CN109581518A - One kind is without synchronizing current acquisition transmission and the acquisition of frequency domain measurement SIP data and processing method - Google Patents
One kind is without synchronizing current acquisition transmission and the acquisition of frequency domain measurement SIP data and processing method Download PDFInfo
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Abstract
本发明一种无需同步电流采集传输和频域测量SIP数据采集和处理方法,其特点是利用绝对相位计算方法事先计算发射机所能发射的所有频率电流的初始相位和振幅归一化系数,在初始相位和振幅归一化系数的基础之上生成初始相位表文件;即生成发射频率表与初始相位表;其某一频率的激励电流在任意时刻的相位值,则利用其起始发射时间和该频率电压数据的采集时间,按照相对相位计算方法获得;再根据长度自动约束全相位频谱分析获得的电压振幅和相位,即能够得到该频点处的复电阻率。本发明以摆脱系统对高性能的同步电流采集和实时传输设备或者高精度的频域观测装置的依赖性,提高了SIP法的灵活性,实现在GPS信号微弱等复杂环境下顺利开展SIP法观测。
The present invention is a SIP data acquisition and processing method without synchronous current acquisition and transmission and frequency domain measurement. The initial phase table file is generated on the basis of the initial phase and amplitude normalization coefficients; that is, the emission frequency table and the initial phase table are generated; the phase value of the excitation current of a certain frequency at any time is used to use its initial emission time and The acquisition time of the frequency voltage data is obtained according to the relative phase calculation method; then the voltage amplitude and phase obtained by the full-phase spectrum analysis are automatically constrained according to the length, that is, the complex resistivity at the frequency point can be obtained. The invention improves the flexibility of the SIP method by getting rid of the dependence of the system on the high-performance synchronous current acquisition and real-time transmission equipment or the high-precision frequency domain observation device, and realizes the smooth development of the SIP method observation in complex environments such as weak GPS signals. .
Description
技术领域technical field
本发明属于地球物理电磁探测领域,具体涉及一种无需同步电流采集传输 和频域测量频率域激发极化法(SIP法)数据采集和处理方法。The invention belongs to the field of geophysical electromagnetic detection, and in particular relates to a frequency domain stimulated polarization method (SIP method) data acquisition and processing method without synchronous current acquisition and transmission and frequency domain measurement.
背景技术Background technique
频率域激发极化法(SIP法)是激发极化法的一个重要分支,观测目标是 测区的复电阻率。该方法能够对测区地下介质的电性结构进行更加详尽的描述, 是一种重要的详查手段。SIP法即可以在时间域又能够在频率域实现高密度观 测,与其他地球物理勘探手段相比,SIP法具有多参数测量和综合信息输出的 优势。The frequency domain induced polarization method (SIP method) is an important branch of the induced polarization method, and the observation target is the complex resistivity of the measurement area. This method can describe the electrical structure of the underground medium in the survey area in more detail, and is an important detailed investigation method. Compared with other geophysical exploration methods, the SIP method has the advantages of multi-parameter measurement and comprehensive information output.
目前,现有的SIP数据采集方式和相应的观测系统主要分为两种:At present, the existing SIP data collection methods and corresponding observation systems are mainly divided into two types:
(1)直接采集电压信号和电流信号的振幅和相位,然后利用这些频率域参 数计算测区复电阻率;(1) Directly collect the amplitude and phase of the voltage signal and the current signal, and then use these frequency domain parameters to calculate the complex resistivity of the measurement area;
(2)同步采集电压信号和电流信号的时域数据,然后进行离散傅里叶变换 (DFT),并利用变换的频率域参数结果求测区复电阻率。(2) Simultaneously collect the time domain data of the voltage signal and the current signal, then perform discrete Fourier transform (DFT), and use the transformed frequency domain parameter results to obtain the complex resistivity of the measurement area.
第一种方法需要实现高精度的频率域测量,观测系统主要由大功率发射机、 高精度频域测量接收机、电极等装置构成。其中接收机由虚分量通道、实分量 通道、相关检测单元等关键模块构成。而现有的相位测量方法对发射机和接收 机的要求都很高。首先要求激励电流波形失真要尽量小,且零点要较为稳定, 同时接收机也要具备很高的零点稳定性。但是,野外观测的电磁信号一般都较 为微弱,相位测量精度难以得到保证。另外,幅度测量虽然相对相位测量要容 易一些,但是当环境噪声较大时,要完成高精度振幅测量则需加大供电电流来 提高信噪比。总的来说,频率域数据采集方法要求观测系统具有相当高的精度和稳定度,因而会提高观测成本,不利于开展野外工作。The first method needs to achieve high-precision frequency domain measurement. The observation system is mainly composed of high-power transmitters, high-precision frequency-domain measurement receivers, electrodes and other devices. The receiver is composed of key modules such as imaginary component channel, real component channel, and correlation detection unit. However, the existing phase measurement methods have high requirements on both the transmitter and the receiver. First of all, it is required that the distortion of the excitation current waveform should be as small as possible, and the zero point should be relatively stable, and the receiver should also have a high zero point stability. However, the electromagnetic signals observed in the field are generally weak, and the phase measurement accuracy cannot be guaranteed. In addition, although the amplitude measurement is easier than the phase measurement, when the ambient noise is large, to complete the high-precision amplitude measurement, it is necessary to increase the power supply current to improve the signal-to-noise ratio. In general, the frequency-domain data acquisition method requires the observation system to have quite high accuracy and stability, which increases the cost of observation and is not conducive to field work.
