南北地震带北段上地幔速度结构成像(Ⅰ)——方法与原理

本文详细讨论了利用P_n波走时资料对莫霍面的慢度场层析成像的方法与原理。在地震波慢度场的非均匀分布相对背景场为一挠动量的情况下,其走时为背景场分量与挠动场分量的线性迭加,因此,从观测走时中可提取出相对背景场的异常量。对走时异常分量的表达式作适当的变换即可得出拉冬变换形式,运用反投影重建或拉冬逆变换,可以直接求出慢度场的分布。     

Time-domain hyperbolic Radon transform for separation of P-P and P-SV wavefields

A time-domain hyperbolic Radon transform based method for separating multicomponent seismic data into P-P and P-SV wavefields is presented. This wavefield separation method isolates P-P and P-SV wavefields in the Radon panel due to their differences in slowness, and an inverse transform of only part of the data leads to separated wavefields. A problem of hyperbolic Radon transform is that it works in the time domain entailing the inversion of large operators which is prohibitively time-consuming. By applying the conjugate gradient algorithm during the inversion of hyperbolic Radon transform, the computational cost can be kept reasonably low for practical application. Synthetic data examples prove that P-P and P-SV wavefield separation by hyperbolic Radon transform produces more accurate separated wavefields compared with separation by high-resolution parabolic Radon transform, and the feasibility of the proposed separation scheme is also verified by a real field data example.     

Fast hyperbolic deconvolutive Radon transform using generalized Fourier slice theorem

The hyperbolic Radon transform has a long history of applications in seismic data processing because of its ability to focus/sparsify the data in the transform domain. Recently, deconvolutive Radon transform has also been proposed with an improved time resolution which provides improved processing results. The basis functions of the (deconvolutive) Radon transform, however, are time-variant, making the classical Fourier based algorithms ineffective to carry out the required computations. A direct implementation of the associated summations in the time–space domain is also computationally expensive, thus limiting the application of the transform on large data sets. In this paper, we present a new method for fast computation of the hyperbolic (deconvolutive) Radon transform. The method is based on the recently proposed generalized Fourier slice theorem which establishes an analytic expression between the Fourier transforms associated with the data and Radon plane. This allows very fast computations of the forward and inverse transforms simply using fast Fourier transform and interpolation procedures. These canonical transforms are used within an efficient iterative method for sparse solution of (deconvolutive) Radon transform. Numerical examples from synthetic and field seismic data confirm high performance of the proposed fast algorithm for filling in the large gaps in seismic data, separating primaries from multiple reflections, and performing high-quality stretch-free stacking.     

多项式Radon变换

Radon变换是数据处理中广泛应用的一种方法技术.本文介绍了次数为“2”的多项式Radon变换.讨论了多项式正反Radon变换的公式、实现方法和有关计算参数的选择.通过理论模型试算，对多项式、线性、抛物线三种Radon变换进行了比较.对实际资料进行了多项式Radon变换处理，给出了消除地震反射记录中线性干扰的算例.     

Multiple attenuation using λ-f domain high-resolution Radon transform

The parabolic Radon transform has been widely used in multiple attenuation. To further improve the accuracy and efficiency of the Radon transform, we developed the 2- fdomain high-resolution Radon transform based on the fast and modified parabolic Radon transform presented by Abbad. The introduction of a new variable 2 makes the transform operator frequency-independent. Thus, we need to calculate the transform operator and its inverse operator only once, which greatly improves the computational efficiency. Besides, because the primaries and multiples are distributed on straight lines with different slopes in the 2-fdomain, we can easily choose the filtering operator to suppress the multiples. At the same time, the proposed method offers the advantage of high-resolution Radon transform, which can greatly improve the precision of attenuating the multiples. Numerical experiments suggest that the multiples are well suppressed and the amplitude versus offset characteristics of the primaries are well maintained. Real data processing results further verify the effectiveness and feasibility of the method.     

High-resolution frequency-domain Radon transform and variable-depth streamer data deghosting

Receiver ghost reflections adversely affect variable-depth streamer (VDS) data acquisition. In addition, the frequency notches caused by the interference between receiver ghosts and primary waves strongly affect seismic data processing and imaging. We developed a high-resolution Radon transform algorithm and used it to predict receiver ghosts from VDS data. The receiver ghost reflections are subtracted and removed from the raw data. We propose a forward Radon transform operator of VDS data in the frequency domain and, based on the ray paths of the receiver ghosts, we propose an inverse Radon transform operator. We apply the proposed methodology to model and field data with good results. We use matching and subtracting modules of commercially available seismic data processing software to remove the receiver ghosts. The frequency notches are compensated and the effective frequency bandwidth of the seismic data broadens.     

