频率域高精度波场延拓算子构建技术
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摘要
随着油气勘探开发的不断深入,面临的勘探和开发对象也越来越复杂,其中包括复杂构造油气藏、岩性油气藏和裂缝油气藏等的勘探开发。因此,对地震偏移成像提出了更高的精度要求。
本文基于频率域高精度波场延拓算子构建技术,提出了两种新的频率域波场延拓算子:PADE高阶近似的波场延拓算子和有理式近似的波场延拓算子。从方法理论、精度分析、计算效率、参考速度的选择等四个方面与常规频率域算子对比,证明了它们的高成像精度和效率,具有重要的价值。具体包含以下几个方面的研究:
(1)方法理论:对于非均匀介质的单程波方程,为了避免k_0( z_i )/ k_z ( z_i )中的k_z ( z i)=0,常规的近似方法是对k_0( z_i )/ k_z ( z_i )进行Taylor展开或PADE展开。本文的PADE高阶近似算子采用一种新的PADE展开方法,与常规的PADE展开相比,其具有更高的精度;有理式近似算子采用一阶分式近似,二阶抛物近似,其系数根据横向速度对比给定,满足频散误差最小。然后把近似后的k_0( z_i )/ k_z ( z_i )分解为1+a,通过推导,单程波方程可以表示为类似SSF的分裂步框架,分为时移项插值和频移项两步延拓,极大地提高了计算效率。
(2)精度分析:对SSF算子、PADE高阶近似算子、有理式近似算子以及FFD算子的成像精度从横向速度对比、传播角度和相对误差的关系以及频散误差分析两方面进行了研究。结果表明,PADE高阶近似算子和有理式近似算子的成像精度明显优于SSF算子。PADE高阶近似算子适应中等横向速度对比介质,有理式近似算子适应强横向速度对比介质。从对SEG/EAGE模型的偏移试验来看,PADE高阶近似算子、有理式近似算子可以达到与FFD算子相当的偏移成像效果。
(3)计算效率:SSF算子每延拓一层需要2次FFT,PADE高阶近似算子以及有理式近似算子需3次FFT和一次插值。FFD算子(相当于5次FFT)需2次FFT和一次FD校正。在相同的硬件条件下,对同一模型进行试算,PADE高阶近似算子的CPU时间比SSF增加31%,有理式近似算子的CPU时间比SSF算子增加44%,但远小于FFD的CPU时间。
(4)参考速度选择研究:从参考速度大于和小于真实速度两方面研究了参考速度的选择对SSF算子、PADE高阶近似算子和有理式近似算子的影响。结果表明:不论参考速度大于或小于真实速度,PADE高阶近似算子和有理式近似算子的成像精度均比SSF算子有显著改进。
(5)实际资料数值模拟:利用本文提出的高精度波场延拓算子分别对生物礁滩储层和J井地震响应进行数值模拟,模拟剖面与原始地震剖面有很高的吻合度,说明地质模型的建模和数值模拟是准确的,也验证了本文频率域高精度波场延拓算子的实际资料成像能力。
With the deepening of oil and gas exploration and development, exploration tar-gets and conditions have become more and more complex, which includes the explo-ration and development of complex structure oil and gas reservoirs, lithological res-ervoirs and fractured reservoirs. Therefore, there is a higher requirement of seismic migration imaging accuracy.
This paper based on the building technology of high-accuracy wave field extrap-olation operators in frequency domain raises two high-precision wave field continua-tion operators: PADE high-order approximate operator and rational fraction approxi-mation operator. We compared high-accuracy wave field extrapolation operators with general operator in frequency domain in methodology, accuracy analysis, computa-tional efficiency and selection of reference velocity. The results show that they have high imaging accuracy and efficiency, and they are of great value. This paper contains the following specific aspects:
Frist, methodology: For non-uniform medium wave equation, in order to avoid k_z ( zi) =0, the normal approximation is Taylor expansion and PADE expansion. PADE high-order approximate operator uses a new PADE expansion method, which has a higher accuracy compared with the conventional PADE expansion. Rational fraction approximation operator uses fraction approximation at the first-order and parabolic approximation at the second-order. Coefficient is determined with the given lateral velocity contrast, which meets the minimum error dispersion. Than we de-compose k_0( zi ) / k_z ( zi )with1+a. Though deduction, one-way wave equation can be expressed as a split-step framework similar to SSF and be expressed as two-step ex-tension: Frequency shift and interpolation in time shift, which is greatly improved the computational efficiency.
