波动方程反问题与广义RADON变换反演的一种关系

本文把波动方程反问题与广义Radon 变换的反演相联系。在假定弱散射条件下,把波动方程反问题转化成广义Radon 变换的反演问题,即如何从一系列关于目标函数在某类子流形上的积分值,去求出目标函数.这种转化提供了一种研究波动方程反问题的途径。     

波动方程CT技术在地震数据处理中的应用

本文从畸变的Born近似的微扰技术出发,给出了利用广义Radon变换和Fourier积分算子的理论反演介质间断性的原理.将声学的广义Radon变换与经典Radon变换进行类比,近似地导出了声学广义Radon变换的反演公式. 本文对于反射地震学的情况,提出了一种拟线性化方法,考虑了成象点的一次散射场,从某种程度上减少了Born近似对弱散射的苛求. 利用同一模型的理论记录和物理实验记录的反演计算结果对提出的方法进行了验证,并讨论了进一步提高成象精度的方法.     

地震逆散射偏移与反演综述

随着油气勘探领域逐渐向深层、复杂型、隐蔽性油气藏转移,油气资源的勘探难度越来越大,传统反射地震勘探技术难以满足日益增长的油气勘探需求,亟需发展适合复杂地质构造的地震波偏移反演新技术.针对地球深部非均匀结构体引起的地震散射波,发展地震逆散射偏移反演理论和技术将有可能解决复杂构造成像反演的技术难题.本文回顾地震波逆散射偏移反演理论的发展历史和基本原理,以逆广义Radon变换求解线性化逆散射问题为基础,介绍逆散射理论在介质结构成像、物性参数反演、多次波衰减等方面的技术延伸,同时将其应用到合成数据和实际数据资料,探讨地震勘探逆散射方法的技术优势和应用潜力.     

1990年中国地球物理学会第六届年会中有关层析成象的学术内容

1990年10月13—17日在武昌召开了中国地球物理学会第六届年会,在计算地球物理,深部构造、震源物理和勘探地球物理方法等四个专题中报告了与CT理论和技术有关的内容40余篇论文,涉及广义Radon变换的应用,井间成象问题,跨孔地震层析成象的反     

1990年中国地球物理学会第6届年会中有关层析成象的学术内容

1990年10月13-17日在武昌召开了中国地球物理学会第6届年会,在计算地球物理,深部构造、震源物理和勘探地球物理方法等四个专题中报告了与CT理论和技术有关的内容40余篇,涉及广义Radon变换的应用,非间成象问题,跨孔地震层析成象的反演方法,数据不     

参考波速线性变化时的声波方程逆散射反演

声波方程的逆散射反演乃是求解双曲型偏微分方程系数项反问题的一种解析方法,一般利用Born近似把这一非线性反问题线性化,并给出了恒参考波速介质中反问题解的解析表达式.由于Born近似假定波速扰动为一级无穷小,因此,在大多数情况下,恒参考波速介质模型的反问题的解无法得以应用.本文研究介质参考波速沿某个方向线性变化时的声散射理论,导出了声波方程逆散射问题解的解析表达式,从而既可使Born近似的假定在大多数情况下能得以满足,又可利用快速Fourier变换快速实现介质波速扰动的反演成象.     

一类广义Radon变换的逆问题

由于CT技术的出现,Radon变换受到人们的重视,已被应用于许多领域,但是,还有一些问题(如地球物理中的层析成像问题),已知的数据往往是未知函数在曲线上的积分值,而不是古典Radon变换中的直线。这就使得人们不得不考虑所谓广义的Radon变换:即已知点函数在曲线上的积分值,要求恢复此函数。使我们感到欣慰的是,这方面的工作已取得了不少的进展。     

实际地球介质中的波的新研究进展—四川地震学、非线性地震学与构造活动波研

本文介绍实际地球介质（地球物理介质、地质介质）中的波的激发与传播问题的某些新的研究方向与进展。首先简要说明实际地球介质的一般特性。其次分别介绍随时间变化的三维非均匀地球介质中的地震波和非线性地球介质中的地震波的传播问题，也就是四维地震学和非线性地震学的研究进展。本文最后研究了三种类型（广义瑞利型、广义勒夫型和广义导波型）的构造活动波的激发与传播特性，并用它们来解释过去已发现的几种不同类型的地震活动波。     