三维Radon变换的一种快速解析方法

3D Radon变换及其反变换是X-CT三维图像重建理论的核心,它在其他许多学科领域也有广泛应用。3D Radon变换的表达式是一个三重积分,按照定义直接计算相当费时。为此,研究一种新的快速的方法实现3D Radon变换,对X-CT图像重建理论及相关领域的发展有重要意义。本文以算法仿真常用椭球模型为基础,通过求解椭球模型与空间任意平面的面积,实现了用解析的方法快速得到模型的Radon变换,进一步比较了它与传统方法的优缺点,最后根据Radon反变换重建出原物体模型;计算机仿真结果验证了这种方法的正确。     

基于波动方程预测和双曲Radon变换联合压制表面多次波

基于波动方程预测的表面多次波压制方法可处理复杂地下介质的地震资料,但计算成本较高.基于滤波的多次波压制方法计算效率较高,但其成功应用仅局限于一次波和多次波有明显时差差别的地震数据,对来自速度逆转等复杂介质数据则较难获得满意的压制效果.本文将波动方程预测的反馈迭代法和滤波法有效结合,采用GPU(图形处理器)和CPU协同并行加速计算粗略预测表面多次波,随后在双曲Radon域比较分析原始数据和预测的多次波,设计合理有效的Butterworth型自适应滤波器,滤出原始数据Radon域中的多次波能量,进行Radon反变换后,在时空域将多次波从原始数据中减去,得多次波压制结果.文中对理论模拟的单炮数据、复杂的SMAART模型以及实际地震数据进行了计算,结果表明,结合基于波动方程预测和双曲Radon变换的方法有效突破了两种方法各自的局限性,可高效高精度地压制复杂地下介质的表面多次波.     

Restoration of missing offsets by parabolic Radon transform1

Restoration of missing offsets and trace interpolation is an interesting and important problem in seismic data processing. Based on the parabolic Radon transform, a method is presented for missing offset restoration, resampling and regularization of prestack individual CMP gathers. The method is also valid for resampling spatially aliased seismic data. The method is based on the parabolic assumption of the seismic events which is generally verified after a partial NMO correction in the CMP organization of the data. The essence of the method consists of a band-limited forward parabolic Radon transform of the data containing zero traces at the missing offset locations. The curvature range is chosen to map properly the coherent energy while the zero traces map beyond that range. After inverse transform the originally zero traces are partly filled with information. Several iterations of forward and inverse transform, every time replacing the zero traces in the original gather with the partially reconstructed ones, almost fully restore the zero traces. Efficient and fast algorithms can be built up to process data having a uniform geometry. Examples on synthetic as well as on field data demonstrate clearly the robustness of the method.     

High‐resolution Radon transforms for improved dipole acoustic imaging

Imaging using dipole acoustic logging reflections has become a research topic of increasing interest in recent years. Extracting reflections from the whole waveform is both important and extremely difficult because the reflections are obscured by large‐amplitude direct waves. A method of wavefield separation based on high‐resolution Radon transforms has been applied to separate the reflected waves. First, an analysis of the common offset gathers shows that the linear Radon transform can be used to separate the direct and reflected wave fields. However, traditional linear Radon transforms cannot focus the wave event using the least squares method. An improved high‐resolution linear Radon transform is achieved using the principles of maximum entropy and Bayesian methods based on previous studies. The separation method is tested using synthetic data for hard and soft formations, a void model, and a fault model. The high‐resolution Radon transform method is used to process a field dataset and exhibits improved results compared with those of the standard method.     

3D parallel inversion of time-domain airborne EM data

To improve the inversion accuracy of time-domain airborne electromagnetic data, we propose a parallel 3D inversion algorithm for airborne EM data based on the direct Gauss–Newton optimization. Forward modeling is performed in the frequency domain based on the scattered secondary electrical field. Then, the inverse Fourier transform and convolution of the transmitting waveform are used to calculate the EM responses and the sensitivity matrix in the time domain for arbitrary transmitting waves. To optimize the computational time and memory requirements, we use the EM “footprint” concept to reduce the model size and obtain the sparse sensitivity matrix. To improve the 3D inversion, we use the OpenMP library and parallel computing. We test the proposed 3D parallel inversion code using two synthetic datasets and a field dataset. The time-domain airborne EM inversion results suggest that the proposed algorithm is effective, efficient, and practical.     

快速3D抛物Radon变换地震数据保幅重建

为解决3D AVO地震数据快速保幅重建问题,在传统3D抛物Radon变换的基础上提出一种3D快速高阶抛物Radon变换方法.该方法将传统抛物Radon变换与正交多项式相结合,通过正交多项式系数描述地震数据AVO信息,确保重建后的地震数据具有良好保幅效果.同时,该方法引入新变量λ_x=q_xf和λ_y=q_yf,通过对q_xf和q_yf的整体采样,消除了3D高阶抛物Radon变换算子对频率的依赖,使变换算子的求逆过程仅需计算一次,大大节省计算时间.理论模型和实际地震资料的处理结果表明,该方法重建效率高,保幅效果良好.     

