Bayesian inference of the Cole–Cole parameters from time- and frequency-domain induced polarization

The inversion of induced‐polarization parameters is important in the characterization of the frequency electrical response of porous rocks. A Bayesian approach is developed to invert these parameters assuming the electrical response is described by a Cole–Cole model in the time or frequency domain. We show that the Bayesian approach provides a better analysis of the uncertainty associated with the parameters of the Cole–Cole model compared with more conventional methods based on the minimization of a cost function using the least‐squares criterion. This is due to the strong non‐linearity of the inverse problem and non‐uniqueness of the solution in the time domain. The Bayesian approach consists of propagating the information provided by the measurements through the model and combining this information with a priori knowledge of the data. Our analysis demonstrates that the uncertainty in estimating the Cole–Cole model parameters from induced‐polarization data is much higher for measurements performed in the time domain than in the frequency domain. Our conclusion is that it is very difficult, if not impossible, to retrieve the correct value of the Cole–Cole parameters from time‐domain induced‐polarization data using standard least‐squares methods. In contrast, the Cole–Cole parameters can be more correctly inverted in the frequency domain. These results are also valid for other models describing the induced‐polarization spectral response, such as the Cole–Davidson or power law models.     

Inversion of 2D spectral induced polarization imaging data

Laboratory measurements of various materials suggest that more information can be obtained by measuring the in‐phase and out‐of‐phase potentials at a number of frequencies. One common model used to describe the variation of the electrical properties with frequency is the Cole‐Cole model. Apart from the DC resistivity (ρ) and chargeability (m) parameters used in conventional induced‐polarization (IP) surveys, the Cole‐Cole model has two additional parameters, i.e. the time (τ) and relaxation (c) constants. Much research has been conducted on the use of the additional Cole‐Cole parameters to distinguish between different IP sources. Here, we propose a modified inversion method to recover the Cole‐Cole parameters from a 2D spectral IP (SIP) survey. In this method, an approximate inversion method is initially used to construct a non‐homogeneous starting model for the resistivity and chargeability values. The 2D model consists of a number of rectangular cells with constant resistivity (ρ), chargeability (m), time (τ) and relaxation (c) constant values in each cell. A regularized least‐squares optimization method is then used to recover the time and relaxation constant parameters as well as to refine the chargeability values in the 2D model. We present results from tests carried out with the proposed method for a synthetic data set as well as from a laboratory tank experiment.     

基于相关辨识的逆重复m序列伪随机电磁法

分析了变频法和2n系列伪随机电磁法的场源信号特点,提出了基于相关辨识的逆重复m序列伪随机电磁法.逆重复m序列伪随机信号具有与白噪声类似的自相关函数,在频带内,频谱等间距均匀分布.由Wiener-Hopf方程,分析了逆重复m序列伪随机相关辨识大地系统冲激响应的原理.理论证明,合理地选择产生逆重复m序列的几个参数可以很好地压制各种干扰,高精度地辨识大地系统.讨论了影响测量精度与勘探分辨率的信号参数设计原则,为进一步研制具有自主产权的高分辨精细电磁勘探仪器和方法奠定了基础.     

COMPARISON OF TIME,FREQUENCY, AND PHASE MEASUREMENTS IN INDUCED POLARIZATION*

In comparing the similarity between time, frequency, and phase measurements as used in the induced polarization method of geophysical prospecting, parameters must first be defined and the basis for comparison established. The conditions for mathematical equivalence then follow in a natural sequence. Laboratory measurements are made on a variety of rock samples to indicate the type of comparison and correlation expected from field measurements. Results indicate that frequency domain and phase measurements are equivalent, but two frequency domain measurements are needed to produce the same amount of polarization information as a single phase measurement. Frequency and time domain measurements will be similar but never equivalent due to the basic differences in their respective parameter definitions.     

