补偿吸收衰减的地质雷达数据叠前偏移方法研究
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摘要
至今,在使用显式外推算子的地质雷达数据叠前深度偏移中几乎都忽略了电磁波的吸收,受野外数据采集方法的限制,常用的偏移方法也主要解决共偏移距数据问题。本文提出了针对多偏移距数据,在频率—空间域叠前深度偏移中考虑吸收效应的方法,分别从电磁波方程和声波方程实现偏移,两种方法均为基于波动方程理论,均考虑介质吸收特性的有限差分算法,在波场外推中同时实现对吸收衰减的补偿。
在获得合成雷达波数据剖面时,从麦克斯韦方程组出发,利用微分形式方程组的旋度方程推导正演模拟的FDTD差分格式。求得满足数值稳定性的Courant条件后设定时间、空间网格的单位元胞尺寸,采用Yee网格进行网格的剖分,设置正演模型的空间电磁参数。为了在有限的研究区域获得无限空间的波场模拟,在区域边界处引入PML吸收边界,并获得了较好的效果。
由麦克斯韦方程出发,推导含传导电流项的频率域电磁波方程,参照电导率参数分析电磁波的速度、吸收衰减与频率之间的关系,得到衰减介质中电磁波的传播规律。认为在高频低电导率、低相对介电常数的情况下,在较高的频率范围内容易达到电磁波的“平台效应”状态,而不同时满足这些条件时,电磁波在衰减介质中的频散现象则不能忽略。设计了在介质内部模拟直达波数据的方式,分别在无吸收性和中等吸收性介质中模拟数据,将其用于讨论电磁波在横向上的衰减特征。
本文由含传导电流项的麦克斯韦方程出发推导有限差分波场外推算子。为了考虑横向速度变化的问题,在空间域设计三阶精度的褶积算子,该算子包含吸收衰减与复速度的函数关系,由它获得同时延拓波场值和波场垂向导数的反延拓算子矩阵,通过反延拓对波场传播效应的消除作用,在完成有限差分叠前深度偏移的同时,实现对吸收衰减的补偿。
在无吸收的情况下,对三种模型的合成数据进行电磁波方程偏移,可知该方法对于不精确的速度结构,也能够使尺寸较小的绕射体准确归位,水平层成像结果平直光滑,对倾斜界面拐点的绕射能量也能很好地归位,该方法均具有较好的横向和纵向分辨率。讨论了双边激发对于充分反映介质横向信息的优势。在有吸收的情况下,对合成数据进行不考虑吸收衰减和补偿吸收衰减的偏移,表明该方法对吸收引起的能量衰减实现补偿的同时,能够改善由吸收引起的纵向拉伸畸变,可以在一定程度上消除同相轴不合理的上翘或下拉现象,完成数据的正确归位。对含随机噪声数据的偏移表明,该方法能够实现在反延拓的过程中,以反褶积过程对噪声进行的滤波是有效的,在较低信噪比的条件下仍具有较好的抗噪效果,体现了频率域延拓的优势。
对实测数据进行补偿吸收衰减的电磁波方程偏移表明,该方法能够补偿微弱的层位信息,按照衰减的程度进行补偿,改善同相轴在横向上连续性,补偿能量的同时,提高纵向分辨力。讨论了叠加处理对干扰信息压制的效果。提出以频谱比曲线确定合理的补偿偏移频带宽度。
由声波方程出发,分析其代替电磁波方程的近似情况,并给出单独延拓波场值的有限差分叠前偏移算法。两种方法的偏移效果对比发现,电磁波方程对于深部衰减较大的部分能量能够实现补偿,而声波方程考虑吸收项时具有近似性,只能对衰减较小的信息发挥振幅加强、提高分辨率的作用,对于深层信息补偿能力不足。
In prestack depth migration using explicit extrapolators, the attenuation of the electromagnetic wave for ground penetrating radar (GPR) has been almost neglected so far. Conventional migration techniques aim at processing common-offset data. This paper presents one method for multi offset data prestack depth migration with considering absorption effect in frequency-space domain. Migration can be realized separately from electromagnetic wave equation and wave equation. The two methods are both based on wave equation theory and consider medium absorption finite difference method and realize compensation to absorption attenuation in the course of wave extrapolation.
The finite-difference time-domain (FDTD) scheme for wave field simulation can be derived from the Maxwell’s curl equations. The size of a cell and the interval of time are determined by Courant condition that is a numerical stability condition. In order to eliminate the effects of boundaries, the perfectly matched layer (PML) absorption boundary condition is used in this paper. The absorption effect of the PML boundary is very nice.