地球构造反演问题的新途径

本文讨论地球内部构造反演问题的某些新途径.其内容如下:地球构造反问题与固有值反问题;反散射问题中介质间断性的成象与因果广义Radon变换,包含地球构造反问题的新提法,反散射问题的线性化,古典Radon变换与广义Radon变换,线性化反问题的渐近解,渐近解和偏移格式.     

Radon Transform Methods and Their Applications in Mapping Mantle Reflectivity Structure

This paper reviews the fundamentals of Radon-based methods using examples from global seismic applications. By exploiting the move-out or curvature of signal of interest, Least-squares and High-resolution Radon transform methods can effectively eliminate random or correlated noise, enhance signal clarity, and simultaneously constrain travel time and ray angles. The inverse formulation of the Radon transform has the added benefits of phase isolation and spatial interpolation during data reconstruction. This study presents a ‘cookbook’ for Radon-based methods in analyzing shear wave bottom-side reflections from mantle interfaces, also know as SS precursors. We demonstrate that accurate and flexible joint Radon- and frequency-domain approaches are particularly effective in resolving the presence and depth of known and postulated mantle reflectors.     

沿圆曲线的Radon变换数值解

研究具有紧支集且在支集内连续的二元函数沿上半圆曲线的Radon变换反演问题。基于对投影函数的Fourier变换，反演问题可以归结为具有弱奇性及震荡核的Abel积分方程的求解。我们证明了当圆曲线中心及半径在一定范围内变化时，在已知沿上半圆曲线的Radon变换情况下，这个积分方程的解具有唯一性，并给出了消除Abel积分方程弱奇性的数值方法。在考虑投影数据噪声的情况下，给出了多次加权改善系数矩阵条件数稳定的数值方法，并通过数值模拟验证所提出方法的有效性。      

Inversion-based deblending using migration operators

In this paper, we compare the denoising- and inversion-based deblending methods using Stolt migration operators. We use Stolt operator as a kernel to efficiently compute apex-shifted hyperbolic Radon transform. Sparsity promoting transforms, such as Radon transform, can focus seismic data into a sparse model to separate signals, remove noise or interpolate missing traces. Therefore, Radon transforms are a suitable tool for either the denoising- or the inversion-based deblending methods. The denoising-based deblending treats blending interferences as random noise by sorting the data into new gathers, such as common receiver gather. In these gathers, blending interferences exhibit random structures due to the randomization of the source firing times. Alternatively, the inversion-based deblending treats blending interferences as a signal, and the transform models this signal by incorporating the blending operator to formulate an inversion problem. We compare both methods using a robust inversion algorithm with sparse regularization. Results of synthetic and field data examples show that the inversion-based deblending can produce more accurate signal separation for highly blended data.     

各向异性Radon变换及其在多次波压制中的应用

即使采用分辨率很高的双曲Radon变换,对速度各向异性发育介质及长偏移距情况下的地震数据,其Radon域内能量仍不收敛.为了克服此难题,我们在Radon变换的积分路径中考虑了非双曲走时的影响,通过引入非双曲时差公式中的各向异性非椭圆率η参数,可以准确描述出长偏移距条件下来自同一层位的时距曲线,并推导了由偏移距、慢度、非椭圆率三参数控制的积分曲线正反变换公式,我们称之为各向异性Radon变换.离散化求解时,各向异性Radon变换是时变的,频率域快速算法已不适用,本文采用了最优相似系数加权Gauss-Seidel迭代算法,保持其计算精度的同时也有较高的计算效率.将此方法应用在模型数据以及实际长偏移距海上地震数据的多次波压制处理中,收到了较好的处理效果.     

3D高阶抛物Radon变换地震数据保幅重建

本文结合传统3D抛物Radon变换（PRT）和AVO数据正交多项式拟合,给出了3D高阶抛物Radon变换方法（HOPRT）.该变换增加了描述AVO数据变化的梯度信息和曲率信息,拓展了传统3D抛物Radon变换方法,使其在具有AVO特征的数据重建中具有更高的准确度,从而提高AVO分析的可靠性.文中给出了3D高阶抛物Radon变换进行地震数据保幅重建的流程.理论模型和实际地震资料的重建结果显示了本文方法的优点.     

井孔高分辨率Radon变换算子研究

本文针对井间和3D VSP波场的线性特征,研究井孔地震波场线性高分辨率Radon变换算子,用于井孔地震波场分析与纵横波分离.在Radon变换原理分析基础上,采用基于柯西分布的高分辨率线性Radon变换对井孔数据进行Radon变换,其间通过对离散倾角叠加算子求取的研究,及对影响Radon能量收敛的重要参数阻尼因子算法的改进,使数据在Radon域以能量团的形式呈现,得到很好的收敛效果,基本解决了Radon域数据的一定程度的拖尾现象,消除了各能量团之间的平滑效应,采用柯西分布来规则化数据,提高了Radon域的分辨率,Radon域能量也收敛到一个点上,有利于上下行波或纵横波波场分离.最后通过反演结果和模型试算验证了该方法的可行性和稳定性.