而第二种观测方法系统组成包括大功率发射机、接收机、电流检测装置、 同步电流传输装置、电极以及配套电缆等相关外围设备。该系统对仪器硬件要 求较高,尤其是系统的同步性、实时性以及辅助装置的抗噪声能力等。The system composition of the second observation method includes high-power transmitter, receiver, current detection device, synchronous current transmission device, electrodes and supporting cables and other related peripheral equipment. The system has high requirements on instrument hardware, especially the synchronization, real-time performance of the system and the anti-noise ability of auxiliary devices.
发明内容SUMMARY OF THE INVENTION
本发明目的旨在简化传统SIP观测系统,提高SIP法的灵活性和应用范围, 提出了一种新的SIP数据采集和处理算法。以摆脱系统对高性能的同步电流采 集和实时传输设备或者高精度的频域观测装置的依赖性,降低观测成本;提高 了SIP法的灵活性,实现在GPS信号微弱等复杂环境下顺利开展SIP法观测。The purpose of the present invention is to simplify the traditional SIP observation system, improve the flexibility and application range of the SIP method, and propose a new SIP data acquisition and processing algorithm. In order to get rid of the system's dependence on high-performance synchronous current acquisition and real-time transmission equipment or high-precision frequency domain observation devices, the observation cost is reduced; the flexibility of the SIP method is improved, and the SIP can be successfully carried out in complex environments such as weak GPS signals. law observation.
为实现上述目的,本发明的技术方案是:For achieving the above object, the technical scheme of the present invention is:
一种无需同步电流采集传输和频域测量SIP数据采集和处理方法,其特征 在于:包括初始相位表生成、相对相位计算和绝对相位计算,所述相对相位计 算是与电流传输时间相关的相位移动,所述绝对相位计算是电流信号的初始相 位;A method for SIP data acquisition and processing without synchronization of current acquisition and transmission and frequency domain measurement, characterized in that it includes initial phase table generation, relative phase calculation, and absolute phase calculation, wherein the relative phase calculation is a phase shift related to current transmission time , the absolute phase calculation is the initial phase of the current signal;
首先,利用绝对相位计算方法事先计算发射机所能发射的所有频率电流的 初始相位和振幅归一化系数,在初始相位和振幅归一化系数的基础之上生成初 始相位表文件;即生成发射频率表与初始相位表;First, use the absolute phase calculation method to calculate the initial phase and amplitude normalization coefficients of all frequency currents that the transmitter can transmit in advance, and generate the initial phase table file on the basis of the initial phase and amplitude normalization coefficients; Frequency table and initial phase table;
其次,某一频率的激励电流在任意时刻的相位值,则利用其起始发射时间 和该频率电压数据的采集时间,按照相对相位计算方法获得;Secondly, the phase value of the excitation current of a certain frequency at any time can be obtained according to the relative phase calculation method by using its initial emission time and the acquisition time of the frequency voltage data;
最后,再根据长度自动约束全相位频谱分析获得的电压振幅和相位,即能够 得到该频点处的复电阻率;Finally, the voltage amplitude and phase obtained by the full-phase spectrum analysis are automatically constrained according to the length, that is, the complex resistivity at the frequency point can be obtained;
所述的长度自动约束全相位频谱分析由长度自动约束全相位矩阵变换、自卷 积加窗和傅里叶变换三部分组成。The length auto-constrained full-phase spectrum analysis is composed of three parts: length auto-constrained full-phase matrix transformation, self-convolution windowing and Fourier transform.
所述的绝对相位计算方法为:The absolute phase calculation method is:
由原始数据构成全相位矩阵,同时由激励信号频率fin和对应的采样率fs加 数据长度约束N至N点自卷积窗,N点自卷积窗与全相位矩阵再经加窗傅里叶 变换,求得信号绝对相位;The full-phase matrix is formed from the original data, and the self-convolution window of N to N points is constrained by the excitation signal frequency f in and the corresponding sampling rate f s plus the data length. Lie transform to obtain the absolute phase of the signal;
所述的数据长度约束是对全相位变换的长度N进行约束使其满足整周期截 断。因为SIP法的激励信号多为一系列频率不同的方波,所以N应该由激励信 号频率fin和对应的采样率fs来决定:The data length constraint is to constrain the length N of the full-phase transformation to satisfy the full-cycle truncation. Because the excitation signal of the SIP method is mostly a series of square waves with different frequencies, N should be determined by the excitation signal frequency f in and the corresponding sampling rate f s :
其中,d1和d2均为整数。d1需满足令符号||||内的值为整数,参数d2要保证 窗长大于预设的阈值σ,该阈值与采样率有关,如表1所示。Wherein, d 1 and d 2 are both integers. d 1 needs to satisfy that the value in the symbol |||| is an integer, and parameter d 2 needs to ensure that the window length is greater than the preset threshold σ, which is related to the sampling rate, as shown in Table 1.
表1不采样率下的窗长阈值Table 1 Window length threshold without sampling rate
令则d2根据下式计算:make Then d2 is calculated according to the following formula:
其中,ceil()表示向上取整。Among them, ceil() means round up.
