孔隙介质核磁共振弛豫测量多指数反演影响因素研究

孔隙介质核磁共振（NMR）弛豫信号的多指数反演在NMR岩芯分析与测井解释中起着关键作用.为了在不同信噪比条件下快速反演出高分辨率的弛豫时间谱，本文利用NMR正演模拟信号以及实验室NMR岩芯分析数据，研究横向弛豫时间布点数、原始回波采集个数、时间域数据压缩方式等对反演结果的影响.同时，在不同信噪比（SNR）下对不同的反演算法(SVD、BRD、SIRT)进行比较，考察反演算法对信噪比的敏感程度，并讨论了相应的校正方法.另外，还分析了信噪比对长、短弛豫组分的影响.研究表明在充分采集有用回波的情况下，减少回波个数，反演得到的弛豫时间谱趋向发散；增加布点数可以提高分辨率，但是需要更多的计算时间；时间域数据压缩可以加快反演计算速度；不同算法对信噪比的敏感程度不同，发展相应的校正方法可以提高反演质量.     

微地震资料贝叶斯理论差分进化反演方法

微地震监测难以拾取准确初至,为了提高反演定位精度和减小多解性,研究了微地震贝叶斯差分进化反演方法.从分析讨论理论模型反演残差及其协方差分布特征出发,结合对比不加噪音和加入不同程度的噪音后残差协方差极小点位置移动、分布梯度变化特征,提出了先验信息解估计方法.针对后验估计中,由于难以获得先验信息解的方差估计致使无法计算加权系数问题,通过分析残差变化特征和解的变化关系,研究了利用残差求取加权系数的方法.为了加快寻优速度,讨论了差分进化反演方法,在变异操作方面使用差分策略,即利用种群中个体间的差分向量对个体进行扰动,实现个体变异,充分有效利用群体分布特性,提高算法的搜索能力,避免遗传算法中变异方式的不足.通过理论模型测试本方法的反演效果,并且和搜索方法反结果进行比较.测试结果证明本反演方法,对于不同程度初至干扰,反演结果向准确解逼近程度比搜索方法要好得多,实际资料的反演结果也好于搜索方法.     

(T2,D)二维核磁共振测井混合反演方法与参数影响分析

一维核磁共振(1D NMR)测井技术在流体识别中具有一定的局限性.二维核磁共振(2D NMR)测井能同时测量到多孔介质中横向弛豫时间(T₂)和扩散系数(D)等信息,利用这两个参数区分流体性质,较一维核磁共振测井技术具有明显的优越性.针对梯度场下的2D NMR测井弛豫机理和数学模型,提出了适用于求解大型稀疏矩阵方程的反演方法-基于非负最小二乘法(LSQR)和截断奇异值分解(TSVD)法的混合算法.为验证方法的有效性,先根据多回波观测模式合成回波串数据,然后再用混合反演算法进行反演,反演得到横向弛豫时间(T₂)和扩散系数(D),并构建T₂-D二维谱图.结果对比表明,该混合反演算法得到的T₂-D二维谱与流体模型一致性好,计算精度均比单一反演方法有较大改善,表明该混合反演方法可用于油气储集层2D NMR测井的反演和流体识别.此外,分别对油水同层和气水同层模型进行了正演模拟和反演实验, 系统考察了不同磁场梯度、不同回波间隔组合对反演效果的影响,为2D NMR参数设计提供依据.     

分层多指数磁共振弛豫信号反演方法研究

磁共振测深技术传统反演方法包括平滑反演和分块反演,通过分别获取初始振幅和平均弛豫时间构建地层含水量及有效孔隙度.然而,这些方法局限于单指数拟合方式,损失了大部分有效采集信息,受限于多孔地质环境解释,并在某些情况下无法刻画含水层清晰分界面.针对上述问题,本文建立了基于MRS全数据的多指数反演方法,依据全部采集时间下的有效信息,通过弛豫时间e指数分解,推导出新的磁共振正演核函数,结合泛函极小值方程,直接反演建立含水量,弛豫时间及地层深度三个重要参数关系,适用于复杂地质环境解释.为得到快速稳定的反演结果和更清晰的含水层分界面,本文借鉴分块反演思想,进一步构建了新的反演目标函数,利用基于不等式约束的空间信赖域算法进行优化,最终实现了一种基于分层反演与多指数结合的磁共振弛豫信号反演方法.模型数据以及实测算例表明该方法的效果和优势,并具备较高的计算效率,本研究为地面磁共振反演提供了一种新的思路与方法.     