The electromagnetic wave equation in frequency field can be derived from Maxwell’s curl equations and electromagnetic wave diffuse rule in attenuation medium can be obtained from analyzing the relationships of electromagnetic wave velocity and absorption attenuation and frequency by consulting conductance parameter. Upper frequency range can be easy to arrive at electromagnetic wave“flat domino effect”in condition of high frequency low conductance. If the condition can’t be satisfied, the frequency dispersion can’t be ignored. In zero absorbency and middle absorbency medium separately design simulated direct wave data system in medium bosom and discuss electromagnetic wave attenuation character in lateral direction.
This paper derives finite difference wave field extrapolate operator from Maxwell equation with conduct current. Considering lateral velocity transformation design three step precision convolution operator which contain the function of absorption attenuation and complex velocity. Then obtain continuation wave field and vertical derivative inverse continuation matrix and realize not only finite difference prestack depth migration but also compensation to absorption attenuation by eliminating wave field propagation with inverse continuation.
Under the condition without absorption, use electromagnetism wave equation migration for 3 kinds of synthetic data models. This method can also make diffraction body of lesser size accurate homing for not accurate speed structure and make horizontal layer result level smooth. For inclining diffraction energy of interface inflection point it also can well homing and this method has better and lateral and longitudinal resolution capacity. It discusses the advantage of double excitation for fully reflection medium lateral information. Under the condition that has absorption, for composing data, we carry out the migration without considering absorption attenuation and compensation absorption attenuation. It shows that this method can realize energy attenuation absorption arouses compensation, at the same time, it can improve longitudinal tension distortion resulting from absorption and it can eliminate up and down phenomenon of phase axis in some degree and complete the correct homing of data. The migration for data with stochastic noise shows that this method can be used in the course of inverse extrapolation and it is effective to use deconvolution for filtering noise and under the condition of very low signal-to-noise ratio it still has better effect and it embodies advantage of extrapolation in frequency field.
The electromagnetism wave equation migration that compensates absorption attenuation for actual measurement data shows that this method can compensate weak layer position information and compensate according to the level of attenuation and improve phase axis in lateral continuity and increase longitudinal resolution while compensating energy. It discusses the effect of stack to suppressing for disturbing information and put forward the curve of frequency spectra ratio determines the reasonable compensation migration bandwidth.
Based on the equation of sound wave, we analyze its approximation after substituting electromagnetic wave equation and give finite difference prestack migration with separate extrapolation wave field. The results of two methods contrast we discover that electromagnet wave equation can be recovered for the partial energies of greater deep attenuation, while the equation of sound wave without absorption and it can only strengthen amplitude and enhance differentiate to less attenuation information and the compensation ability is low for deep layer information.
在获得合成雷达波数据剖面时,从麦克斯韦方程组出发,利用微分形式方程组的旋度方程推导正演模拟的FDTD差分格式。求得满足数值稳定性的Courant条件后设定时间、空间网格的单位元胞尺寸,采用Yee网格进行网格的剖分,设置正演模型的空间电磁参数。为了在有限的研究区域获得无限空间的波场模拟,在区域边界处引入PML吸收边界,并获得了较好的效果。
由麦克斯韦方程出发,推导含传导电流项的频率域电磁波方程,参照电导率参数分析电磁波的速度、吸收衰减与频率之间的关系,得到衰减介质中电磁波的传播规律。认为在高频低电导率、低相对介电常数的情况下,在较高的频率范围内容易达到电磁波的“平台效应”状态,而不同时满足这些条件时,电磁波在衰减介质中的频散现象则不能忽略。设计了在介质内部模拟直达波数据的方式,分别在无吸收性和中等吸收性介质中模拟数据,将其用于讨论电磁波在横向上的衰减特征。
本文由含传导电流项的麦克斯韦方程出发推导有限差分波场外推算子。为了考虑横向速度变化的问题,在空间域设计三阶精度的褶积算子,该算子包含吸收衰减与复速度的函数关系,由它获得同时延拓波场值和波场垂向导数的反延拓算子矩阵,通过反延拓对波场传播效应的消除作用,在完成有限差分叠前深度偏移的同时,实现对吸收衰减的补偿。
在无吸收的情况下,对三种模型的合成数据进行电磁波方程偏移,可知该方法对于不精确的速度结构,也能够使尺寸较小的绕射体准确归位,水平层成像结果平直光滑,对倾斜界面拐点的绕射能量也能很好地归位,该方法均具有较好的横向和纵向分辨率。讨论了双边激发对于充分反映介质横向信息的优势。在有吸收的情况下,对合成数据进行不考虑吸收衰减和补偿吸收衰减的偏移,表明该方法对吸收引起的能量衰减实现补偿的同时,能够改善由吸收引起的纵向拉伸畸变,可以在一定程度上消除同相轴不合理的上翘或下拉现象,完成数据的正确归位。对含随机噪声数据的偏移表明,该方法能够实现在反延拓的过程中,以反褶积过程对噪声进行的滤波是有效的,在较低信噪比的条件下仍具有较好的抗噪效果,体现了频率域延拓的优势。
对实测数据进行补偿吸收衰减的电磁波方程偏移表明,该方法能够补偿微弱的层位信息,按照衰减的程度进行补偿,改善同相轴在横向上连续性,补偿能量的同时,提高纵向分辨力。讨论了叠加处理对干扰信息压制的效果。提出以频谱比曲线确定合理的补偿偏移频带宽度。
由声波方程出发,分析其代替电磁波方程的近似情况,并给出单独延拓波场值的有限差分叠前偏移算法。两种方法的偏移效果对比发现,电磁波方程对于深部衰减较大的部分能量能够实现补偿,而声波方程考虑吸收项时具有近似性,只能对衰减较小的信息发挥振幅加强、提高分辨率的作用,对于深层信息补偿能力不足。
