摘要
为了能从解析近似的角度研究海洋声学环境对反射地震观测数据的影响,尤其是海面对自由表面多次波和鬼波的影响,对从1951年到2024年上半年公开发表的海面散射文献进行了整理和筛选.作为这项工作的总结,分别介绍了海面散射研究的简要历史、“冻结”海面模型、主要海面散射理论、常用海面散射平均场和平均反射系数公式以及对这些公式的数值和实验验证.此外,还建立了基于Neumann级数和Rytov级数的平均场公式,并给出了不同震源深度所对应的掠入射炮检距.本文得到的主要认识和结论为:(1)海面对反射地震观测数据的影响机制有两种;一种为粗糙面相干反射,由粗糙面平均反射系数刻画;另一种为非相干后向散射,由粗糙面后向散射系数刻画.(2)除了Kirchhoff反射系数以外,其他海面散射理论所给出的平均反射系数均为两项之和,一项为镜像反射系数,另一项为与海面形状有关的高通滤波算子;除微扰反射系数外,高通滤波算子的形式只与Rayleigh参数和海面的功率密度谱有关,与相关长度无关;微扰反射系数中的高通滤波算子与Rayleigh参数和相关长度与波长的比值有关,只能在远大于波长以及远小于波长的条件下得到简单的表达式;当相关长度与波长相当时,必须利用反射系数的积分表达式,从而只能得到数值解;Kirchhoff反射系数为以Rayleigh参数为指数的e指数函数,与海面形状无关.(3)在Rayleigh参数比较小时,除微扰理论外,所有理论给出的陡倾角(反射角小于等于30°)平均反射系数均趋近于Kirchhoff反射系数,与相关长度无关,但是掠入射(入射角接近于90°)反射系数与Kirchhoff反射系数有所不同;当Rayleigh参数趋近于零时,粗糙海面趋近于光滑海面,所有理论给出的陡入射反射系数均趋近于-1,与相干长度无关;这个结论对于掠入射不成立.(4)当相关长度大于波长时,海面陡倾角微扰反射系数只与平均波高有关,所含有的高通滤波算子为关于时间的二阶导数算子;海面缓倾角(反射角大于30°)微扰反射系数与海面形状有关,所含高通滤波算子为关于时间的3/2阶导数算子;当相干长度与波长相当时,高通滤波算子为形式复杂的积分表达式,难以化为简单的滤波算子;当相干长度小于波长时,二阶近似下的高通滤波算子为关于时间的一阶导数和二阶导数的组合,一阶近似下的滤波算子为关于时间的一阶导数.(5)自由表面多次波和检波点鬼波主要为海面上的陡倾角反射;震源鬼波主要为海面上的缓倾角反射;震源-检波点鬼波的震源侧反射一般为缓倾角反射,而检波点侧的海面反射一般为陡倾角反射.(6)在反射地震理论中常用的Kirchhoff近似和射线理论完全可用于预测海面反射场,条件是要选取合适的反射系数和能够进行理论系综平均的海面模型.(7)若利用随机生成的海面进行海面散射数值模拟,则应利用MonteCarlo法进行系综平均.
