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CN118549989B - A frequency domain electromagnetic device and numerical simulation method for hole surrounding rock detection - Google Patents

A frequency domain electromagnetic device and numerical simulation method for hole surrounding rock detection Download PDF

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CN118549989B
CN118549989B CN202411008865.2A CN202411008865A CN118549989B CN 118549989 B CN118549989 B CN 118549989B CN 202411008865 A CN202411008865 A CN 202411008865A CN 118549989 B CN118549989 B CN 118549989B
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柳建新
刘嵘
李金泰
欧健
刘文祥
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    • G01VGEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
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Abstract

本发明涉及勘探电磁法技术领域,公开一种用于孔洞围岩探测的频率域电磁装置与数值模拟方法。该频率域电磁装置包括偏心发射组件及接收线圈组件;偏心发射组件包括两个半圆形发射线圈;接收线圈组件包括多个接收线圈。采用偏心发射组件发射频率域电磁波,使用多个不同平面线圈接收磁场响应,加强接收线圈对不同方向信号差异,具备方向辨识能力;该频率域电磁装置使用多旋转角度、多线圈发射、多线圈接收、多频率测量的方式提升数据采集效率与可靠性。本发明提出在柱坐标系下开展数值模拟,并分别使用电性异常体的剩余电导率与剩余磁导率计算二次磁场虚部和实部,响应快速,有助于将孔洞围岩探测精度提升到工程实际需求。

The present invention relates to the technical field of exploration electromagnetic methods, and discloses a frequency domain electromagnetic device and numerical simulation method for hole surrounding rock detection. The frequency domain electromagnetic device includes an eccentric transmitting component and a receiving coil component; the eccentric transmitting component includes two semicircular transmitting coils; the receiving coil component includes multiple receiving coils. An eccentric transmitting component is used to transmit frequency domain electromagnetic waves, and multiple different planar coils are used to receive magnetic field responses, so as to enhance the difference of signals in different directions of the receiving coil and have the ability to identify directions; the frequency domain electromagnetic device uses multiple rotation angles, multiple coils to transmit, multiple coils to receive, and multiple frequencies to measure to improve data collection efficiency and reliability. The present invention proposes to carry out numerical simulation in a cylindrical coordinate system, and use the residual conductivity and residual permeability of the electrical anomaly to calculate the imaginary and real parts of the secondary magnetic field respectively, which has a fast response and helps to improve the accuracy of hole surrounding rock detection to the actual engineering needs.

Description

一种用于孔洞围岩探测的频率域电磁装置与数值模拟方法A frequency domain electromagnetic device and numerical simulation method for hole surrounding rock detection

技术领域Technical Field

本发明涉及勘探电磁法技术领域,具体涉及一种用于孔洞围岩探测的频率域电磁装置与数值模拟方法。The invention relates to the technical field of exploration electromagnetic methods, and in particular to a frequency domain electromagnetic device and a numerical simulation method for hole surrounding rock detection.

背景技术Background Art

地下隐伏水体是隧道工程建设、矿产开采工作中存在潜在地质灾害源头,精准探明地下富水区位置与规模可以有效避免地下工程作业风险。Hidden underground water bodies are potential sources of geological disasters in tunnel construction and mineral mining. Accurately exploring the location and scale of underground water-rich areas can effectively avoid the risks of underground engineering operations.

利用已有钻孔布置电磁装置对其周边低阻水体开展超前探测是一种先进的地球物理方法。然而,由于钻孔内探测施工空间有限、孔内任意位置探测信号来源为三维全空间的原因,目前的孔内电磁装置探测信号,还不具备分辨富水体方向的能力。现有的数值模拟方法,没有考虑电性异常体同时存在剩余电导率与磁导率,且传统微分方程法三维数值模拟需要耗费大量时间求解大型方程组,或停留在层状介质一维解析解。现有技术可参见文章1(An Iterative Inversion Method using Transient Electromagnetic Data toPredict Water-filled Caves during the Excavation of a Tunnel[J]. Geophysics,84(2): E83-E103)和文章2(杨海燕, 肖占山, 刘志新, 岳建华, 胡海涛, 苏本玉, 李哲.2023. 水平层状介质孔中张量瞬变电磁响应的解析分析[J]. 地球物理学报,66(5):2167-2180)。It is an advanced geophysical method to use electromagnetic devices to arrange existing boreholes to conduct advance detection of low-resistance water bodies around them. However, due to the limited detection construction space in the borehole and the fact that the detection signal at any position in the hole comes from the three-dimensional space, the current electromagnetic device detection signal in the hole does not have the ability to distinguish the direction of the water-rich body. The existing numerical simulation method does not take into account the existence of residual conductivity and magnetic permeability of electrical anomalies, and the traditional three-dimensional numerical simulation of differential equations requires a lot of time to solve large equations, or stays at the one-dimensional analytical solution of layered media. For the existing technology, please refer to Article 1 (An Iterative Inversion Method using Transient Electromagnetic Data to Predict Water-filled Caves during the Excavation of a Tunnel[J]. Geophysics, 84(2): E83-E103) and Article 2 (Yang Haiyan, Xiao Zhanshan, Liu Zhixin, Yue Jianhua, Hu Haitao, Su Benyu, Li Zhe. 2023. Analytical analysis of tensor transient electromagnetic response in horizontal layered medium holes[J]. Chinese Journal of Geophysics, 66(5): 2167-2180).