所述的根据长度自动约束全相位频谱分析获得的电压振幅和相位,计算步 骤为:The described voltage amplitude and phase obtained by automatic constraint full-phase spectrum analysis according to the length, the calculation steps are:
(1)根据频率信息对“初始相位表”进行查表,找到当前频率对应的电流 初始相位和振幅归一化系数;(1) According to the frequency information, the "initial phase table" is looked up to find the current initial phase and amplitude normalization coefficient corresponding to the current frequency;
(2)根据发射频率表提供的时间信息以及当前电压数据开始采集的时间, 可以获得当前数据时间与该频率信号起始发射时间之间的时间偏移量Δt,另外, A/D采集过程中,由于硬件启动间隔会造成128个数据点丢失,所以在计算Δt 时需考虑丢失数据点造成的时间偏差,该值与当前采样率fs有关,数据段任意 时刻的Δt计算方法如下:(2) According to the time information provided by the transmission frequency table and the time when the current voltage data starts to be collected, the time offset Δt between the current data time and the start time of the frequency signal transmission can be obtained. In addition, during the A/D collection process , since the hardware startup interval will cause 128 data points to be lost, the time deviation caused by the missing data points needs to be considered when calculating Δt. This value is related to the current sampling rate f s . The calculation method of Δt at any time in the data segment is as follows:
其中,fin是当前频率;where f in is the current frequency;
nskip是当前计算的数据段在电压数据块中的起始位置;n skip is the starting position of the currently calculated data segment in the voltage data block;
tini(fin)是当前频率电流起始发射时间;t ini (f in ) is the current frequency current start emission time;
tnow(fin)是当前电压信号开始采集时间;t now (f in ) is the current voltage signal acquisition time;
(3)利用长度自动约束全相位频谱分析计算电压的相位和振幅,且DFT长 度N与同频率电流信号的全相位矩阵相同;(3) Utilize the phase and the amplitude of the full-phase spectrum analysis calculation voltage to automatically constrain the length, and the DFT length N is identical with the full-phase matrix of the current signal of the same frequency;
(4)计算正在处理的电压信号同步的电流信号的相位,计算公式如下:(4) Calculate the phase of the current signal synchronized with the voltage signal being processed, and the calculation formula is as follows:
(5)利用公式(8)和公式(9)计算该频点的复电阻率相位和振幅:(5) Use formula (8) and formula (9) to calculate the complex resistivity phase and amplitude of this frequency point:
其中和分别为当前电压和电流的相位值;in and are the phase values of the current voltage and current, respectively;
其中,是电压振幅,是振幅归一化系数,I(fin)是当前电 流强度;in, is the voltage amplitude, is the amplitude normalization coefficient, and I(f in ) is the current current intensity;
最后对计算结果进行校正获得实测复电阻率信息。Finally, the calculated results are corrected to obtain the measured complex resistivity information.
所述的绝对相位解算是利用长度自动约束全相位频谱分析实现的。The absolute phase solution described is achieved by using length auto-constrained full-phase spectrum analysis.
所述的发射频率表是一个“频率-时间表”,里面包含以下信息:信号类型、 发射频率、电流强度以及发射持续时间等。The transmission frequency table is a "frequency-schedule", which contains the following information: signal type, transmission frequency, current strength and transmission duration.
所述的初始相位表是一个利用长度自动约束全相位频谱分析计算获得的 “初始相位-振幅-频率表”,包含的信息为:信号频率、初始相位、振幅归一化 系数以及长度约束值N。The initial phase table is an "initial phase-amplitude-frequency table" obtained by using the length automatic constraint full-phase spectrum analysis calculation, and the information contained is: signal frequency, initial phase, amplitude normalization coefficient and length constraint value N .
所述的相位和振幅解算方法是根据频率信息对“初始相位表”进行查表, 找到当前频率对应的电流初始相位和振幅归一化系数,然后根据发射频率表提 供的时间信息以及当前电压数据开始采集的时间,可以获得当前数据时间与该 频率信号起始发射时间之间的时间偏移量△t,利用该频点处的电压相位和该频 率电流的起始相位、频率以及时间偏移量四者之间的关系计算出复电阻率在频 点fin处的相位,振幅则可以利用归一化方法获得。The phase and amplitude solution method is to look up the "initial phase table" according to the frequency information, find the current initial phase and amplitude normalization coefficient corresponding to the current frequency, and then according to the time information provided by the transmitting frequency table and the current voltage. The time when the data starts to be collected, the time offset Δt between the current data time and the initial transmission time of the frequency signal can be obtained, using the voltage phase at the frequency point and the starting phase, frequency and time offset of the current at this frequency The relationship between the four shifts calculates the phase of the complex resistivity at the frequency point f in , and the amplitude can be obtained by the normalization method.
本发明与现有技术相比具有实质性特点和显著性效果:Compared with the prior art, the present invention has substantial features and significant effects:
本发明无需同步电流采集传输和频域测量装置,利用绝对相位计算方法和 相对相位计算方法结合频率时间表来求电流的相位,而振幅则利用归一化手段 获得。相位计算无需额外的校正手段即可获得高精度的相位计算结果,与传统 DFT和加窗DFT相比具有精度高和算法简单的优势。其特点为:The present invention does not need synchronous current acquisition and transmission and frequency domain measurement device, uses absolute phase calculation method and relative phase calculation method combined with frequency schedule to obtain the current phase, and the amplitude is obtained by normalization. The phase calculation can obtain high-precision phase calculation results without additional correction means, and has the advantages of high precision and simple algorithm compared with traditional DFT and windowed DFT. Its features are:
1.简化了传统SIP观测系统,摆脱了系统对高性能的同步电流采集和实时 传输设备或者高精度的频域观测装置的依赖性,降低了观测成本;1. Simplify the traditional SIP observation system, get rid of the dependence of the system on high-performance synchronous current acquisition and real-time transmission equipment or high-precision frequency domain observation device, and reduce the observation cost;
2.改进了传统复电阻率计算方法,采用长度自动约束全相位频谱分析提高 了相位计算精度2. The traditional complex resistivity calculation method is improved, and the full-phase spectrum analysis is automatically constrained by the length to improve the phase calculation accuracy
3.提高了SIP法的灵活性,在GPS信号微弱等复杂环境下也能够顺利开展 SIP法观测。3. The flexibility of the SIP method is improved, and the SIP method observation can be carried out smoothly in complex environments such as weak GPS signals.