地震作用下横断层地质金属成矿带电法找矿成果研究

深部矿产资源勘探是未来勘探的必然趋势.地震作用下的横断层地质构造对金属矿、 能源矿等矿产资源的分布具有重要影响,拥有较大的找矿潜力.对于地震作用下横断层地质等条件复杂的场合,采用高密度电阻率法、 激发极化法和可控源音频大地电磁法等单一电法勘探可能存在找矿效果不佳的问题,有必要研究更为有效的找矿技术方法.首先阐述了激发极化法、CSAMT法等电法勘探的基本内容和各自优缺点;然后,在分析地震作用下横断层地质特征的基础上,研究并提出了基于激发极化法和CSAMT的综合找矿法.基于激发极化法和CSAMT的综合找矿法能有效反映地下地电差异,在大深度范围有效反应地电断面电阻、 极化率参数,互相校正验证;结合已有地质物探资料,推断地下异常,提高横断层的金属矿产勘探效率和效果.将本文的研究成果应用于某横断层地质区域的金属矿勘探实践,取得了良好的勘探效果.实践表明本文所提方法有效、 可行.     

电阻率层析成像和激电测深对栾川铅锌矿的联合勘探

在栾川铅锌矿的物探工作中，采用了电阻率层析成像和激电测深两种方法，电阻率层析成像法采用温纳装置或偶极装置，电极数量和极距视情况而定，主要调查工作区内隐伏构造情况，激电测深采用对称四极测深法，最小AB／2距为3M，最大AB／2距为500M，主要研究激电测深参数的变化规律，对于含矿构造而言，激电参数呈异常高值反映，视极化率在15－40％，两种方法的联合应用，具有快速而准确的特点，在探矿工作中取得了良好的效果。     

New Methodology for Computation of the Earth’s Polarizability from Telluric Borehole Logging Measurements Taken at Different Frequencies

An important approach for computation of the earths polarizability is achieved by developing a novel method with new parameters called Natural Percent Frequency Effect (NPFE) and Natural Metal Factor (NMF) resulting from telluric logging data taken at different frequencies. The essential advantage of the developed approach relies on using natural electrical currents instead of an artificial electrical source usually needed in the standard frequency domain applied in the induced polarization method. Furthermore, a good qualitative correlation has been found between the new parameters and those of the traditional induced polarization method obtained in time and frequency domains. The new method has been tested in well 32 in the Rouez mine in France, where sulphide mineralization is well known to occur.     

海洋天然气水合物可控源电磁法的响应特征:一维正演模拟

We discuss the feasibility of using controlled-source electromagnetic （CSEM） in the frequency domain for prospecting marine gas hydrates. Based on the Ocean Drilling Program （ODP） Leg 164 log data, we have established several 1-D resistivity models which have different gas hydrate concentrations. Meanwhile, we analyzed the electromagnetic response of marine gas hydrates in the frequency domain based on these models. We also studied the relationship between electrical field magnitude or phase and parameters such as receiver-transmitter distance and frequency. Our numerical modeling results provide us with a quantitative reference for exploration and resource evaluation of marine gas hydrates.     

基于逆重复m序列的精细探测电法发送机设计

介绍了基于伪随机相关辨识理论的电法发送机设计思想.通过分析逆重复m序列伪随机信号的性质，产生原理，以及伪随机信号系统辨识的原理，研究了其在电法勘探应用中的可行性.用工程软件MATLAB仿真产生了逆重复m信号的波形，并分析了频谱和自相关函数，对产生伪随机信号的序列长度和时钟频率等参数的选择作出讨论，以说明其作为电法勘探场源的优良特点.作出了电法发送机系统初步设计，包括主控单元、逆变器、GPS同步，电流测量等模块，发送机信号控制单元采用硬件描述语言VHDL设计，并用CPLD可编程逻辑器件LC4256V实现了硬件产生m序列和逆重复m序列，及各种控制信号.宽频带、密频比，抗干扰能力强是其主要特点，在电法勘探中有良好的应用前景.     

多周期全波形激电抗干扰数据处理方法及在大规模探测中的应用分析

激电法是金属矿产勘查中一种十分重要的电法勘探分支方法,但是各种电磁干扰的存在限制了激电法在大规模探测中的应用.近年来,国内外先后实现了三维分布式全波形激电探测仪器系统的研发和推广,全波形数据记录为激电信号的抗干扰处理提供了新的空间.本文针对多周期全波形采样的激电数据提出了一套基于统计分析的时间序列抗干扰数据处理方法,主要包括：经验模态分解用于分离低频趋势项干扰;相关分析用于消除突发性强噪声干扰;稳健统计用于多周期时间序列叠加;分段稳健平均和低频相对相位谱用于时/频域激电参数提取.将上述数据处理方法应用于由国产分布式电法系统实测的三维全波形激电数据,并与线性拟合、均值叠加等常处理方法进行对比,发现新方法可以有效识别和压制激电数据中的强噪声干扰,提高大供电极距和低频点探测时的激电数据质量,从而进一步推动激电法在深部矿产资源勘查中的应用.

