双程波动方程数值模拟和照明分析方法研究
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摘要
在石油地震勘探过程中,地震波场特征的数值模拟和照明分析对于帮助人们认识和分析地震波的传播规律、指导野外地震资料采集和观测系统设计、改善地震数据的处理质量、减少地下速度建模的不确定性、协助确定油气藏解释方案具有重要意义。
本文在前人工作的基础上,采用单程波延拓算子中的SSF算子和FFD算子对单程声波方程进行了数值模拟和照明分析,进一步研究了采用交错网格有限差分方法对双程声波方程和双程弹性波方程的数值模拟和照明分析方法。在实际计算中发现合理地选择模拟参数,将对模拟和照明的运算效率和计算效果产生重要影响,因此本文针对有限差分方法中频散问题、稳定性问题和边界条件进行了具体分析和研究,给出了任意偶数阶差分精度的纵波、横波频散关系式,详细推导和建立了差分格式的稳定性条件。采用完全匹配层(PML)吸收边界条件进行边界影响的研究。通过大量的数值计算表明,采用完全匹配层吸收边界条件,只需半个波长厚度的PML,就可以很好地吸收边界反射波,其吸收效果远远优于阻尼衰减边界条件。对各种模型数据进行地震记录模拟和照明计算,取得了满意的结果。
通过进一步研究还发现:单程声波方程的计算结果信噪比高,仅含有一次反射波,便于波场识别和分析,效率很高,但是单程波算子存在倾角限制,对于横向速度变化较大的模型误差较大,并且反射界面的反射系数是近似的;双程波动方程交错网格有限差分方法则可以处理横向速度任意变化的模型,模拟精度很高,并且界面反射系数不存在近似。若不需要考虑转换波问题,可采用双程声波方程进行计算,计算速度较快,仅含有纵波。双程弹性波方程的结果和实际情况最为接近,波场信息丰富。
In the process of petroleum seismic exploration, wave-equation forward modeling and illumination analysis both have great significance to help people understand and analyze the seismic wave propagation law, provide guidance for seismic data acquisition and seismic survey design, improve seismic data processing quality, reduce the uncertainty of subsurface velocity modeling and determine interpretation scheme of oil and gas reservoir.
Based on previous researches and following the order from simple to complex, I conduct a further study on the seismic wave-equation forward modeling schemes and illumination analysis methods based on the one-way acoustic wave equation, two-way acoustic wave equation and two-way elastic wave equation, and then program to realize them respectively. The computation results of different velocity models indicate that the methods are correct and satisfied.
At first, I make a research on the one-way acoustic wave equation seismic numerical simulation and illumination analysis. The one-way acoustic wave equation modeling is an simulation method which extrapolate wave field in the frequency wave-number domain and correct the perturbation due to transversely variable velocity in the frequency-space domain. By using SSF operator and FFD operator, Zero-offset synthetic records are gained. On the basis of positioning principle, I develop a faster method to get nonzero- offset common shot records that receive the extrapolated wave field on the surface of the model directly at each geophone, without extra lateral stacking. According to this kind of method, P-P common shot records and P-SV common shot records are simulated effectively. Based on one-way seismic simulation, seismic illumination analysis is conducted through which the results of Zero-offset seismic illumination, source illumination, source-receiver illumination and plane wave source illumination are achieved. The conclusions are that zero-offset seismic illumination is an ideal vertical incidence illumination, the results of source illumination and two-side receiving illumination are similar,while the one-side receiving case is different from them,in the case of small incident angles, SSF operator and FFD operator have no major difference, while not the case when the incident angle is greater than 40 degrees.The same as one-way wave simulation, the one-way wave seismic illumination has high efficiency.
Then I make a research on the seismic numerical simulation and illumi- nation analysis based on two-way acoustic wave equation and two-way elastic wave equation. The numerical simulation methods of these two kinds of wave equations are similar. Adopting their own one order velocity-stress wave equation, I deduce their staggered-grid finite-difference algorithm in detail and program them correctly.Considering the intrinsic problems of finite-difference technique such as numerical dispersion, stability problem and boundary reflection, I give out the grid-dispersion relations for the P and S waves, stability condition and the discrete formula of perfectly matched layers of arbitrary even order accuracy, analyze detailedly the influence of different stability parameter, different passion ratio and different spatial sampling ratio on the grid-dispersion.According to the theoretical analysis, grid discrete slows the wave propagation, and along the axis, the numerical dispersion is most severe and decreases as the incident angle increasing,in the diagonal direction the dispertion is lowest.The smaller is the stability parameter,the more severe is the dispertion.Then I adopt the perfectly matched absorbing layer to reduce the boundary reflection.Through a large amount of experiments,I find that half of the p-wave length of the PML layers can absorb the boundary reflection effectively,and then,I do comparisons of two different boundary conditions and two kind of different modeling accuracy. After numerical simulation, source illumination is computed.Based on two kinds of lens with high velocity and low velocity and acoustic wave equation, source illumination is computed, which reveals the defocusing effect of high velocity and focusing effect of low velocity. The multiple sources illumination of the model is even. Adopting poynting's theorem,I compute the elastic illumination vector in the first time.Two-way elastic equation can describe wave propagation and seismic illumination more accourately. The illumation changes obviously as the source position.So in order to acquisite high quality seismic data, we should change the position with even and high illumation to excite and receive seismic wave.
According to the above research, conclusions are as follows: the one-way wave equation can provide synthetic records with high SNR, including only reflected waves or diffracted waves, which is useful for wave field recognition and analyzation. The computation efficiency is also very high, while the coefficient of reflection is approximate. Two-way acoustic wave equation can deal with the coefficient of reflection correctly and provide accurate wave field. The two-way elastic wave equation gives the most realistic results and can model many kinds of waves in the cost of computation. Thus, we can choose the proper type of wave equation to use in the practical work.