附图说明Description of drawings
图1是绝对相位计算方法。Figure 1 shows the absolute phase calculation method.
图2是本发明的SIP法数据采集和处理流程。Fig. 2 is the data collection and processing flow of the SIP method of the present invention.
图3本发明初始相位表生成方法。FIG. 3 is a method for generating an initial phase table of the present invention.
图4是复电阻率计算结果校正算法。Fig. 4 is the correction algorithm of the calculation result of complex resistivity.
图5是不同算法获得的复电阻率计算值和理论值对比图。Figure 5 is a comparison diagram of the calculated and theoretical values of complex resistivity obtained by different algorithms.
图6是工频干扰下的SIP复电阻率计算值和理论值对比图。Figure 6 is a comparison diagram of the calculated value and theoretical value of SIP complex resistivity under power frequency interference.
图7是SIP野外实测结果。上图是复电阻率振幅曲线,下图是相位曲线。Figure 7 is the field measurement result of SIP. The upper graph is the complex resistivity amplitude curve, and the lower graph is the phase curve.
图8是SIP观测数据处理软件界面。Figure 8 is the SIP observation data processing software interface.
具体实施方式Detailed ways
以下结合附图详细说明本发明的具体实施方式The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
首先,本发明通过现有理论分析证明复电阻率的“实部和虚部”与“振幅 和相位”是等效的,二者可相互转化。据此,某一频点的复电阻率可利用该频 率的电压振幅和相位,以及与该段电压数据同步的电流信号的振幅和相位获得。 此外,电压信号的振幅和相位可以通过对原始采样数据进行时频变换直接求取。 但是因为同步电流数据的缺失,电流信号的频谱信息不能用这种方式计算。First of all, the present invention proves that "real part and imaginary part" and "amplitude and phase" of complex resistivity are equivalent through existing theoretical analysis, and the two can be converted into each other. Accordingly, the complex resistivity of a certain frequency can be obtained by using the voltage amplitude and phase of the frequency, and the amplitude and phase of the current signal synchronized with the voltage data of this segment. In addition, the amplitude and phase of the voltage signal can be directly obtained by performing time-frequency transformation on the original sampled data. However, due to the lack of synchronous current data, the spectral information of the current signal cannot be calculated in this way.
这种情况下,本发明利用绝对相位计算方法和相对相位计算方法结合频率 时间表来求电流的相位,而振幅则利用归一化手段获得。绝对相位计算方法是 利用长度自动约束全相位频谱分析实现的。In this case, the present invention uses the absolute phase calculation method and the relative phase calculation method in combination with the frequency schedule to obtain the phase of the current, and the amplitude is obtained by normalization. The absolute phase calculation method is implemented using the length auto-constrained full-phase spectrum analysis.
本发明的方法无需额外的校正手段即可获得高精度的相位计算结果,与传 统DFT和加窗DFT相比具有精度高和算法简单的优势。The method of the invention can obtain a high-precision phase calculation result without additional correction means, and has the advantages of high precision and simple algorithm compared with the traditional DFT and the windowed DFT.
本发明利用绝对相位计算方法,包括相对相位计算和绝对相位计算,前者 指的是与电流传输时间相关的相位移动,而后者指的是电流信号的初始相位。 首先,计算发射机所能发射的所有频率电流的初始相位和振幅归一化系数,并 在此基础之上生成初始相位表文件,即生成发射频率表与初始相位表;其次, 某一频率的激励电流在任意时刻的相位值,则利用其起始发射时间和该频率电 压数据的采集时间,按照相对相位计算方法获得;最后,再根据长度自动约束 全相位频谱分析获得的电压振幅和相位,就能够得到该频点处的复电阻率。The present invention utilizes an absolute phase calculation method, including relative phase calculation and absolute phase calculation, the former refers to the phase shift related to the current transit time, and the latter refers to the initial phase of the current signal. First, calculate the initial phase and amplitude normalization coefficients of all frequency currents that the transmitter can transmit, and then generate the initial phase table file on this basis, that is, generate the transmitting frequency table and the initial phase table; The phase value of the excitation current at any time is obtained by using its initial emission time and the acquisition time of the voltage data at this frequency according to the relative phase calculation method; finally, the voltage amplitude and phase obtained by the full-phase spectrum analysis are automatically constrained according to the length, The complex resistivity at this frequency can be obtained.
对于SIP法发射机而言,其输出的某一频率电流x(fin)的初始相位是一定的, 至少在短期内该数值不变。这样,该信号在任意时刻的相位可由公式(1)计算 获得。For the SIP method transmitter, the initial phase of the output current x(f in ) at a certain frequency is constant, at least in a short period of time, the value does not change. In this way, the phase of the signal at any time can be calculated and obtained by formula (1).
phase_It(fin)=mod(Δt×fin)×2π+phase_Iini(fin) (1)phase_I t (f in )=mod(Δt×f in )×2π+phase_I ini (f in ) (1)
其中:fin和phase_Iini(fin)分别是当前电流的频率和初始相位,Δt是电流开始发射时刻到数据采集时刻的时间差。Where: f in and phase_I ini (f in ) are the frequency and initial phase of the current current, respectively, and Δt is the time difference from the moment when the current starts transmitting to the moment when the data is collected.
