基于Hilbert-Huang变换的大地电磁信号处理方法与应用研究
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摘要
大地电磁测深(Magnetotelluric, MT)是一种以天然交变电磁场为场源的电磁勘探方法,电磁场信号弱、频带宽、极易受各种噪声的干扰,是典型的非线性、非平稳信号。处理MT信号最传统的方法是Fourier变换,而Fourier变换是以平稳信号为理论基础的,与MT信号的非平稳特性相矛盾,且传统方法对MT信号的处理提出了许多前提条件,因此用Fourier变换分析MT信号有着明显的缺陷。Hilbert-Huang变换(Hilbert-Huang transform, HHT)是最新发展起来的,在多个领域已被证明了的分析非平稳信号的强有力工具。本文在分析总结国内外研究成果的基础上,把HHT变换应用到大地电磁信号的处理中来,从基于HHT的大地电磁信号去噪、时频分析、功率谱估计和阻抗估算等几个方面研究其在MT信号处理中的应用方法和应用效果,试图寻找处理MT信号的新途径。
本文从HHT变换的原理出发,研究了经验模态分解(Empirical Mode Decomposition, EMD)的方法及EMD分解的完备性与局部正交性,给出了EMD分解的流程图,并结合大地电磁信号分析的特点,就EMD分解中存在的端点效应等几个问题,给出了本研究中解决相关问题的方法。以仿真信号为例,给出了HHT方法处理信号的基本流程,分析了Hilbert-Huang变换处理大地电磁信号的优越性。
Hilbert-Huang变换为信号的去噪提供了一条良好的途径。其EMD分解出来的模态函数(Intrinsic Mode Function, IMF)序列是多通带滤波的结果,且可以完全重构。据此,可以根据噪声的特征构造时空滤波器或采用硬(软)阈值的方法对大地电磁信号进行消噪处理。本文研究了大地电磁测深信号与噪声的特征,提出了基于EMD分解的大地电磁信号去噪原理、方法和步骤,对大地电磁信号中常见的脉冲干扰、矩形干扰、周期干扰和三角波干扰等几种噪声进行了消噪处理,并对实例进行了分析,结果表明本文提出的噪声抑制方法是正确的,有效的抑制了噪声,改善了受干扰数据的质量,获得了稳定的参数估计值。
时频分析是分析处理非平稳信号的有力工具,它将信号表示为时间和频率的联合函数,揭示信号的时变特征。HHT时频谱克服了其它一些方法的缺陷,具有完全的局部时频特性,可准确描述大地电磁信号的时变特征。基于这些特点,本文在对比研究了短时傅立叶变换、Winger-ville分布、小波变换等几种常用时频分析方法处理大地电磁信号的基础上,给出了MT信号的Hilbert时频谱特征,并研究了Hilbert时频谱在MT信号的噪声识别,分段平稳和数据筛选中的应用方法和应用效果。
在MT信号处理中最传统也是最主要的谱估计方法还是基于Fourier变换的经典周期图法。而Fourier变换与大地电磁信号非线性,非平稳性的本质相矛盾,这必然导致谱估计的误差。本文在给出Fourier谱估计存在不足的基础上,提出了用Hilbert边际谱来估计大地电磁功率谱的方法,讨论了边际谱的物理意义和分辨率,采用了整体平均和阈值收缩等几种提高谱估计精度的方法,并比较研究了仿真信号和实测大地电磁信号的Fourier谱和Hilbert边际谱,分析了用Hilbert边际谱来估计大地电磁功率谱方法的优越性。
大地电磁法主要以视电阻率曲线和相位曲线的形态特征作为分析大地结构与电性分布的基本依据,因此阻抗估算是大地电磁法研究中最基本的内容之一。而由于MT信号表现出非平稳的特征,引起阻抗估算结果也具有时变特征,因此,从瞬时谱上统计估算参量比Fourier分析更有利于实现稳健估计。论文提出了从HHT瞬时谱上统计估算阻抗张量的瞬时谱方法,给出了基于HHT边际谱估算阻抗张量的数学模型及其流程图；用数值模拟验证了方法的正确性,并对实测MT数据进行了分析；建立了基于HHT的大地电磁资料处理流程,并对一测线进行了处理分析。结果表明由HHT瞬时谱统计估算的阻抗张量最小化了大地电磁信号非平稳性带来的估算偏差,估算参量具有更好的稳健性,曲线形态也更加合理,圆滑,且在低信噪比情况下本文方法较传统方法有更强的抗干扰能力。
通过以上几个方面的研究表明Hilbert-Huang变换是一种有效的处理非平稳信号的方法,能成功的应用于大地电磁信号去噪、时频分析、功率谱估计和阻抗估算等几个方面,且具有一定的优越性,为大地电磁信号处理提供了一种新的途径。
Magnetotelluric(MT) sounding is a kind of electromagnetic exploration method which uses natural alternating electromagnetic field as a field source. While MT signal is a typical non-linear and non-stationary signal because it is weak, bandwidth and highly vulnerable to be disturbed. The traditional methods of analysis determine the spectra using variations of the Fourier Transform (FT) and must assume that the signals under analysis are stationary over the record length. Because the FT is based on the theory of stationary signal and is ambivalent to the characteristic of MT signal. Therefore, analysis method of MT signal using Fourier transform has obvious flaws. In recent years, the Hilbert-Huang Transform (HHT) has been regarded as a powerful tool for adaptive analysis of non-linear and non-stationary signals and has received much attention in the signal processing community. This paper proposes for the first time the adoption of a new method of analysis for MT data, and focuses on noise suppressing, time-frequency analysis, power spectrum estimation and impedance estimation that are facilitated by applying the HHT.