广义Radon变换与叠前地震数据处理

在本文中,首先讨论了与几种地震层析成像对应的Radon变换公式,并导出了叠前地震记录的数学模型.在分析叠前地震记录与广义Radon变换的关系的基础上,讨论了速度分析、滤波、动校正、叠加等地震数据处理的数学物理意义.为展示广义Radon变换在地震数据处理中的应用,给出了用于滤波和消除多次波的方法及算例.     

地震波场反演的BG－逆散射方法

本文讨论利用三维反射地震数据进行波场反演的一种方法，旨在取得高分辨率的地球模型．这种方法用Ｂａｃｋｕｓ－Ｇｉｌｂｅｒｔ的理论构造波动方程非线性反问题的逐次线性化迭代格式，用逆散射原理导出泛函的Ｆｒｅｃｈｅｔ导数，并用最佳折衷准则求解线性化后的方程组．根据迭代过程中不断提高分辨率的思想和减少计算成本的原则，设计了可供实用的反演算法流程．     

Scattering pattern analysis and true-amplitude generalized Radon transform migration for acoustic transversely isotropic media with a vertical axis of symmetry

In multi-parameter ray-based anisotropic migration/inversion, it is essential that we have an understanding of the scattering mechanism corresponding to parameter perturbations. Because the complex nonlinearity in the anisotropic inversion problem is intractable, the construction of true-amplitude linearized migration/inversion procedures is needed and important. By using the acoustic medium assumption for transversely isotropic media with a vertical axis of symmetry and representing the anisotropy with P-wave normal moveout velocity, Thomsen parameter δ and anelliptic parameter η, we formalize the linearized inverse scattering problem for three-dimensional pseudo-acoustic equations. Deploying the single-scattering approximation and an elliptically anisotropic background introduces a new linear integral operator that connects the discontinuous perturbation parameters with the multi-shot/multi-offset P-wave scattered data. We further apply the high-frequency asymptotic Green's function and its derivatives to the integral operator, and then the scattering pattern of each perturbation parameter can be explicitly presented. By naturally establishing a connection to generalized Radon transform, the pseudo-inverse of the integral operator can be solved by the generalized Radon transform inversion. In consideration of the structure of this pseudo-inverse operator, the computational implementation is done pointwise by shooting a fan of rays from the target imaging area towards the acquisition system. Results from two-dimensional numerical tests show amplitude-preserving images with high quality.     

Tomography and the Herglotz-Wiechert inverse formulation

In this paper, linearized tomography and the Herglotz-Wiechert inverse formulation are compared. Tomographic inversions for 2-D or 3-D velocity structure use line integrals along rays and can be written in terms of Radon transforms. For radially concentric structures, Radon transforms are shown to reduce to Abel transforms. Therefore, for straight ray paths, the Abel transform of travel-time is a tomographic algorithm specialized to a one-dimensional radially concentric medium. The Herglotz-Wiechert formulation uses seismic travel-time data to invert for one-dimensional earth structure and is derived using exact ray trajectories by applying an Abel transform. This is of historical interest since it would imply that a specialized tomographic-like algorithm has been used in seismology since the early part of the century (seeHerglotz, 1907;Wiechert, 1910). Numerical examples are performed comparing the Herglotz-Wiechert algorithm and linearized tomography along straight rays. Since the Herglotz-Wiechert algorithm is applicable under specific conditions, (the absence of low velocity zones) to non-straight ray paths, the association with tomography may prove to be useful in assessing the uniqueness of tomographic results generalized to curved ray geometries.     

跨孔地震层析成像的级联方法

对厚度小于1/4波长的超薄波速干扰体进行高分辨率成像,作者曾采用走时反演和波场反演相结合的方法,体现了由低分辨率向高分辨率逐步逼近的思想.级联算法是这种思想的进一步发展,我们将具有不同分辨率的算法串联起来,以达到高分辨率成像的目的.本文介绍一种三级串联的算法,并进行了算法分析,数值计算的例子说明这种级联算法分辨率高、稳定性好,只需要地震资料而不要求其它先验信息,因此能较好地满足实际应用的要求.     