以上分析表明,一旦发射电流的振幅和频率固定了,那么其在任何时刻的 频率域参数就都是可以确知的。此外,电压信号的频域信息可以利用原始数据 进行时频转换获得。这样,复电阻率参数可以根据公式(2)和公式(3)计算获 得。The above analysis shows that once the amplitude and frequency of the emission current are fixed, its frequency domain parameters at any time can be known with certainty. In addition, the frequency domain information of the voltage signal can be obtained by time-frequency conversion using the original data. In this way, the complex resistivity parameter can be calculated according to formula (2) and formula (3).
phase_ρ(fin)=phase_U(fin)-Δphase_I(fin)-phase_Iini(fin)phase_ρ(f in )=phase_U(f in )-Δphase_I(f in )-phase_I ini (f in )
=phase_U(fin)-mod(Δt×fin)×2π-phase_Iini(fin) (2)=phase_U(f in )-mod(Δt×f in )×2π-phase_I ini (f in ) (2)
Amp_ρ(fin)=Amp_U(fin)/Amp_Iini(fin). (3)Amp_ρ(f in )=Amp_U(f in )/Amp_I ini (f in ). (3)
公式(2)表明复电阻率在频点fin处的相位是由该频点处的电压相位 phase_U和该频率电流的起始相位phase_Iini、频率fin以及传输时间Δt(发射起始 时间tini和电压数据采集时间tn之间的差值)四者共同决定的。而振幅则可以利用 归一化方法获得。Formula (2) shows that the phase of the complex resistivity at the frequency point f in is determined by the voltage phase phase_U at the frequency point and the initial phase phase_I ini of the frequency current, the frequency f in and the transmission time Δt (the transmission start time t The difference between ini and voltage data acquisition time t n ) is jointly determined by the four. The amplitude can be obtained by the normalization method.
这样,在无同步电流数据采集和传输设备的情况下,根据以下几个参数: 当前电流频率fin、电流强度(振幅)A、初始相位phase_Iini以及传输时间Δt(相 对发射开始时间而言),就可以确定当前激励电流信号的频域信息。这就是本发 明设计SIP数据实时算法的理论基础。In this way, in the absence of synchronous current data acquisition and transmission equipment, according to the following parameters: current current frequency f in , current intensity (amplitude) A, initial phase phase_I ini and transmission time Δt (relative to the start time of transmission) , the frequency domain information of the current excitation current signal can be determined. This is the theoretical basis for designing the SIP data real-time algorithm in the present invention.
本发明的关键问题是相位的计算,包括相对相位计算和绝对相位计算。前者 指的是与电流传输时间相关的相位移动,而后者指的是电流信号的初始相位。The key problem of the present invention is the calculation of the phase, including the calculation of the relative phase and the calculation of the absolute phase. The former refers to the phase shift relative to the current transit time, while the latter refers to the initial phase of the current signal.
在信号频率稳定且已知的情况下,复电阻率相位计算误差可能来自电压相 位误差phase_Uerr(fin)、电流初始相位误差phase_Iinierr(fin)以及时间误差Δterr。前 两者是由算法准确度决定的,第三项则是由时间记录的准确度控制的。电流起 始相位和电压相位都利用绝对相位计算方法来获得。When the signal frequency is stable and known, the complex resistivity phase calculation error may come from the voltage phase error phase_U err (f in ), the current initial phase error phase_I inierr (f in ), and the time error Δt err . The first two are determined by the accuracy of the algorithm, and the third is controlled by the accuracy of the time record. Both the current starting phase and the voltage phase are obtained using the absolute phase calculation method.
最基本也是最常用的相位计算方法为傅里叶变换,对于离散信号而言为离 散傅里叶变换(DFT)。直接DFT和加窗DFT都会在一定程度上受到频谱泄露 作用的影响。当不存在频率误差或者频率误差很小时,加窗反而会使频谱泄露 作用更加明显。另外,窗函数在抑制旁瓣泄露的同时还会引起主瓣模糊,这种 作用在频率分量较为密集的多频信号处理中尤为明显。The most basic and most commonly used phase calculation method is the Fourier transform, which is the discrete Fourier transform (DFT) for discrete signals. Both direct DFT and windowed DFT are affected to some extent by spectral leakage effects. When there is no frequency error or the frequency error is very small, adding window will make the spectral leakage effect more obvious. In addition, the window function can also cause blurring of the main lobe while suppressing the leakage of the side lobes. This effect is especially obvious in the multi-frequency signal processing with dense frequency components.
为获得较为精确的频谱参数,尤其是相位,本发明采用了长度自动约束全相 位频谱分析,该方法具有计算量小、相位精度高的优点。因为本发明对相位计 算精度要求非常高,所以对全相位变换加入了一些约束条件。In order to obtain more accurate spectrum parameters, especially the phase, the present invention adopts the full-phase spectrum analysis with automatic length constraint, and this method has the advantages of small calculation amount and high phase precision. Because the present invention has very high requirements on the phase calculation accuracy, some constraints are added to the full phase transformation.
所述的长度自动约束全相位频谱分析由全相位矩阵变换、长度自动约束自卷 积加窗和傅里叶变换三部分组成。The length auto-constrained full-phase spectrum analysis consists of three parts: full-phase matrix transformation, auto-length auto-constrained self-convolution windowing and Fourier transform.
如图1所示,本发明所述绝对相位计算方法为:原始数据构成全相位矩阵, 同时由激励信号频率fin和对应的采样率fs加数据长度约束N获得N点自卷积 窗,自动长度约束N点自卷积窗与全相位矩阵再经加窗傅里叶变换,求得信号 绝对相位。As shown in Figure 1, the absolute phase calculation method of the present invention is as follows: the original data constitutes a full-phase matrix, and at the same time, an N-point self-convolution window is obtained from the excitation signal frequency f in and the corresponding sampling rate f s plus the data length constraint N, The automatic length-constrained N-point self-convolution window and the full-phase matrix are then subjected to windowed Fourier transform to obtain the absolute phase of the signal.