本文在前人工作的基础上,采用单程波延拓算子中的SSF算子和FFD算子对单程声波方程进行了数值模拟和照明分析,进一步研究了采用交错网格有限差分方法对双程声波方程和双程弹性波方程的数值模拟和照明分析方法。在实际计算中发现合理地选择模拟参数,将对模拟和照明的运算效率和计算效果产生重要影响,因此本文针对有限差分方法中频散问题、稳定性问题和边界条件进行了具体分析和研究,给出了任意偶数阶差分精度的纵波、横波频散关系式,详细推导和建立了差分格式的稳定性条件。采用完全匹配层(PML)吸收边界条件进行边界影响的研究。通过大量的数值计算表明,采用完全匹配层吸收边界条件,只需半个波长厚度的PML,就可以很好地吸收边界反射波,其吸收效果远远优于阻尼衰减边界条件。对各种模型数据进行地震记录模拟和照明计算,取得了满意的结果。
通过进一步研究还发现:单程声波方程的计算结果信噪比高,仅含有一次反射波,便于波场识别和分析,效率很高,但是单程波算子存在倾角限制,对于横向速度变化较大的模型误差较大,并且反射界面的反射系数是近似的;双程波动方程交错网格有限差分方法则可以处理横向速度任意变化的模型,模拟精度很高,并且界面反射系数不存在近似。若不需要考虑转换波问题,可采用双程声波方程进行计算,计算速度较快,仅含有纵波。双程弹性波方程的结果和实际情况最为接近,波场信息丰富。
In the process of petroleum seismic exploration, wave-equation forward modeling and illumination analysis both have great significance to help people understand and analyze the seismic wave propagation law, provide guidance for seismic data acquisition and seismic survey design, improve seismic data processing quality, reduce the uncertainty of subsurface velocity modeling and determine interpretation scheme of oil and gas reservoir.
Based on previous researches and following the order from simple to complex, I conduct a further study on the seismic wave-equation forward modeling schemes and illumination analysis methods based on the one-way acoustic wave equation, two-way acoustic wave equation and two-way elastic wave equation, and then program to realize them respectively. The computation results of different velocity models indicate that the methods are correct and satisfied.
At first, I make a research on the one-way acoustic wave equation seismic numerical simulation and illumination analysis. The one-way acoustic wave equation modeling is an simulation method which extrapolate wave field in the frequency wave-number domain and correct the perturbation due to transversely variable velocity in the frequency-space domain. By using SSF operator and FFD operator, Zero-offset synthetic records are gained. On the basis of positioning principle, I develop a faster method to get nonzero- offset common shot records that receive the extrapolated wave field on the surface of the model directly at each geophone, without extra lateral stacking. According to this kind of method, P-P common shot records and P-SV common shot records are simulated effectively. Based on one-way seismic simulation, seismic illumination analysis is conducted through which the results of Zero-offset seismic illumination, source illumination, source-receiver illumination and plane wave source illumination are achieved. The conclusions are that zero-offset seismic illumination is an ideal vertical incidence illumination, the results of source illumination and two-side receiving illumination are similar,while the one-side receiving case is different from them,in the case of small incident angles, SSF operator and FFD operator have no major difference, while not the case when the incident angle is greater than 40 degrees.The same as one-way wave simulation, the one-way wave seismic illumination has high efficiency.
Then I make a research on the seismic numerical simulation and illumi- nation analysis based on two-way acoustic wave equation and two-way elastic wave equation. The numerical simulation methods of these two kinds of wave equations are similar. Adopting their own one order velocity-stress wave equation, I deduce their staggered-grid finite-difference algorithm in detail and program them correctly.Considering the intrinsic problems of finite-difference technique such as numerical dispersion, stability problem and boundary reflection, I give out the grid-dispersion relations for the P and S waves, stability condition and the discrete formula of perfectly matched layers of arbitrary even order accuracy, analyze detailedly the influence of different stability parameter, different passion ratio and different spatial sampling ratio on the grid-dispersion.According to the theoretical analysis, grid discrete slows the wave propagation, and along the axis, the numerical dispersion is most severe and decreases as the incident angle increasing,in the diagonal direction the dispertion is lowest.The smaller is the stability parameter,the more severe is the dispertion.Then I adopt the perfectly matched absorbing layer to reduce the boundary reflection.Through a large amount of experiments,I find that half of the p-wave length of the PML layers can absorb the boundary reflection effectively,and then,I do comparisons of two different boundary conditions and two kind of different modeling accuracy. After numerical simulation, source illumination is computed.Based on two kinds of lens with high velocity and low velocity and acoustic wave equation, source illumination is computed, which reveals the defocusing effect of high velocity and focusing effect of low velocity. The multiple sources illumination of the model is even. Adopting poynting's theorem,I compute the elastic illumination vector in the first time.Two-way elastic equation can describe wave propagation and seismic illumination more accourately. The illumation changes obviously as the source position.So in order to acquisite high quality seismic data, we should change the position with even and high illumation to excite and receive seismic wave.
According to the above research, conclusions are as follows: the one-way wave equation can provide synthetic records with high SNR, including only reflected waves or diffracted waves, which is useful for wave field recognition and analyzation. The computation efficiency is also very high, while the coefficient of reflection is approximate. Two-way acoustic wave equation can deal with the coefficient of reflection correctly and provide accurate wave field. The two-way elastic wave equation gives the most realistic results and can model many kinds of waves in the cost of computation. Thus, we can choose the proper type of wave equation to use in the practical work.
引文
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