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.     

关于区域性的地震面波层析反演方法的讨论

讨论了在地球表面局部区域进行面波层析反演时所用的各种反演方法，指出各种方法用于区域性层析反演时的优缺点，并就由面波资料对区域性的地壳和上地幔结构进行反演的方法──分块反演方法、本征函数展开法、球面雷当变换方法、Ｔａｒａｎｔｏｌａ概率方法和波形反演的方法进行了讨论。指出了各种方法的优缺点及适用范围，并对一些方法进行了数值模拟，给出了计算实例。关键词     

反演模型分辨率的估算方法

反演问题的时空间分辨率或称时空分辨长度是评估模型精细程度的重要参数,决定了该模型应用的范围和价值,但是分辨长度估算却是比反演更复杂和麻烦的数学问题。除了层析成像中广泛利用理论模型恢复试验定性提取空间分辨长度外,通过求解分辨率矩阵可定量获得分辨长度。通过矩阵操作给出的分辨率矩阵包括三类：直接分辨率矩阵、正则化分辨率矩阵和混合分辨率矩阵。这三类矩阵包含了反演本身不同侧面的信息,因此在一个反演应用中,同时提供这三类分辨率矩阵可更全面地评估反演模型分辨率分布。最近An（2012）提出了从大量随机理论模型及其解中统计出分辨率矩阵的方法。这种分辨率矩阵是从模拟真实反演实验的输入和输出模型中通过反演得到的,因此这种分辨率矩阵更能反映整个反演所涉及到的更多因素和过程;同时由于这种分辨率矩阵计算过程无需进行矩阵操作且不依赖于具体正演和反演方法,因此可以被应用于更普遍的反演问题。实际应用证明统计分辨率分析方法适用于对二维和三维层析成像反演模型进行分辨率分析。     

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。      

DEBUBBLING: A GENERALIZED LINEAR INVERSE APPROACH*

On seismograms recorded at sea bubble pulse oscillations can present a serious problem to an interpreter. We propose a new approach, based on generalized linear inverse theory, to the solution of the debubbling problem. Under the usual assumption that a seismogram can be modelled as the convolution of the earth's impulse response and a source wavelet we show that estimation of either the wavelet or the impulse response can be formulated as a generalized linear inverse problem. This parametric approach involves solution of a system of equations by minimizing the error vector (ΔX = X^obs– X^cal) in a least squares sense. One of the most significant results is that the method enables us to control the accuracy of the solution so that it is consistent with the observational errors and/or known noise levels. The complete debubbling procedure can be described in four steps: (1) apply minimum entropy deconvolution to the observed data to obtain a deconvolved spike trace, a first approximation to the earth's response function; (2) use this trace and the observed data as input for the generalized linear inverse procedure to compute an estimated basic bubble pulse wavelet; (3) use the results of steps 1 and 2 to construct the compound source signature consisting of the primary pulse plus appropriate bubble oscillations; and (4) use the compound source signature and the observed data as input for the generalized linear inverse method to determine the estimated earth impulse response—a debubbled, deconvolved seismogram. We illustrate the applicability of the new approach with a set of synthetic seismic traces and with a set of field seismograms. A disadvantage of the procedure is that it is computationally expensive. Thus it may be more appropriate to apply the technique in cases where standard analysis techniques do not give acceptable results. In such cases the inherent advantages of the method may be exploited to provide better quality seismograms.     

回折波CT成像及其应用

本文评述在研究岩石圈结构时，根据已往采用广角反射波和折射波的信息进行正反演的为研究岩石圈结构。这种研究方法对那种成层性比较发育的地区效果比较好，而对于花岗岩地区或成层性不好的地区，这种方法就无能为力了。这样我们运用了回折波时间场和回折波ＣＴ成像方法相结合的系统来研究下地介质的速度结构，这种方法精度高，简单易行。并用把这种方法与以往用的正反演解释方法相比较，二者结果一致。     

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.