In prestack depth migration using explicit extrapolators, the attenuation of the electromagnetic wave for ground penetrating radar (GPR) has been almost neglected so far. Conventional migration techniques aim at processing common-offset data. This paper presents one method for multi offset data prestack depth migration with considering absorption effect in frequency-space domain. Migration can be realized separately from electromagnetic wave equation and wave equation. The two methods are both based on wave equation theory and consider medium absorption finite difference method and realize compensation to absorption attenuation in the course of wave extrapolation.
The finite-difference time-domain (FDTD) scheme for wave field simulation can be derived from the Maxwell’s curl equations. The size of a cell and the interval of time are determined by Courant condition that is a numerical stability condition. In order to eliminate the effects of boundaries, the perfectly matched layer (PML) absorption boundary condition is used in this paper. The absorption effect of the PML boundary is very nice.
The electromagnetic wave equation in frequency field can be derived from Maxwell’s curl equations and electromagnetic wave diffuse rule in attenuation medium can be obtained from analyzing the relationships of electromagnetic wave velocity and absorption attenuation and frequency by consulting conductance parameter. Upper frequency range can be easy to arrive at electromagnetic wave“flat domino effect”in condition of high frequency low conductance. If the condition can’t be satisfied, the frequency dispersion can’t be ignored. In zero absorbency and middle absorbency medium separately design simulated direct wave data system in medium bosom and discuss electromagnetic wave attenuation character in lateral direction.
This paper derives finite difference wave field extrapolate operator from Maxwell equation with conduct current. Considering lateral velocity transformation design three step precision convolution operator which contain the function of absorption attenuation and complex velocity. Then obtain continuation wave field and vertical derivative inverse continuation matrix and realize not only finite difference prestack depth migration but also compensation to absorption attenuation by eliminating wave field propagation with inverse continuation.
Under the condition without absorption, use electromagnetism wave equation migration for 3 kinds of synthetic data models. This method can also make diffraction body of lesser size accurate homing for not accurate speed structure and make horizontal layer result level smooth. For inclining diffraction energy of interface inflection point it also can well homing and this method has better and lateral and longitudinal resolution capacity. It discusses the advantage of double excitation for fully reflection medium lateral information. Under the condition that has absorption, for composing data, we carry out the migration without considering absorption attenuation and compensation absorption attenuation. It shows that this method can realize energy attenuation absorption arouses compensation, at the same time, it can improve longitudinal tension distortion resulting from absorption and it can eliminate up and down phenomenon of phase axis in some degree and complete the correct homing of data. The migration for data with stochastic noise shows that this method can be used in the course of inverse extrapolation and it is effective to use deconvolution for filtering noise and under the condition of very low signal-to-noise ratio it still has better effect and it embodies advantage of extrapolation in frequency field.
The electromagnetism wave equation migration that compensates absorption attenuation for actual measurement data shows that this method can compensate weak layer position information and compensate according to the level of attenuation and improve phase axis in lateral continuity and increase longitudinal resolution while compensating energy. It discusses the effect of stack to suppressing for disturbing information and put forward the curve of frequency spectra ratio determines the reasonable compensation migration bandwidth.
Based on the equation of sound wave, we analyze its approximation after substituting electromagnetic wave equation and give finite difference prestack migration with separate extrapolation wave field. The results of two methods contrast we discover that electromagnet wave equation can be recovered for the partial energies of greater deep attenuation, while the equation of sound wave without absorption and it can only strengthen amplitude and enhance differentiate to less attenuation information and the compensation ability is low for deep layer information.
引文
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