所述的数据长度约束是对全相位变换的自卷积窗长度N进行约束使其满足 整周期截断。因为SIP法的激励信号多为一系列频率不同的方波,所以N应该 由激励信号频率fin和对应的采样率fs来决定:The data length constraint is to constrain the self-convolution window length N of the full-phase transformation to satisfy the full-cycle truncation. Because the excitation signal of the SIP method is mostly a series of square waves with different frequencies, N should be determined by the excitation signal frequency f in and the corresponding sampling rate f s :
其中,d1和d2均为整数。d1需满足令符号||||内的值为整数,参数d2要保证 窗长大于预设的阈值σ,该阈值与采样率有关,如表1所示。Wherein, d 1 and d 2 are both integers. d 1 needs to satisfy that the value in the symbol |||| is an integer, and parameter d 2 needs to ensure that the window length is greater than the preset threshold σ, which is related to the sampling rate, as shown in Table 1.
表2不采样率下的窗长阈值Table 2 Window length threshold without sampling rate
令则d2根据下式计算:make Then d2 is calculated according to the following formula:
其中,ceil()表示向上取整。Among them, ceil() means round up.
本发明所述SIP法数据采集和处理方法具体实现流程如下:The specific implementation flow of the SIP method data acquisition and processing method of the present invention is as follows:
如图2所示,SIP数据采集和处理流程图,首先,生成发射频率表与初始 相位表,其次,制定一个“频率-时间表”(以下简称“发射频率表”),里面包 含以下信息:信号类型、发射频率、电流强度以及发射时间等。然后将发射频 率表存入发射机和采集站。观测系统开始工作后,发射机按照“发射频率表” 开始依次循环发射电流。然后接收机随时可以开始采集电压数据。这一点比目 前常用SIP数据采集方法的局限性小。为保证能采集到所有频率的电压信号, 总的采集时间不能小于一次循环的总时间。然后计算复电阻率振幅和相位,计 算步骤为:As shown in Figure 2, the SIP data acquisition and processing flow chart, first, generate the transmission frequency table and initial phase table, secondly, formulate a "frequency-timetable" (hereinafter referred to as "transmission frequency table"), which contains the following information: Signal type, transmission frequency, current strength and transmission time, etc. The transmit frequency table is then stored in the transmitter and acquisition station. After the observation system starts to work, the transmitter starts to circulate the emission current in turn according to the "transmission frequency table". The receiver is then ready to start collecting voltage data. This is less limited than the current commonly used SIP data collection methods. To ensure that voltage signals of all frequencies can be collected, the total collection time cannot be less than the total time of one cycle. Then calculate the complex resistivity amplitude and phase, the calculation steps are:
(1)根据频率信息对“初始相位表”进行查表,找到当前频率对应的电流 初始相位和振幅归一化系数;(1) According to the frequency information, the "initial phase table" is looked up to find the current initial phase and amplitude normalization coefficient corresponding to the current frequency;
(2)根据发射频率表提供的时间信息以及当前电压数据开始采集的时间, 可以获得当前数据时间与该频率信号起始发射时间之间的时间偏移量Δt,另外, A/D采集过程中,由于硬件启动间隔会造成128个数据点丢失,所以在计算Δt 时需考虑丢失数据点造成的时间偏差,该值与当前采样率fs有关,数据段任意 时刻的Δt计算方法如下:(2) According to the time information provided by the transmission frequency table and the time when the current voltage data starts to be collected, the time offset Δt between the current data time and the start time of the frequency signal transmission can be obtained. In addition, during the A/D collection process , since the hardware startup interval will cause 128 data points to be lost, the time deviation caused by the missing data points needs to be considered when calculating Δt. This value is related to the current sampling rate f s . The calculation method of Δt at any time in the data segment is as follows:
其中,fin是当前频率;where f in is the current frequency;
nskip是当前计算的数据段在电压数据块中的起始位置;n skip is the starting position of the currently calculated data segment in the voltage data block;
tini(fin)是当前频率电流起始发射时间;t ini (f in ) is the current frequency current start emission time;
tnow(fin)是当前电压信号开始采集时间;t now (f in ) is the current voltage signal acquisition time;
(3)利用长度自动约束全相位频谱分析计算电压的相位和振幅,且DFT长度N 与同频率电流信号的全相位变换自卷积窗长度相同;(3) The phase and amplitude of the voltage are calculated by using the length automatic constraint full-phase spectrum analysis, and the DFT length N is the same as the full-phase transform self-convolution window length of the current signal of the same frequency;
(4)计算正在处理的电压信号同步的电流信号的相位,计算公式如下:(4) Calculate the phase of the current signal synchronized with the voltage signal being processed, and the calculation formula is as follows:
(5)利用公式(8)和公式(9)计算该频点的复电阻率相位和振幅:(5) Use formula (8) and formula (9) to calculate the complex resistivity phase and amplitude of this frequency point:
其中和分别为当前电压和电流的相位值。in and are the phase values of the current voltage and current, respectively.
其中,是电压振幅,是振幅归一化系数,I(fin)是当前电流强度。in, is the voltage amplitude, is the amplitude normalization factor and I(f in ) is the current current intensity.
最后对计算结果进行校正获得实测复电阻率信息。Finally, the calculated results are corrected to obtain the measured complex resistivity information.
