inversion imagingalgorithm is described. the amount of calculation of the singularity inversion imagingalgorithm of inverse scattering sequence is much larger than the Beylkin singularity inversion method, each item in inverse scattering sequence is a high dimensionalparametric integral, more integral higher of item, and more dimension order, so,usually computing speed of numerical integral is almost unacceptable. According tothe features of the integrand, these high-dimensional integrals are arranged with thehigh dimensional convolution form, and we calculate the high dimensional parametricintegral convolution theorem and the fast Fourier transform method, which greatlyimproves the computational speed. The theoretical model calculation results show thatthe singularity inversion imaging algorithm based on inverse scattering series canconstruct the complex underground medium for effective imaging, and at the sametime suppress the multiple waves in the process of imaging.
The mineral seismic field test will be done and both the singularity inversionimaging results and the conventional reflection imaging results will be get andcompared. The mineral seismic field test will be done using French Sercel seismicinstrument and the vibroseis as the source. Two kinds of observation system are testedin seismic data acquisition in the experiments, one is the conventional reflectionseismic observation system of unilateral excitation raceway mode, the other is theobservation system of detector array fixed and shot rolling. The conventionalreflection seismic data of the first kind of observation system are processed to becompared with the imaging results. The singularity inversion imaging of seismicacquisition data containing all two observation system are studied, and good imagingresults are obtained.
引文
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