In this paper, starting with the principle of the HHT transform, the empirical mode decomposition (EMD) and the completeness and local orthogonality of EMD are studied. The flow chart of EMD is given. And combined with the characteristic of MT signal, some noduses that exist on the EMD, such as fluctuations, end effects and sifting-stopping criteria, are studied and given the method to resolve the relevant problems. Taking a simulative signal as an example, the basic flow of signal processing based on HHT is given and the superiority of Hilbert-Huang transform to analyze the MT signals is verified.
The innovation of the HHT method brings a new way to filter data and reduce noise. The EMD filters signal with different time scales and is adaptive to signal. The intrinsic mode function (IMF) is result of multi-band filtering and can be completely reconstructed. Using the structural characteristics of the IMF, some new space-time filters and a hard (soft) threshold method can be realized to de-noise. This paper studies the characteristics of MT signal and its noise. The principle and step of de-noising method based on EMD are given. Some noises, such as impulse jamming, rectangle disturbing and sine wave noise, are analyzed and processed for the actual MT data. The results show that the de-noising method is effective and the quality of MT data is improved greatly. The EMD method can achieves stationary and reliable parameter estimations.
Time-frequency analysis is a powerful tool for non-stationary signal processing. It will express signal as a joint function of time and frequency and reveal the time-varying characteristics of the signal. HHT method has overcome the shortcomings of other ways, completes abolition of the role of the window function and is not restricted with nuclear function and Heisenberg principle. Hilbert-Huang spectrum can precisely describe the nonlinear and non-stationary characteristics of MT signals. This paper compares the different time-frequency spectrums that are from several commonly method such as short time Fourier transform, Wigner-Ville distribution and Wavelet transform. Based on these characteristics, the time-frequency characteristics of HHT spectrum of MT signal are studied. Then Hilbert time-frequency spectrum is used in the MT signal noise recognition, data filtering and sub-smooth. Its application methods and application results are studied in this thesis.
Power spectrum estimation takes an important role in MT signal processing. The most traditional and the most important power spectrum estimation method is the classical periodogram method which bases on the Fourier transform. The Fourier transform contradicts the non-linear, non-stationary nature of MT signal, which will inevitably lead to spectral estimation error. A new spectrum estimation method based on Hilbert-Huang transform is proposed in this paper. Firstly the marginal spectrum method based on HHT is presented and the linear property of marginal spectrum is demonstrated. Then, compared with the FT method, the physical signification and the preponderance of marginal spectrum for MT signal are further discussed. And some methods to improve the precision of spectrum estimation are proposed in detail. Finally the simulative data and the practical MT data are analyzed. The simulation and results of real data indicate that the HHT method suits the nature of MT signal much more.
The characteristics of apparent resistivity and phase curves are mainly basis for analyzing the structure of the earth and distribute of conduction in MT sounding. Therefore analyzing, calculating and processing of impedance are one of the most basis and importance works. The non-stationary characteristics of MT signal cause that impedance estimation results have time-varying characteristics. Therefore, using time-frequency analysis methold to estimate parameters from the instantaneous spectrum are more conducive to robust estimation comparing with Fourier methold. This paper proposes a kind of instantaneous spectrum method to estimate impedance tensor based on the HHT marginal spectrum. The flow chart and mathematics model are given. Some simulative signal and a place of measured MT signals is processed. The results shows that the impedance tensor obtained from the HHT transient spectrum minimizes the estimation warp brought about by the non-stationary characteristics of MT data, and the estimated parameter is more stable and reliable than that from conventional methods. The parameter curves are less bars and more smooth, reasonable. The interpretability of data has been significantly improved.