多尺度孔隙岩石的核磁共振扩散耦合现象及其探测方法

油藏岩石的孔隙连通性是反映流体渗流难易程度的重要参数,对渗透率、有效孔隙度等岩石物理参数的评价具有重要作用.连通的孔隙中,核磁共振(NMR)弛豫的交换会产生扩散耦合现象,可作为孔隙连通性的表征和探测方法.本文提出利用横向弛豫T 2-T 2脉冲序列测量岩石的扩散耦合现象.运用随机游走方法模拟多孔岩石的核磁共振响应特征,分析扩散耦合的影响因素,推导表征扩散耦合强度的弛豫交换速率计算公式.结果表明:孔隙间的扩散耦合强度与T 2-T 2脉冲序列的混合时间呈正相关性,基于双孔弛豫交换模型推导的弛豫交换速率计算公式能够准确表征双尺度孔隙系统的扩散耦合强度.在孔隙尺寸不满足快扩散条件时,会出现与扩散耦合无关的非对角峰信号.针对含多类型孔隙的碳酸盐岩模型,随混合时间的增加,扩散耦合强度变大,一维T 2谱的形态畸变程度加重,在T 2-T 2二维谱中,代表微裂缝、粒间小孔、溶蚀大孔的信号能量变化趋势不同,反映不同类型孔隙间的连通性存在差异.本文的分析与讨论丰富了核磁共振弛豫在岩石物理性质评价中的应用方向,对利用核磁共振评价复杂孔隙岩石的孔隙结构和连通性提供了新思路和新方法.     

地震层析成像反演中解的定量评价及其应用

对地震层析成像非线性问题线性化处理之后,各种反演算法归纳成为对不适定方 程的求解．地震层析成像反演算法的解的物理意义是给出地质结构,因此对于解的可靠性及 分辨率研究非常重要．然而许多反演算法不能给出解的评价方法,因而对解的可信度产生怀 疑．本研究根据解估计的分辨率矩阵的原理,提出ＬＳＱＲ（Ｌｅａｓｔ Ｓｑｕａｒｅ ＱＲ）算法解协方差矩 阵的评价算法,用相关分析可以为那些在求解过程中得不到分辨率矩阵的反演方法提供解的 定量评价．并用本文提出的解的定量评价方法试评了一个实际地壳模型的地震层析成像的 速度重建结果．     

火山Mogi模型形变反演的虚拟观测法及方差分量估计

针对Mogi模型垂直位移与水平位移联合反演中的病态问题,改进火山形变总体最小二乘(Total Least Squares,TLS)联合反演的虚拟观测法,并使用方差分量估计(Variance Components Estimation,VCE)方法确定病态问题的正则化参数.将附有先验信息的参数作为观测方程,与垂直位移和水平位移的观测方程联合解算,推导了三类观测方程联合反演的求解公式及基于总体最小二乘方差分量估计确定正则化参数的表达式,给出了算法的迭代流程.通过算例实验,研究了总体最小二乘联合反演的虚拟观测法在火山Mogi模型形变反演中的应用;算例结果表明,三类数据的联合平差及方差分量估计方法可以确定权比因子并得到修正后的压力源参数,具有一定的实际参考价值.     

连续GPS观测中的相关噪声分析

分析了中国地壳运动观测网络GPS基准站位置时间序列中相关噪声的特性.利用最大似然估计反演了幂指数噪声的谱指数;考察了多种噪声模型,发现除闪烁噪声之外,约50%台站的东分量中的相关噪声可用"随机漫步噪声+一阶高斯-马尔可夫噪声"模型来描述,与其它分析机构产出的全球解并不一致,显示出处理策略的不同能够造成相关噪声的差异.白噪声和闪烁噪声的大小存在明显的地理分异,东南沿海台站的噪声要大于西北内陆台站.考虑相关噪声时,各站的速率估计方差要增大一个数量级以上,水平分量多在1mm/a以内,而垂向分量则较大.     