如图3所示,本发明初始相位表生成方法。在正式进行SIP法观测之前, 采集SIP发射机产生的所有频率的信号,然后利用长度自动约束全相位频谱分 析计算它们的初始相位和归一化振幅系数,并在此基础之上生成“初始相位- 振幅-频率表”(以下简称“初始相位表”),该表包含的信息为:信号频率、初 始相位、振幅归一化系数以及长度约束值N。初始相位表文件格式见表2。其 中,第一列是激励电流频率,第二列和第三列是直接采样数据的初始相位和振 幅归一化系数。第四列和第五列是利用谐波滤波器处理后的数据的初始相位和 振幅归一化系数。因为野外观测环境复杂,当工频干扰较强时需先进行工频滤 波,滤波器会对原始采样数据的振幅和相位造成一定影响,尤其是相位,所以 初始频率表中加入了发射电流滤波后的频谱信息以供野外实时数据处理需要。As shown in FIG. 3 , the method for generating an initial phase table of the present invention is shown. Before the SIP method is formally observed, the signals of all frequencies generated by the SIP transmitter are collected, and then their initial phases and normalized amplitude coefficients are calculated by using the length automatic constrained full-phase spectrum analysis, and on this basis, the "initial phase" is generated. - Amplitude-frequency table" (hereinafter referred to as "initial phase table"), the information contained in this table is: signal frequency, initial phase, amplitude normalization coefficient and length constraint value N. The initial phase table file format is shown in Table 2. Among them, the first column is the excitation current frequency, and the second and third columns are the initial phase and amplitude normalization coefficients of the directly sampled data. The fourth and fifth columns are the initial phase and amplitude normalization coefficients of the data processed with the harmonic filter. Because the field observation environment is complex, when the power frequency interference is strong, it is necessary to perform power frequency filtering first. The filter will have a certain impact on the amplitude and phase of the original sampled data, especially the phase. Therefore, the transmission current filter is added to the initial frequency table. spectrum information for real-time data processing in the field.
表3“初始相位表”文件格式Table 3 "Initial Phase Table" file format
初始相位表生成过程。两个虚线框中的数据处理过程完全相同。表3是一 个发射频率表示例。FD代表信号波形为方波。各频率信号持续循环发射。发射 结束时间是指当前频率信号发送结束时间与第一个频率信号发射开始时间之间 的差值。比如,假设表3中128Hz信号是00:00:00时刻开始发送的,则该频率 信号在00:00:50结束发生,同时64Hz信号开始发射至00:01:40结束,以下信 号依次类推。Initial phase table generation process. The data processing process in the two dashed boxes is exactly the same. Table 3 is an example of a transmit frequency table. FD represents that the signal waveform is a square wave. Each frequency signal is continuously cyclically transmitted. The transmission end time refers to the difference between the current frequency signal transmission end time and the first frequency signal transmission start time. For example, assuming that the 128Hz signal in Table 3 starts to be sent at 00:00:00, the frequency signal ends at 00:00:50, and the 64Hz signal starts to transmit until 00:01:40, and the following signals are deduced in turn.
表4发射频率表Table 4 Transmit frequency table
因为频率域电磁法的测量结果中包含了系统自身响应,所以还需要通过标 定数据对计算结果进行校正,这样最终可获得测区真实复电阻率信息。Because the measurement results of the electromagnetic method in the frequency domain include the response of the system itself, it is necessary to correct the calculation results through the calibration data, so that the real complex resistivity information of the measurement area can be finally obtained.
如图4所示,复电阻率计算结果校正方法。由于每次观测使用的频率值不 一定完全相同,而标定的频点数又有限,所以首先需要利用插值法计算校正系 数。根据信号频率fin,查标定数据表找到fin的临近点,然后利用插值法计算fin处的频谱校正系数,最后利用计算的校正系数对原始计算结果进行修正。本发 明采用的插值算法为抛物线插值,所以先查表找到三个与fin最接近的频点:fk-1、 fk和fk+1。然后根据公式计算插值结果:As shown in Figure 4, the complex resistivity calculation result correction method. Since the frequency values used for each observation are not necessarily the same, and the number of frequency points to be calibrated is limited, the correction coefficient needs to be calculated by interpolation method first. According to the signal frequency f in , check the calibration data table to find the adjacent points of f in , then use the interpolation method to calculate the spectral correction coefficient at f in , and finally use the calculated correction coefficient to correct the original calculation result. The interpolation algorithm adopted in the present invention is parabolic interpolation, so first look up the table to find three frequency points closest to f in : f k-1 , f k and f k+1 . Then calculate the interpolation result according to the formula:
其中,r(f)代表频率f处的振幅或相位标定结果。where r(f) represents the amplitude or phase scaling result at frequency f.
复电阻率校正公式如下:The complex resistivity correction formula is as follows:
φ(fin)=φ(fin)-φc(fin)φ(f in )=φ(f in )-φ c (f in )
ρ(fin)=ρ(fin)/ρc(fin) (11)ρ(f in )=ρ(f in )/ρ c (f in ) (11)
其中,φc(fin)和ρc(fin)分别为观测系统在频率fin处自身响应的振幅和相位, 根据公式(10)计算获得。Among them, φ c (fin ) and ρ c ( fin ) are the amplitude and phase of the self-response of the observation system at the frequency f in , respectively, and are obtained by calculation according to formula (10).
上述数据采集和处理方法流程,参见图1部分。For the flow of the above data collection and processing method, see Figure 1.
通过仿真实验可以不同算法获得的复电阻率计算值和理论值对比图。The calculated and theoretical values of complex resistivity obtained by different algorithms can be compared through simulation experiments.
如图5所示,图中实线代表理论复电阻率曲线;点画线代表利用同步电压 和电流数据获得的结果,离散点代表新方法计算结果;“*”、“Δ”和“□”分别 代表长度自动约束全相位频谱分析、加窗DFT和直接DFT三种方法的计算结 果。上图为复电阻率振幅,下图为相位。As shown in Figure 5, the solid line in the figure represents the theoretical complex resistivity curve; the dotted line represents the results obtained by using the synchronous voltage and current data, and the discrete points represent the calculation results of the new method; "*", "Δ" and "□" respectively It represents the calculation results of the three methods of length auto-constrained full-phase spectrum analysis, windowed DFT and direct DFT. The upper graph is the complex resistivity amplitude and the lower graph is the phase.