综上所述,急需一种具备方向辨识能力且响应快速的装置及方法以解决现有技术中存在的问题。In summary, there is an urgent need for a device and method with direction recognition capability and fast response to solve the problems existing in the prior art.

发明内容Summary of the invention

本发明的目的在于提供一种用于孔洞围岩探测的频率域电磁装置,该频率域电磁装置针对圆形或矩形发射线圈信号横向分辨率差的缺陷,采用包括两个半圆形发射线圈的偏心发射组件发射频率域电磁波,使用距离发射线圈一定距离的多个不同平面线圈接收磁场响应,加强接收线圈对不同方向信号差异,具备很强的方向辨识能力;针对孔洞空间有限的特点,该频率域电磁装置使用多旋转角度、多线圈发射、多线圈接收、多频率测量的方式提升数据采集效率与可靠性。具体技术方案如下:The purpose of the present invention is to provide a frequency domain electromagnetic device for hole surrounding rock detection. In order to solve the problem of poor lateral resolution of circular or rectangular transmitting coil signals, the frequency domain electromagnetic device uses an eccentric transmitting assembly including two semicircular transmitting coils to transmit frequency domain electromagnetic waves, and uses multiple different planar coils at a certain distance from the transmitting coil to receive the magnetic field response, thereby enhancing the difference of signals in different directions of the receiving coil and having a strong direction identification ability. In view of the limited space of the hole, the frequency domain electromagnetic device uses multiple rotation angles, multiple coils for transmission, multiple coils for reception, and multiple frequency measurements to improve data collection efficiency and reliability. The specific technical scheme is as follows:

一种用于孔洞围岩探测的频率域电磁装置,包括具有直轴线的装置本体;A frequency domain electromagnetic device for detecting surrounding rocks of a hole, comprising a device body having a straight axis;

所述装置本体包括偏心发射组件以及接收线圈组件;所述偏心发射组件包括两个半圆形发射线圈,两个半圆形发射线圈的圆心均位于直轴线上,且两个半圆形发射线圈的中心与直轴线错开设置;所述接收线圈组件位于两个半圆形发射线圈之间,且接收线圈组件包括沿直轴线并列设置的多个接收线圈,多个所述接收线圈的中心均位于直轴线上;The device body includes an eccentric transmitting assembly and a receiving coil assembly; the eccentric transmitting assembly includes two semicircular transmitting coils, the centers of the two semicircular transmitting coils are both located on the straight axis, and the centers of the two semicircular transmitting coils are staggered with the straight axis; the receiving coil assembly is located between the two semicircular transmitting coils, and the receiving coil assembly includes a plurality of receiving coils arranged in parallel along the straight axis, and the centers of the plurality of receiving coils are all located on the straight axis;

直轴线垂直于两个半圆形发射线圈各自所在平面,且两个半圆形发射线圈在垂直于直轴线的同一平面上投影不存在重叠区域。The straight axis is perpendicular to the planes where the two semicircular transmitting coils are located respectively, and there is no overlapping area when the two semicircular transmitting coils are projected on the same plane perpendicular to the straight axis.

优选的,半圆形发射线圈与接收线圈之间以及相邻的两个接收线圈之间均间隔设置。Preferably, the semicircular transmitting coil and the receiving coil are spaced apart, as well as between two adjacent receiving coils.