     

Theoretical and experimental study of time domain-induced polarization in water-saturated sands

A theoretical model of spectral-induced polarization (IP) of sand is presented. In the proposed model, contacts of sand grains and intergrain solution-filled space are considered as electrical current passages of varying thickness, which differ in values of ion transport number. Ion-selective narrow passages are considered as active zones, large passages as passive. The proposed model describes spectral IP characteristics for the medium where the length of passive zones is much greater than the length of active ones. The model is called short narrow pores (SNP) model. The SNP model predicts a growth of IP time constant with increase of length of ion-selective zone. Both the time domain and frequency domain parameters are described. The parameters of Cole–Cole model corresponding to the SNP model were also found.The behaviour of model parameters is compared with experimental data obtained on natural and sieved sands using time domain technique. The natural sand spectra correspond neither to the simple SNP model nor simple Cole–Cole model with single time constant because the lengths of ion-selective zones vary, reflecting the grain-size distribution.The spectra of sieved sand compared with the theoretical SNP spectra reveal close correspondence between experimental data and theoretical parameters. For four sieved sands, both the theoretical and experimental data show that the time constant of the IP is proportional to the square of the average grain size.     

Higher-order statistics correlation stacking for DC electrical data in the wavelet domain

DC (direct current) electrical and shallow seismic methods are indispensable to the near surface geophysical exploration, but the near surface areas are very difficult environments for any geophysical exploration due to the random noise caused by near surface inhomogeneities. As a new algorithm based on higher-order statistics theory, the higher-order correlation stacking algorithm for seismic data smoothing in the wavelet domain has been developed and applied efficiently to filter some correlation noise that the conventional second-order correlation stacking could not inhibit. In this paper, this higher-order statistics correlation stacking technology is presented for DC electrical data in wavelet domain. Taking into account the single section and multiple section data, we present two new formulations of correlation stacking for DC electrical data. Synthetic examples with Gaussian noise are designed to analyze the overall efficiency of the new algorithm and to determine its efficacy. Meanwhile, comparison with the traditional least-squares optimization inversion method for field examples from electrical imaging surveys and time-domain IP measurement in China shows its significant advantages. The quality of the new algorithm also has been assessed by physical simulation experiments. This new technology in DC electrical exploration measurements provides a new application in engineering and mining investigation.     

含激电效应的CSAMT一维正演研究

地电体对频率域电磁波激发源的响应为电磁感应和激电效应的综合响应.传统CSAMT法进行数据正反演时认为大地介质电阻率是与频率无关的实数,而实际上因为激电效应,地下可极化体的电阻率是一个与频率相关的复数.为推进二者总体响应研究,并扩展激电法的应用范围,同时提高电磁法勘探的精度,本文基于Dias模型,以复电阻率代替不考虑地电体极化效应的直流电阻率,对CSAMT场源一维层状模型进行了正演模拟,为提取CSAMT信号中所含激电信息提供理论基础.结果表明,考虑激电参数后,视电阻率及相位响应曲线出现明显异常（包括远场、过渡场、近场）;极化前后振幅比值异常峰值、相位差值异常峰值可直观体现激电异常;异常峰值与极化层层厚、埋深以及电阻率变化有连续的对应关系.认为从频率域电磁法信号中提取激电信息有乐观的前景.     

利用相关域小波变换进行SWD资料预处理

随钻地震(SWD)的波场十分复杂,对钻头有效信号和地表机械干扰成分的分析是SWD重要的资料预处理步骤.本文利用有效信号和噪声带有周期性或时延差异等时间结构特征,引入相关域小波变换进行SWD信号检测和分析.有效信号在钻柱内往复多次传播,因而带有严格的周期性,泥浆泵等机械发出的噪声也是周期性的,这些成分在自相关域内可以得到很好的凸显.SWD波场的各种成分,由于到达各个接收道的时延不同,在互相关域的特定时延处也能够得到凸显.利用小波变换对这些在相关域内得到凸显的成分进行多分辨分析,能够获得优势频率范围、周期、衰减等主要特征.根据这些信息,设计出合理的SWD处理方法,初步得到了有效信号的直达波.数据试处理结果表明,相关域小波变换是随钻地震的一个有效的预处理方法.     