Second, accuracy analysis: From the relationship of lateral velocity contrast, transmission angle, the relative error and error analysis of the dispersion, we com-pared the accuracy of SSF operator, PADE high-order approximate operator and ra-tional fraction approximation operator. The results show that the imaging precision of PADE high-order approximate operator and the rational fraction approximation oper-ator have a great improver then SSF operator. PADE high-order approximate operator adapts medium of lateral velocity contrast. The rational fraction approximation oper-ator adapts medium of strong lateral velocity. From the imaging precision of SEG / EAGE model, we can see PADE high-order approximate operator, the rational frac-tion approximation operator can achieve a considerable imaging precision of migra-tion compared with the FFD operator.
Third, computational efficiency: SSF operator needs two FFT in one extension, PADE high-order approximate operator and rational fraction approximation operator need three FFT and one interpolation. The FFD operator needs five FFT, which is in-cluded with two FFT and one FD. Under the same hardware, we test on the same model. the CPU time of PADE high-order approximate operator caused 31% compu-ting time more than SSF operator, and rational fraction approximation operator caused 44% computing time more than SSF operator.
Fourth, selection of reference velocity: From the reference velocities is larger or smaller than true velocities, the paper studies the influence of SSF operator, PADE high-order approximate operator and the rational fraction approximation operator in reference velocities selection. The results show that whether the reference velocities is larger or smaller than true velocities, the imaging precision of PADE high-order ap-proximate operator and the rational fraction approximation operator have a great im-prover than SSF operator.
Fifth, numerical simulation of the actual data: This paper uses high-precision wave field continuation operator to do numerical simulation of reef reservoir and J well. Simulation of seismic profile has a high degree of the original agreement. It de-scribes the geological model of the modeling and numerical simulation is accurate, it also proved accurate imaging capabilities of frequency domain wave field continua-tion operator in the actual data.
本文基于频率域高精度波场延拓算子构建技术,提出了两种新的频率域波场延拓算子:PADE高阶近似的波场延拓算子和有理式近似的波场延拓算子。从方法理论、精度分析、计算效率、参考速度的选择等四个方面与常规频率域算子对比,证明了它们的高成像精度和效率,具有重要的价值。具体包含以下几个方面的研究:
(1)方法理论:对于非均匀介质的单程波方程,为了避免k_0( z_i )/ k_z ( z_i )中的k_z ( z i)=0,常规的近似方法是对k_0( z_i )/ k_z ( z_i )进行Taylor展开或PADE展开。本文的PADE高阶近似算子采用一种新的PADE展开方法,与常规的PADE展开相比,其具有更高的精度;有理式近似算子采用一阶分式近似,二阶抛物近似,其系数根据横向速度对比给定,满足频散误差最小。然后把近似后的k_0( z_i )/ k_z ( z_i )分解为1+a,通过推导,单程波方程可以表示为类似SSF的分裂步框架,分为时移项插值和频移项两步延拓,极大地提高了计算效率。
(2)精度分析:对SSF算子、PADE高阶近似算子、有理式近似算子以及FFD算子的成像精度从横向速度对比、传播角度和相对误差的关系以及频散误差分析两方面进行了研究。结果表明,PADE高阶近似算子和有理式近似算子的成像精度明显优于SSF算子。PADE高阶近似算子适应中等横向速度对比介质,有理式近似算子适应强横向速度对比介质。从对SEG/EAGE模型的偏移试验来看,PADE高阶近似算子、有理式近似算子可以达到与FFD算子相当的偏移成像效果。
(3)计算效率:SSF算子每延拓一层需要2次FFT,PADE高阶近似算子以及有理式近似算子需3次FFT和一次插值。FFD算子(相当于5次FFT)需2次FFT和一次FD校正。在相同的硬件条件下,对同一模型进行试算,PADE高阶近似算子的CPU时间比SSF增加31%,有理式近似算子的CPU时间比SSF算子增加44%,但远小于FFD的CPU时间。
(4)参考速度选择研究:从参考速度大于和小于真实速度两方面研究了参考速度的选择对SSF算子、PADE高阶近似算子和有理式近似算子的影响。结果表明:不论参考速度大于或小于真实速度,PADE高阶近似算子和有理式近似算子的成像精度均比SSF算子有显著改进。
(5)实际资料数值模拟:利用本文提出的高精度波场延拓算子分别对生物礁滩储层和J井地震响应进行数值模拟,模拟剖面与原始地震剖面有很高的吻合度,说明地质模型的建模和数值模拟是准确的,也验证了本文频率域高精度波场延拓算子的实际资料成像能力。
With the deepening of oil and gas exploration and development, exploration tar-gets and conditions have become more and more complex, which includes the explo-ration and development of complex structure oil and gas reservoirs, lithological res-ervoirs and fractured reservoirs. Therefore, there is a higher requirement of seismic migration imaging accuracy.