为验证算法的可靠性,在信号I的基础上加入模拟工频干扰作为激励电流。 工频干扰由一组50Hz及其奇数倍频率的正弦波组成。然后重复上面的仿真和 数据处理过程。In order to verify the reliability of the algorithm, on the basis of the signal I, the simulated power frequency interference is added as the excitation current. Power frequency interference consists of a group of sine waves of 50Hz and its odd multiples. Then repeat the above simulation and data processing procedures.
如图6所示,复电阻率计算结果见图6,不同符号和线型代表的算法与图5 一致。采用的数据处理方法与无谐波干扰情况下的类似,只是前期加入了工频 滤波。As shown in Figure 6, the complex resistivity calculation results are shown in Figure 6, and the algorithms represented by different symbols and line types are consistent with those in Figure 5. The data processing method adopted is similar to that without harmonic interference, except that power frequency filtering is added in the early stage.
采用方差分析法讨论了上述几种方法的复电阻率计算精度。并将结果汇总 于表4。仿真试验证明无工频干扰的情况下,传统的需同步电流的SIP数据处 理方法的计算精度高于本发明提出的新算法,但是在有工频干扰的情况下,本 发明所述新算法则优于传统算法。而对于新算法自身而言,直接DFT、加窗DFT 以及长度自动约束全相位频谱分析获得的振幅精度基本一致,但是利用本发明 所述长度自动约束全相位频谱分析获得的相位精度明显高于前两者。The calculation accuracy of the complex resistivity of the above several methods is discussed by variance analysis. The results are summarized in Table 4. The simulation test proves that in the case of no power frequency interference, the calculation accuracy of the traditional SIP data processing method requiring synchronous current is higher than that of the new algorithm proposed by the present invention, but in the case of power frequency interference, the new algorithm of the present invention is outperforms traditional algorithms. For the new algorithm itself, the amplitude accuracy obtained by direct DFT, windowed DFT and length auto-constrained full-phase spectrum analysis is basically the same, but the phase accuracy obtained by using the length auto-constrained full-phase spectrum analysis of the present invention is significantly higher than the previous one. both.
表5不同SIP数据算法的均方误差Table 5 Mean square error of different SIP data algorithms
如图7所示,是本发明所述SIP法的野外试验结果,以表3作为发射频率 表,数据采集时间约半小时,共获得三通道电压数据。As shown in Figure 7, it is the field test result of the SIP method of the present invention. Table 3 is used as the transmission frequency table, and the data acquisition time is about half an hour, and three channels of voltage data are obtained in total.
SIP法野外试验测得的复电阻率振幅和相位曲线比较光滑,且三通道基本一 致,通道1高频段相位稍低于另外两个通道的测量结果。The complex resistivity amplitude and phase curves measured by the SIP method in the field test are relatively smooth, and the three channels are basically the same. The high-frequency phase of channel 1 is slightly lower than the measurement results of the other two channels.
结果表明,本发明提出的SIP实时数据采集和处理方法可以在无同步电流 采集传输设备和频域测量装置的情况下,顺利完成SIP观测。另外,常规SIP 法数据采集要求电压数据和电流数据必须严格同步采集,相比较而言,本发明 这种只采集电压数据的SIP数据采集方法更加灵活方便。The results show that the SIP real-time data acquisition and processing method proposed by the present invention can successfully complete the SIP observation without synchronous current acquisition and transmission equipment and frequency domain measurement devices. In addition, the conventional SIP method for data collection requires that voltage data and current data must be collected strictly synchronously. In comparison, the SIP data collection method of the present invention that only collects voltage data is more flexible and convenient.
如图8所示,SIP观测数据处理软件界面,图中给出了长度自动约束全相 位频谱分析和加窗傅里叶变换法获得的SIP法观测结果对比。As shown in Figure 8, the SIP observation data processing software interface, the figure shows the comparison of the SIP observation results obtained by the length automatic constraint full-phase spectrum analysis and the windowed Fourier transform method.
图8中,(a)和(b)是原始电压采样数据的时域波形和频域波形。(c)和 (d)是复电阻率的振幅和相位计算结果。(e)是参数设置和显示部分,其中Array 是装置类型,“4”代表对称四极装置;AB是供电极距;MN是测量极距。这些 参数都是测量开始前根据装置布设方式手动输入的。K是装置系数,由程序根 据输入参数自动计算。fin是当前信号频率,根据数据采集时间和发射频率表判 断的,采样率fs则是根据fin确定的。实线、点画线和虚线分别代表通道1/2/3, “*”代表本发明所述长度自动约束全相位频谱分析计算结果,“Δ”代表加窗傅 里叶变化法计算的结果。In Fig. 8, (a) and (b) are the time-domain waveform and frequency-domain waveform of the original voltage sampling data. (c) and (d) are the amplitude and phase calculations of the complex resistivity. (e) is the parameter setting and display part, where Array is the device type, "4" represents the symmetrical quadrupole device; AB is the supply electrode pitch; MN is the measuring electrode pitch. These parameters were entered manually before the measurement started, depending on how the device was set up. K is the device coefficient, which is automatically calculated by the program based on the input parameters. f in is the current signal frequency, which is determined according to the data acquisition time and the transmission frequency table, and the sampling rate f s is determined according to f in . The solid line, the dotted line and the dashed line represent channel 1/2/3 respectively, "*" represents the calculation result of the length automatic constraint full-phase spectrum analysis of the present invention, and "Δ" represents the calculation result of the windowed Fourier transform method.
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