Feasibility of central loop TEM method for prospecting multilayer water-filled goaf

With deep mining of coal mines, prospecting multilayer water-filled goaf has become a new content that results from geophysical exploration in coalfields. The central loop transient electromagnetic (TEM) method is favorable for prospecting conductive layers because of the coupling relationship between its field structure and formation. However, the shielding effect of conductive overburden would not only require a longer observation time when prospecting the same depth but also weaken the anomalous response of underlying layers. Through direct time domain numerical simulation and horizontal layered earth forward modeling, this paper estimates the length of observation time required to prospect the target, and the distinguishable criterion of multilayer water-filled goaf is presented with observation error according to the effect of noise on observation data. The observed emf curves from Dazigou Coal Mine, Shanxi Province can distinguish multilayer water-filled goaf. In quantitative inversion interpretation of observed curves, using electric logging data as initial parameters restrains the equivalence caused by coal formation thin layers. The deduced three-layer and two-layer water-filled goafs are confirmed by the drilling hole. The result suggests that when observation time is long enough and with the anomalous situation of underlying layers being greater than the observation error, the use of the central loop TEM method to prospect a multilayer water-filled goaf is feasible.     

地球物理方法在城市地震活动断层精确定位中的应用

重点讨论了城市地震活动断层精确定位方法.研究结果表明：面对城市的强干扰背景,利用可控震源,采取频率扫描方法和数据处理的互相关技术,可以有效压制强振动干扰,实现城市市区的地震勘探;对于两盘无明显断距的走滑断层可以利用高分辨率地震勘探方法和电法勘探方法进行联合精确的定位;并结合实例讨论了电法勘探的精确定位方法.     

伪随机编码源激发下的时域电磁信号合成

将伪随机编码技术引入到人工源电磁法后,可以通过加大发射功率以及应用后续的相关处理技术来达到压制噪声、加大探测深度及提高分辨率的目的,因此引起了越来越多学者的关注及研究,但大多数研究集中在资料处理的相关技术上,对模拟电磁信号关注较少.然而,资料处理工作大多是从电磁信号出发的,模拟伪随机编码源激发下的电磁信号不但可以为资料处理环节提供理论数据,而且可以为检测资料处理的效果提供中间结果,因此,模拟电磁信号工作必不可少.本文根据获得接收信号的物理过程来实现伪随机编码源激发下的电磁信号合成.首先用解析公式获得特定地电结构的大地频率域响应,然后通过余弦变换得到时间域阶跃响应,接下来用阶跃响应的时间导数得到大地脉冲响应,通过将大地脉冲响应与伪随机编码源的褶积得到理想接收信号,最后,用低通滤波器来模拟发射设备和接收设备的频带限制,将之和噪声一起加到理想接收信号上,最终模拟出仿真的合成信号.通过和野外实际接收信号对比发现本文合成信号仿真度较高,可以服务于后续的数据处理环节.     

频率域航空电磁法一维正演与探测深度

计算了偶极一偶极方式均匀半空间的频率域航空电磁响应及层状模型的相对异常响应,阐明了大地电导率、磁化系数,以及飞机飞行高度、探测装置、收发距对电磁响应的影响,计算结果说明了频率域航空电磁法的探测能力和探测条件．分析了三层模型的相对异常响应,给出了基于层状模型确定探测深度的方法．在水平共面方式下,收发距8m,飞行高度30m时,在3～4ppm噪声水平条件下,100Ωm大地探测深度为120m．     

电场差分法理论研究

对均匀大地和二层大地的频率域电场差分法理论曲线进行的计算和研究表明,电场差分法是一种以目标地质体和围岩在电阻率和极化率方面的差异为基础,根据测量到的能明显反映激电响应与电磁耦合响应的比值随频率变化的P参数曲线在性态上的差异来圈划油气藏的一种电法勘探方法. 因为它圈划油气藏的物理基础是油气藏上方与围岩上方测量到的电磁耦合响应和激电响应的差异,所以在圈划油气藏方面,该方法与复电阻率法类似,同样具有找油气的优良性能. 此外,该方法与复电阻率法相比,具有对目标地质体和围岩的电阻率和极化率差异反映灵敏、效率高、成本低等优点,所以它是一种值得推广的找油气的电法勘探方法.