This paper based on the building technology of high-accuracy wave field extrap-olation operators in frequency domain raises two high-precision wave field continua-tion operators: PADE high-order approximate operator and rational fraction approxi-mation operator. We compared high-accuracy wave field extrapolation operators with general operator in frequency domain in methodology, accuracy analysis, computa-tional efficiency and selection of reference velocity. The results show that they have high imaging accuracy and efficiency, and they are of great value. This paper contains the following specific aspects:
Frist, methodology: For non-uniform medium wave equation, in order to avoid k_z ( zi) =0, the normal approximation is Taylor expansion and PADE expansion. PADE high-order approximate operator uses a new PADE expansion method, which has a higher accuracy compared with the conventional PADE expansion. Rational fraction approximation operator uses fraction approximation at the first-order and parabolic approximation at the second-order. Coefficient is determined with the given lateral velocity contrast, which meets the minimum error dispersion. Than we de-compose k_0( zi ) / k_z ( zi )with1+a. Though deduction, one-way wave equation can be expressed as a split-step framework similar to SSF and be expressed as two-step ex-tension: Frequency shift and interpolation in time shift, which is greatly improved the computational efficiency.
Second, accuracy analysis: From the relationship of lateral velocity contrast, transmission angle, the relative error and error analysis of the dispersion, we com-pared the accuracy of SSF operator, PADE high-order approximate operator and ra-tional fraction approximation operator. The results show that the imaging precision of PADE high-order approximate operator and the rational fraction approximation oper-ator have a great improver then SSF operator. PADE high-order approximate operator adapts medium of lateral velocity contrast. The rational fraction approximation oper-ator adapts medium of strong lateral velocity. From the imaging precision of SEG / EAGE model, we can see PADE high-order approximate operator, the rational frac-tion approximation operator can achieve a considerable imaging precision of migra-tion compared with the FFD operator.
Third, computational efficiency: SSF operator needs two FFT in one extension, PADE high-order approximate operator and rational fraction approximation operator need three FFT and one interpolation. The FFD operator needs five FFT, which is in-cluded with two FFT and one FD. Under the same hardware, we test on the same model. the CPU time of PADE high-order approximate operator caused 31% compu-ting time more than SSF operator, and rational fraction approximation operator caused 44% computing time more than SSF operator.
Fourth, selection of reference velocity: From the reference velocities is larger or smaller than true velocities, the paper studies the influence of SSF operator, PADE high-order approximate operator and the rational fraction approximation operator in reference velocities selection. The results show that whether the reference velocities is larger or smaller than true velocities, the imaging precision of PADE high-order ap-proximate operator and the rational fraction approximation operator have a great im-prover than SSF operator.
Fifth, numerical simulation of the actual data: This paper uses high-precision wave field continuation operator to do numerical simulation of reef reservoir and J well. Simulation of seismic profile has a high degree of the original agreement. It de-scribes the geological model of the modeling and numerical simulation is accurate, it also proved accurate imaging capabilities of frequency domain wave field continua-tion operator in the actual data.
引文
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