For investigating the influence of the ocean acoustic environment on the reflection seismic data analytically,especially for investigating the influence of the sea surface on the surface-related multiples and the ghosts analytically,the author has made a survey of the open literature on scattering of acoustic waves at the sea surface,which is published during the period from 1951 to the first half of 2024,and screened out some results relevant to the marine reflection seismics.For summarizing the works,the author has included the following materials:(1)a brief history of the research work on the sound wave scattering at the sea surface;(2)some relevant“frozen”sea surface models based on the ocean wave spectrum;(3)dominant theories for treating the sound wave scattering at the sea surface;(4)widely used formulas for the average scattered fields and for the average reflection coefficients in ocean acoustics;(5)a brief summary of the numerical and the experimental validations of the formulas for the scattered fields and for the reflection coefficients,respectively.Furthermore,the author has derived formulas for the average fields scattered at the sea surface by using the corresponding Neumann and Rytov series,respectively,and computed the source-receiver offsets for different source depths,at which the incident waves hit the sea surface at grazing angles.The findings and the conclusions obtained from the above-presented materials are:(1)the mechanisms of the influence of the sea surface on the reflection seismic data are twofold,one is the coherent reflection at rough surfaces,described by the average reflection coefficient,the other is the incoherent backscattering from rough surfaces,formulated as the incoherent backscattering coefficient;(2)except the one given by the Kirchhoff approximation,all the sea surface reflection coefficients have the form of a sum with two terms,one is the mirror reflection coefficient,the other is a high-pass filtering operator which depends on the sea surface model used,and the form of the high-pass filtering operator depends on both the Rayleigh parameter and the power density spectrum of the sea surface,except the reflection coefficient obtained by using the small perturbation theory,which depends on the Rayleigh parameter and on the ratio of the correlation length of the sea surface to the wavelength as well,and only in the case where the ratio is larger than or smaller than 1 is a simple formula available,otherwise the complete integral formulation must be used and only numerical results are obtainable;the Kirchhoff reflection coefficient has the form of an exponential function with the Rayleigh parameter as its exponent,which is independent of the form of the sea surface;(3)when the Rayleigh parameter is small enough,all the steep reflection(the reflection angle is smaller than or equal to 30°)coefficients approach to the one given by the Kirchhoff approximation except the reflection coefficient coming from the perturbation theory,independent of the correlation length of the sea surface,but this is not true for the grazing reflection(the reflection angle is near 90°)coefficient that is different from the Kirchhoff reflection coefficient;when the Rayleigh parameter goes to zero,the rough sea surface approaches to a smooth sea surface,and the steep angle reflection coefficient from all the theories approaches to-1,independent of the correlation length of the sea surface,but this is not true for grazing reflections;(4)when the correlation length is larger than the wavelength,the perturbation reflection coefficient for steep reflections depends only on the average wave height and the corresponding high-pass filter is a differentiation operator of second order with respect to the time,independent of the correlation length of the sea surface;and the perturbation reflection coefficient for gentle reflections(the reflection angle is larger than 30°)depends on the sea surface model used and has the form of a differentiation operator of 3/2 order with respect to the time;when the correlation length is close to the wavelength,the form of the high-pass filtering operator is given as a complex integral and cannot be reduced to a simple form;when the correlation length is smaller than the wavelength,the second-order approximated high-pass filtering operator is a combination of the first-and the second-order differentiation operator with respect to the time,and the first-order approximated high-pass filtering operator is a first-order differentiation operator with respect to the time;(5)the surface-related multiples and the receiver ghosts are caused mainly by the steep incident waves,the source ghosts are caused mainly by grazing incidence,and the source-receiver ghosts are caused by the grazing incidence at the source side and by the steep incident at the receiver side,respectively;(6)the Kirchhoff approximation widely used in reflection seismics and the ray formulation can be used for computing the field scattered at the sea surface,but they must have a proper reflection coefficient included,together with a sea surface model for which an ensemble average can be performed analytically;(7)the Monte Carlo method should be used for obtaining the ensemble averaged field when a randomly generated sea surface is used for numerical simulation of the scattered field at the sea surface.
作者
孙建国
SUN JianGuo(College of Geo-Exploration Science and Technology,Jilin University,Changchun 130026,China)
出处
《地球物理学报》
北大核心
2025年第6期2003-2027,共25页
Chinese Journal of Geophysics
基金
国家重点研发计划(2019YFC0312004)
国家自然科学基金(41974135)资助.
关键词
海面散射
平均场
平均反射系数
自由表面多次波
鬼波
Scattering at the sea surface
Average field
Average reflection coefficient
Surface-related multiples
Ghost