优选的,所述接收线圈中存在一个矩形接收线圈,该矩形接收线圈的中心点与两个半圆形发射线圈的圆心的连线的中点相重合,且两个半圆形发射线圈直径垂直于该矩形接收线圈所在平面。Preferably, there is a rectangular receiving coil in the receiving coil, the center point of the rectangular receiving coil coincides with the midpoint of the line connecting the centers of the two semicircular transmitting coils, and the diameters of the two semicircular transmitting coils are perpendicular to the plane where the rectangular receiving coil is located.

优选的,两个半圆形发射线圈的半径和匝数均相等;在全空间均匀背景条件下,两个半圆形发射线圈在该矩形接收线圈产生的初始磁场相等,不同方位异常体所产生的二次磁场不相等。Preferably, the radius and number of turns of the two semicircular transmitting coils are equal; under the condition of uniform background in the whole space, the initial magnetic fields generated by the two semicircular transmitting coils in the rectangular receiving coil are equal, and the secondary magnetic fields generated by the anomalies in different orientations are not equal.

本发明还公开一种数值模拟方法,针对电磁波随传播距离衰减的特点,提出在柱坐标系下开展高效数值模拟,并分别使用电性异常体的剩余电导率与剩余磁导率计算频率域电磁装置的二次磁场虚部、实部,响应快速,有助于将孔洞围岩探测精度提升到工程实际需求。具体方案如下:The present invention also discloses a numerical simulation method. In view of the characteristics of electromagnetic waves attenuating with propagation distance, it is proposed to carry out efficient numerical simulation in a cylindrical coordinate system, and use the residual conductivity and residual permeability of the electrical anomaly to calculate the imaginary and real parts of the secondary magnetic field of the frequency domain electromagnetic device, respectively. The method has a fast response and helps to improve the detection accuracy of the surrounding rock of the hole to the actual engineering needs. The specific scheme is as follows:

一种数值模拟方法,采用上述的用于孔洞围岩探测的频率域电磁装置进行数值模拟,包括以下步骤:A numerical simulation method, using the above-mentioned frequency domain electromagnetic device for hole surrounding rock detection to perform numerical simulation, comprises the following steps:

步骤S1、定义柱坐标z轴、频率域电磁装置中装置本体的直轴线和孔中心轴线三者重合,在柱坐标系下将孔洞围岩进行网格离散;Step S1, define the cylindrical coordinate z-axis, the straight axis of the device body in the frequency domain electromagnetic device and the center axis of the hole to coincide with each other, and discretize the surrounding rock of the hole in the cylindrical coordinate system;

步骤S2、使用磁偶极子在全空间、均匀背景电导率与磁导率条件下电场与磁场格林函数表达式分别计算半圆形发射线圈在孔洞围岩离散单元所引起的初始电场与接收线圈初始磁场;Step S2, using the magnetic dipole in the whole space, uniform background conductivity and magnetic permeability conditions, the electric field and magnetic field Green's function expressions are used to calculate the initial electric field caused by the semicircular transmitting coil in the discrete unit of the hole surrounding rock and the initial magnetic field of the receiving coil;

步骤S3、使用步骤S2中所得初始电场所形成的电偶极子在全空间、均匀背景电导率与磁导率条件下的磁场格林函数表达式分别乘以电性异常体的剩余电导率与剩余磁导率,分别得到孔内测量二次磁场虚部和实部。Step S3, using the electric dipole formed by the initial electric field obtained in step S2 to form the magnetic field Green's function expression under the conditions of uniform background conductivity and magnetic permeability in the whole space, multiply it by the residual conductivity and residual magnetic permeability of the electrical anomaly body, and obtain the imaginary part and real part of the secondary magnetic field measured in the hole.

优选的,所述步骤S1具体包括:Preferably, the step S1 specifically includes:

设定孔洞围岩背景电导率取值、磁导率均匀取值、电性异常体的剩余电导率取值以及电性异常体的剩余磁导率取值分别为c0、u0、ca和ua;定义柱坐标z轴为孔中心轴线、平面极坐标位于孔深为0处;Set the background conductivity value of the hole surrounding rock, the uniform value of the magnetic permeability, the residual conductivity value of the electrical anomaly body, and the residual magnetic permeability value of the electrical anomaly body to be c0, u0, ca, and ua respectively; define the cylindrical coordinate z axis as the center axis of the hole, and the plane polar coordinate is located at the hole depth of 0;

以z轴为中心在孔深度范围内取柱状围岩,使用柱坐标系将围岩离散为I×J×K个单元,其中:I为z方向离散份数,J为在柱坐标系下按角度离散份数,K为柱坐标系下按半径离散份数。Take the columnar surrounding rock within the hole depth range with the z axis as the center, and use the cylindrical coordinate system to discretize the surrounding rock into I×J×K units, where: I is the number of discrete parts in the z direction, J is the angle in the cylindrical coordinate system Discrete number, K is the radius in the cylindrical coordinate system Discrete number of copies.