Through the above studies, the results show that the Hilbert-Huang transform is an effective method to deal with the non-stationary signals and provides a new way to process MT signal. HHT method has a wide application on MT signal noise suppressing, time-frequency analysis, power spectrum estimation and impedance estimation.
本文从HHT变换的原理出发,研究了经验模态分解(Empirical Mode Decomposition, EMD)的方法及EMD分解的完备性与局部正交性,给出了EMD分解的流程图,并结合大地电磁信号分析的特点,就EMD分解中存在的端点效应等几个问题,给出了本研究中解决相关问题的方法。以仿真信号为例,给出了HHT方法处理信号的基本流程,分析了Hilbert-Huang变换处理大地电磁信号的优越性。
Hilbert-Huang变换为信号的去噪提供了一条良好的途径。其EMD分解出来的模态函数(Intrinsic Mode Function, IMF)序列是多通带滤波的结果,且可以完全重构。据此,可以根据噪声的特征构造时空滤波器或采用硬(软)阈值的方法对大地电磁信号进行消噪处理。本文研究了大地电磁测深信号与噪声的特征,提出了基于EMD分解的大地电磁信号去噪原理、方法和步骤,对大地电磁信号中常见的脉冲干扰、矩形干扰、周期干扰和三角波干扰等几种噪声进行了消噪处理,并对实例进行了分析,结果表明本文提出的噪声抑制方法是正确的,有效的抑制了噪声,改善了受干扰数据的质量,获得了稳定的参数估计值。
时频分析是分析处理非平稳信号的有力工具,它将信号表示为时间和频率的联合函数,揭示信号的时变特征。HHT时频谱克服了其它一些方法的缺陷,具有完全的局部时频特性,可准确描述大地电磁信号的时变特征。基于这些特点,本文在对比研究了短时傅立叶变换、Winger-ville分布、小波变换等几种常用时频分析方法处理大地电磁信号的基础上,给出了MT信号的Hilbert时频谱特征,并研究了Hilbert时频谱在MT信号的噪声识别,分段平稳和数据筛选中的应用方法和应用效果。
在MT信号处理中最传统也是最主要的谱估计方法还是基于Fourier变换的经典周期图法。而Fourier变换与大地电磁信号非线性,非平稳性的本质相矛盾,这必然导致谱估计的误差。本文在给出Fourier谱估计存在不足的基础上,提出了用Hilbert边际谱来估计大地电磁功率谱的方法,讨论了边际谱的物理意义和分辨率,采用了整体平均和阈值收缩等几种提高谱估计精度的方法,并比较研究了仿真信号和实测大地电磁信号的Fourier谱和Hilbert边际谱,分析了用Hilbert边际谱来估计大地电磁功率谱方法的优越性。
大地电磁法主要以视电阻率曲线和相位曲线的形态特征作为分析大地结构与电性分布的基本依据,因此阻抗估算是大地电磁法研究中最基本的内容之一。而由于MT信号表现出非平稳的特征,引起阻抗估算结果也具有时变特征,因此,从瞬时谱上统计估算参量比Fourier分析更有利于实现稳健估计。论文提出了从HHT瞬时谱上统计估算阻抗张量的瞬时谱方法,给出了基于HHT边际谱估算阻抗张量的数学模型及其流程图；用数值模拟验证了方法的正确性,并对实测MT数据进行了分析；建立了基于HHT的大地电磁资料处理流程,并对一测线进行了处理分析。结果表明由HHT瞬时谱统计估算的阻抗张量最小化了大地电磁信号非平稳性带来的估算偏差,估算参量具有更好的稳健性,曲线形态也更加合理,圆滑,且在低信噪比情况下本文方法较传统方法有更强的抗干扰能力。
通过以上几个方面的研究表明Hilbert-Huang变换是一种有效的处理非平稳信号的方法,能成功的应用于大地电磁信号去噪、时频分析、功率谱估计和阻抗估算等几个方面,且具有一定的优越性,为大地电磁信号处理提供了一种新的途径。
Magnetotelluric(MT) sounding is a kind of electromagnetic exploration method which uses natural alternating electromagnetic field as a field source. While MT signal is a typical non-linear and non-stationary signal because it is weak, bandwidth and highly vulnerable to be disturbed. The traditional methods of analysis determine the spectra using variations of the Fourier Transform (FT) and must assume that the signals under analysis are stationary over the record length. Because the FT is based on the theory of stationary signal and is ambivalent to the characteristic of MT signal. Therefore, analysis method of MT signal using Fourier transform has obvious flaws. In recent years, the Hilbert-Huang Transform (HHT) has been regarded as a powerful tool for adaptive analysis of non-linear and non-stationary signals and has received much attention in the signal processing community. This paper proposes for the first time the adoption of a new method of analysis for MT data, and focuses on noise suppressing, time-frequency analysis, power spectrum estimation and impedance estimation that are facilitated by applying the HHT.