波动方程反演的全局优化方法研究

复杂介质波动方程反演是地球物理研究中的重要问题，通常表述为特定目标函数最优化，难点是多参数、非线性和不适定性.局部和全局优化方法都不能实现快速全局优化.本文概述了地震波勘探反演问题的理论基础和研究进展，阐述了反演中优化问题的解决方法和面临的困难，并提出了一种确定性全局优化的新方法.通过在优化参数空间识别并划分局部优化解及其附近区域，只需有限次参数空间划分过程就能发现所有局部解（集合）；基于复杂目标函数多尺度结构分析，提出多尺度参数空间分区优化方法的研究方向.该方法收敛速度快，优化结果不依赖初始解的选取，是对非线性全局优化问题的一个新探索.     

稳定正则化参数估计方法及其在盆地基底重力异常反演中的应用

正则化方法通过带有正则化参数的约束项,将不适定问题转换为一个适定问题.如何选取最优正则化参数一直以来都是正则化研究的难点和热点.本文通过定义解的不稳定性度量来直接估算正则化参数μ的最优值,并将这种正则化参数估计方法应用到二维沉积盆地基底重力反演中.测试该方法在通过对一次野外测量的数据加不同噪声得到的多组数据与多次野外测量中得到的多组数据这两种情况中的反演效果.最后将该方法应用到非洲西海岸的北加蓬次盆进行盆地基底反演,测试该方法的实用性.模型测试的结果显示,在这两种情况下获得的反演解非常接近且能够反演得到较为准确的模型基底深度,故该方法适用于一般情况下只进行一次野外测量的实际重力勘探情况且能得到稳定的最优反演解;实际资料的最优反演结果稳定且符合当地的地质构造背景.在模型测试与实际资料测试中,都能够确定最优正则化参数并得到最优反演结果,证明了该方法在重力反演中的正确性和实用性.     

Pore size distributions and hydraulic conductivities of rocks derived from Magnetic Resonance Sounding relaxation data using multi-exponential decay time inversion

In hydrogeology there is a variety of empirical formulae available for determination of hydraulic conductivity of porous media, all based on the analysis of grain size distributions of aquifer materials. Sensitivity of NMR measurements to pore sizes makes it a good indicator of hydraulic conductivity. Analogous to laboratory NMR, Magnetic Resonance Sounding (MRS) relaxation data are of a multi-exponential (ME) nature due to the distribution of different pore sizes in an investigated rock layer. ME relaxation behaviour will also arise due to the superposition of NMR signals which originate from different layers. It has been shown, that both kinds of ME behaviour coexist in MRS and can principally be separated by ME inversion of the field data. Only a few publications exist that have proposed approaches to qualitatively and quantitatively estimate petrophysical parameters such as the hydraulic conductivity from MRS measurements, i.e. MRS porosity and decay times. The so far used relations for the estimation of hydraulic conductivity in hydrogeology and NMR experiments are compared and discussed with respect to their applicability in MRS. Taking into account results from a variety of laboratory NMR and MRS experiments mean rock specific calibration factors are introduced for a data-base-calibrated estimation of hydraulic conductivity when no on-site calibration of MRS is available. Field data have been analysed using conventional and ME inversion using such mean calibration values. The results for conventional and ME inversion agree with estimates obtained from well core analysis for shallow depths but are significantly improved using a ME inversion approach for greater depths.     

Pore size distributions and hydraulic conductivities of rocks derived from Magnetic Resonance Sounding relaxation data using multi-exponential decay time inversion

In hydrogeology there is a variety of empirical formulae available for determination of hydraulic conductivity of porous media, all based on the analysis of grain size distributions of aquifer materials. Sensitivity of NMR measurements to pore sizes makes it a good indicator of hydraulic conductivity. Analogous to laboratory NMR, Magnetic Resonance Sounding (MRS) relaxation data are of a multi-exponential (ME) nature due to the distribution of different pore sizes in an investigated rock layer. ME relaxation behaviour will also arise due to the superposition of NMR signals which originate from different layers. It has been shown, that both kinds of ME behaviour coexist in MRS and can principally be separated by ME inversion of the field data. Only a few publications exist that have proposed approaches to qualitatively and quantitatively estimate petrophysical parameters such as the hydraulic conductivity from MRS measurements, i.e. MRS porosity and decay times. The so far used relations for the estimation of hydraulic conductivity in hydrogeology and NMR experiments are compared and discussed with respect to their applicability in MRS. Taking into account results from a variety of laboratory NMR and MRS experiments mean rock specific calibration factors are introduced for a data-base-calibrated estimation of hydraulic conductivity when no on-site calibration of MRS is available. Field data have been analysed using conventional and ME inversion using such mean calibration values. The results for conventional and ME inversion agree with estimates obtained from well core analysis for shallow depths but are significantly improved using a ME inversion approach for greater depths.     

Pore geometry of sandstone derived from pulsed field gradient NMR

Several parameters of pore geometry are needed for estimating permeability which is a key parameter for the characterization of reservoir sandstones. Powerful techniques for probing the pore space are the self-diffusion and the relaxation time NMR methods. However, the quality of results depends on the petrophysical model which underlies the interpretation of measurements. We applied the pulsed field gradient nuclear magnetic resonance (PFG-NMR) technique and measured time-dependent self-diffusion coefficients, D(Δ), of water in anhydrite cemented sandstones with low porosity and high tortuosity. The conventional method of fitting data with a function (Padé approximation) of the surface-to-volume ratio and the tortuosity yielded uncertain results. As part of a novel approach, we developed a numerical simulation code based on physical principles and a fractal pore space model. We compared our method with the Padé approximation and tested with data from the literature. For porous media with low tortuosity values and simple geometry such as randomly packed glass beads, both methods are in good agreement and give similar results. In sedimentary rocks, however, the new method of calculation is able to determine more accurate details of the pore geometry. However, its main advantage occurs in porous media with fractal geometry or with constricted pores, where the D(Δ)/D₀ curves deviate from the characteristic shape that is found for randomly packed glass beads.     

三维层状孔隙介质中弹性波的一种积分表达式I：理论

孔隙介质弹性波传播理论在地球物理勘探、地震工程和岩土动力学等领域有着广泛的应用.而孔隙介质中的弹性波受孔隙度、渗透率、流体黏滞系数等参数的影响,因此研究波场的传播特征将有助于分析和提取这些信息.本文在Biot理论的基础上,针对三维层状孔隙介质模型,利用在合成理论地震图的研究中已经被证实具有稳定、高效且适用范围较广的Luco-Apsel-Chen（LAC）广义反透射方法,给出了弹性波场的一种积分形式的半解析解,可通过数值方法高效、准确地计算层状孔隙介质中的理论波场,所以该积分形式的半解析解可为三维层状孔隙介质波场传播特征的理论数值模拟研究提供一种新的途径和手段.     

饱和土半空间中地下圆形衬砌洞室对平面SV波的散射

在Biot饱和多孔介质动力学理论的基础上,利用Fourier-Bessel级数展开法,通过对舍有衬砌洞室的局部场地进行波场分析,得到饱和土半空间中圆柱形衬砌洞室对平面SV波的散射问题的解析解。经验证,本文得到的解可以退化为半空间单相介质的情况。通过与已有的单相弹性介质半空间中圆柱形衬砌洞室对平面SV波散射问题的解析解的对比,验证了此解的正确性。在解析解的基础上,数值计算给出洞口动应力集中放大系数,分析了入射频率和孔洞埋深对柱面上的应力集中因子的影响。     

Bootstrap Calibration and Uncertainty Estimation of Downhole NMR Hydraulic Conductivity Estimates in an Unconsolidated Aquifer