In this paper, starting with the principle of the HHT transform, the empirical mode decomposition (EMD) and the completeness and local orthogonality of EMD are studied. The flow chart of EMD is given. And combined with the characteristic of MT signal, some noduses that exist on the EMD, such as fluctuations, end effects and sifting-stopping criteria, are studied and given the method to resolve the relevant problems. Taking a simulative signal as an example, the basic flow of signal processing based on HHT is given and the superiority of Hilbert-Huang transform to analyze the MT signals is verified.
The innovation of the HHT method brings a new way to filter data and reduce noise. The EMD filters signal with different time scales and is adaptive to signal. The intrinsic mode function (IMF) is result of multi-band filtering and can be completely reconstructed. Using the structural characteristics of the IMF, some new space-time filters and a hard (soft) threshold method can be realized to de-noise. This paper studies the characteristics of MT signal and its noise. The principle and step of de-noising method based on EMD are given. Some noises, such as impulse jamming, rectangle disturbing and sine wave noise, are analyzed and processed for the actual MT data. The results show that the de-noising method is effective and the quality of MT data is improved greatly. The EMD method can achieves stationary and reliable parameter estimations.
Time-frequency analysis is a powerful tool for non-stationary signal processing. It will express signal as a joint function of time and frequency and reveal the time-varying characteristics of the signal. HHT method has overcome the shortcomings of other ways, completes abolition of the role of the window function and is not restricted with nuclear function and Heisenberg principle. Hilbert-Huang spectrum can precisely describe the nonlinear and non-stationary characteristics of MT signals. This paper compares the different time-frequency spectrums that are from several commonly method such as short time Fourier transform, Wigner-Ville distribution and Wavelet transform. Based on these characteristics, the time-frequency characteristics of HHT spectrum of MT signal are studied. Then Hilbert time-frequency spectrum is used in the MT signal noise recognition, data filtering and sub-smooth. Its application methods and application results are studied in this thesis.
Power spectrum estimation takes an important role in MT signal processing. The most traditional and the most important power spectrum estimation method is the classical periodogram method which bases on the Fourier transform. The Fourier transform contradicts the non-linear, non-stationary nature of MT signal, which will inevitably lead to spectral estimation error. A new spectrum estimation method based on Hilbert-Huang transform is proposed in this paper. Firstly the marginal spectrum method based on HHT is presented and the linear property of marginal spectrum is demonstrated. Then, compared with the FT method, the physical signification and the preponderance of marginal spectrum for MT signal are further discussed. And some methods to improve the precision of spectrum estimation are proposed in detail. Finally the simulative data and the practical MT data are analyzed. The simulation and results of real data indicate that the HHT method suits the nature of MT signal much more.
The characteristics of apparent resistivity and phase curves are mainly basis for analyzing the structure of the earth and distribute of conduction in MT sounding. Therefore analyzing, calculating and processing of impedance are one of the most basis and importance works. The non-stationary characteristics of MT signal cause that impedance estimation results have time-varying characteristics. Therefore, using time-frequency analysis methold to estimate parameters from the instantaneous spectrum are more conducive to robust estimation comparing with Fourier methold. This paper proposes a kind of instantaneous spectrum method to estimate impedance tensor based on the HHT marginal spectrum. The flow chart and mathematics model are given. Some simulative signal and a place of measured MT signals is processed. The results shows that the impedance tensor obtained from the HHT transient spectrum minimizes the estimation warp brought about by the non-stationary characteristics of MT data, and the estimated parameter is more stable and reliable than that from conventional methods. The parameter curves are less bars and more smooth, reasonable. The interpretability of data has been significantly improved.
Through the above studies, the results show that the Hilbert-Huang transform is an effective method to deal with the non-stationary signals and provides a new way to process MT signal. HHT method has a wide application on MT signal noise suppressing, time-frequency analysis, power spectrum estimation and impedance estimation.
引文
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