Characterization of hydraulic conductivity (K) in aquifers is critical for evaluation, management, and remediation of groundwater resources. While estimates of K have been traditionally obtained using hydraulic tests over discrete intervals in wells, geophysical measurements are emerging as an alternative way to estimate this parameter. Nuclear magnetic resonance (NMR) logging, a technology once largely applied to characterization of deep consolidated rock petroleum reservoirs, is beginning to see use in near‐surface unconsolidated aquifers. Using a well‐known rock physics relationship—the Schlumberger Doll Research (SDR) equation—K and porosity can be estimated from NMR water content and relaxation time. Calibration of SDR parameters is necessary for this transformation because NMR relaxation properties are, in part, a function of magnetic mineralization and pore space geometry, which are locally variable quantities. Here, we present a statistically based method for calibrating SDR parameters that establishes a range for the estimated parameters and simultaneously estimates the uncertainty of the resulting K values. We used co‐located logging NMR and direct K measurements in an unconsolidated fluvial aquifer in Lawrence, Kansas, USA to demonstrate that K can be estimated using logging NMR to a similar level of uncertainty as with traditional direct hydraulic measurements in unconsolidated sediments under field conditions. Results of this study provide a benchmark for future calibrations of NMR to obtain K in unconsolidated sediments and suggest a method for evaluating uncertainty in both K and SDR parameter values.     

Hydraulic Conductivity Calibration of Logging NMR in a Granite Aquifer,Laramie Range,Wyoming

In granite aquifers, fractures can provide both storage volume and conduits for groundwater. Characterization of fracture hydraulic conductivity (K) in such aquifers is important for predicting flow rate and calibrating models. Nuclear magnetic resonance (NMR) well logging is a method to quickly obtain near-borehole hydraulic conductivity (i.e., K_NMR) at high-vertical resolution. On the other hand, FLUTe flexible liner technology can produce a K profile at comparable resolution but requires a fluid driving force between borehole and formation. For three boreholes completed in a fractured granite, we jointly interpreted logging NMR data and FLUTe K estimates to calibrate an empirical equation for translating borehole NMR data to K estimates. For over 90% of the depth intervals investigated from these boreholes, the estimated K_NMR are within one order of magnitude of K_FLUTe. The empirical parameters obtained from calibrating the NMR data suggest that “intermediate diffusion” and/or “slow diffusion” during the NMR relaxation time may occur in the flowing fractures when hydraulic aperture are sufficiently large. For each borehole, “intermediate diffusion” dominates the relaxation time, therefore assuming “fast diffusion” in the interpretation of NMR data from fractured rock may lead to inaccurate K_NMR estimates. We also compare calibrations using inexpensive slug tests that suggest reliable K_NMR estimates for fractured rock may be achieved using limited calibration against borehole hydraulic measurements.     

饱和土沉积谷场地对平面SV波的散射问题的解析解

把波函数展开方法用于饱和多孔介质中波的传播的研究中,给出了不同土层界面条件（透水条件和不透水条件）下具有饱和土沉积层的圆弧形沉积河谷场地对平面SV波散射问题的解析解. 其中沉积谷软土场地用饱和多孔介质的Biot动力学理论模拟,半空间场地用单相介质弹性动力理论模拟. 对于入射角大于临界入射角时,产生的面波的波函数用有限Fourier级数展开,这种方法适用于较大的入射波频率范围,这是现存的数值方法所不能比拟的一大优点. 文中算例分析了入射波频率和入射角对地震地面运动的影响.     

Wavefield simulation in porous media saturated with two immiscible fluids

Wavefields in porous media saturated by two immiscible fluids are simulated in this paper. Based on the sealed system theory, the medium model considers both the relative motion between the fluids and the solid skeleton and the relaxation mechanisms of porosity and saturation (capillary pressure). So it accurately simulates the numerical attenuation property of the wavefields and is much closer to actual earth media in exploration than the equivalent liquid model and the unsaturated porous medium model on the basis of open system theory. The velocity and attenuation for different wave modes in this medium have been discussed in previous literature but studies of the complete wave-field have not been reported. In our work, wave equations with the relaxation mechanisms of capillary pressure and the porosity are derived. Furthermore, the wavefield and its characteristics are studied using the numerical finite element method. The results show that the slow P3-wave in the non-wetting phase can be observed clearly in the seismic band. The relaxation of capillary pressure and the porosity greatly affect the displacement of the non-wetting phase. More specifically, the displacement decreases with increasing relaxation coefficient.