优选的,所述步骤S2中:Preferably, in step S2:

接收线圈初始磁场包括一次磁场与二次磁场The initial magnetic field of the receiving coil includes a primary magnetic field With the secondary magnetic field ;

一次磁场使用单位强度磁偶极子在均匀全空间背景下产生的磁场格林函数表达式计算,如下:Primary magnetic field The Green function expression of the magnetic field generated by a unit strength magnetic dipole in a uniform full space background The calculation is as follows:

;

其中:t为发射线圈编号,r为接收线圈编号,rt为发射线圈所形成的磁偶极子源位置,rh为接收线圈磁场接收点位置,c0为均匀全空间电导率,f为发射频率,P为发射线圈磁偶极矩强度;Where: t is the transmitting coil number, r is the receiving coil number, rt is the magnetic dipole source position formed by the transmitting coil, rh is the magnetic field receiving point position of the receiving coil, c0 is the uniform full-space conductivity, f is the transmitting frequency, and P is the magnetic dipole moment strength of the transmitting coil;

半圆形发射线圈在孔洞围岩离散单元所引起的初始电场使用磁偶极子在均匀全空间背景下产生的电场格林函数表达式计算,如下:Initial electric field caused by semicircular transmitting coil in discrete units of surrounding rock of hole The Green's function expression of the electric field generated by a magnetic dipole in a uniform full-space background The calculation is as follows:

;

其中:m为深度记录点编号数组M中的元素,其取值1至M的自然数;n为单个记录点的旋转编号数组N中的元素,其取值1至N的自然数;i为围岩在柱坐标系下z方向离散单元编号,取值1至I的自然数;j为围岩在柱坐标系下按角度离散单元编号,取值1至J的自然数;k为在柱坐标系下按半径离散单元编号,取值1至K的自然数;re为中离散单元电场接收点位置;Among them: m is an element in the depth record point number array M, which takes a natural number from 1 to M; n is an element in the rotation number array N of a single record point, which takes a natural number from 1 to N; i is the discrete unit number of the surrounding rock in the z direction in the cylindrical coordinate system, which takes a natural number from 1 to I; j is the angle of the surrounding rock in the cylindrical coordinate system Discrete unit number, a natural number from 1 to J; k is the radius in the cylindrical coordinate system. Discrete unit number, a natural number from 1 to K; re is The location of the electric field receiving point of the discrete unit;

计算离散单元初始电场导致的接收线圈二次磁场,接收线圈二次磁场分为虚部与实部,计算公式如下:Calculate the secondary magnetic field of the receiving coil caused by the initial electric field of the discrete unit , receiving coil secondary magnetic field Imaginary part With real part , the calculation formula is as follows:

;

;

其中:为单位强度电偶极子在均匀全空间背景下产生的磁场表达式;当时,则有:;当i、j、k为均匀围岩背景离散单元编号时,则有:in: is the expression of the magnetic field generated by a unit-strength electric dipole in a uniform full-space background; when and and When , we have: , ; When i, j, k are the discrete unit numbers of the uniform surrounding rock background, then: , .

优选的,所述步骤S3中孔内测量二次磁场实部IP和二次磁场虚部OP采用下式计算:Preferably, in step S3, the real part IP and the imaginary part OP of the secondary magnetic field measured in the hole are calculated using the following formula:

;

;

其中:为对数组取绝对值运算符。in: An absolute value operator for arrays.

优选的,采用上述的用于孔洞围岩探测的频率域电磁装置进行数值模拟之前,还包括对频率域电磁装置进行校验,具体包括:Preferably, before the numerical simulation is performed using the frequency domain electromagnetic device for hole surrounding rock detection, the frequency domain electromagnetic device is also calibrated, specifically including:

步骤一、将频率域电磁装置放入孔洞,保持半圆形发射线圈的圆心连线位于孔中心轴线上,对孔内M个不同深度记录点进行N个不同角度测量;其中:半圆形发射线圈T1的圆心记为TO1,半圆形发射线圈T2的圆心记为TO2;接收线圈组件包括矩形接收线圈R0、圆形接收线圈R1和圆形接收线圈R2;Step 1: Place the frequency domain electromagnetic device into the hole, keep the center line of the semicircular transmitting coil on the central axis of the hole, and perform N different angle measurements on M recording points at different depths in the hole; wherein: the center of the semicircular transmitting coil T1 is recorded as TO1, and the center of the semicircular transmitting coil T2 is recorded as TO2; the receiving coil assembly includes a rectangular receiving coil R0, a circular receiving coil R1 and a circular receiving coil R2;

步骤二、各深度记录点测量过程中保持记录点与圆心TO1和圆心TO2连线的中点TO重合,将频率域电磁装置沿圆心TO1和圆心TO2连线进行转动,直到矩形接收线圈R0旋转180度以上,得到每个记录点N个旋转角度测量数据;Step 2: During the measurement of each depth recording point, keep the recording point coincident with the midpoint TO of the line connecting the center TO1 and the center TO2, rotate the frequency domain electromagnetic device along the line connecting the center TO1 and the center TO2 until the rectangular receiving coil R0 rotates more than 180 degrees, and obtain N rotation angle measurement data for each recording point;

步骤三、每个深度、旋转角度测量过程中,分别使用两个半圆形发射线圈T1和T2发射F个频率的电磁波信号,各接收线圈分别记录所产生的二次磁场实部与虚部,获得孔内测量二次磁场实部IP(T,M,N,R,F)与二次磁场虚部OP(T,M,N,R,F)都是2×M×N×R×F维向量,其中:T为发射线圈编号数组,元素t为取值为1时对应半圆形发射线圈T1,元素t为取值为2时对应半圆形发射线圈T2;M为深度记录点编号数组,其元素m取值1至M的自然数;N为单个记录点的旋转编号数组,其元素n取值1至N的自然数;R为接收线圈编号数组,其元素r取值1至R的自然数,当r=1代表矩形接收线圈R0;F为发射频率编号数组,其元素f取值1至F的自然数;Step 3. During each depth and rotation angle measurement process, two semicircular transmitting coils T1 and T2 are used to transmit electromagnetic wave signals of F frequencies, and each receiving coil records the real and imaginary parts of the generated secondary magnetic field, and the real part of the secondary magnetic field IP (T, M, N, R, F) and the imaginary part of the secondary magnetic field OP (T, M, N, R, F) measured in the hole are obtained. They are both 2×M×N×R×F dimensional vectors, where: T is the transmitting coil number array, and the element t corresponds to the semicircular transmitting coil T1 when the value is 1, and the element t corresponds to the semicircular transmitting coil T2 when the value is 2; M is the depth recording point number array, and its element m takes the value of a natural number from 1 to M; N is the rotation number array of a single recording point, and its element n takes the value of a natural number from 1 to N; R is the receiving coil number array, and its element r takes the value of a natural number from 1 to R, when r=1 represents the rectangular receiving coil R0; F is the transmitting frequency number array, and its element f takes the value of a natural number from 1 to F;

步骤四、提取矩形接收线圈测量数据,对比n角度和f频率条件下半圆形发射线圈T1不同深度的测量数据IP(1,M,n,1,f)、OP(1,M,n,1,f)与半圆形发射线圈T2不同深度的测量数据IP(2,M,n,1,f)、OP(2,M,n,1,f);Step 4: Extract the measurement data of the rectangular receiving coil, and compare the measurement data IP (1, M, n, 1, f), OP (1, M, n, 1, f) of different depths of the semicircular transmitting coil T1 under the conditions of n angle and f frequency with the measurement data IP (2, M, n, 1, f), OP (2, M, n, 1, f) of different depths of the semicircular transmitting coil T2;

步骤五、使用二次磁场实部相对偏差evIP和二次磁场虚部相对偏差evOP两个参数对数据质量进行评估,计算公式如下:Step 5: Use the two parameters of the relative deviation of the real part of the secondary magnetic field evIP and the relative deviation of the imaginary part of the secondary magnetic field evOP to evaluate the data quality. The calculation formula is as follows:

;

.

优选的,所述步骤五中对数据质量进行评估具体是:当evIP<5%且evOP<5%时,认为数据质量合格。Preferably, the data quality is evaluated in step 5 as follows: when evIP<5% and evOP<5%, the data quality is considered qualified.

除了上面所描述的目的、特征和优点之外,本发明还有其它的目的、特征和优点。下面将参照图,对本发明作进一步详细的说明。In addition to the above-described purposes, features and advantages, the present invention has other purposes, features and advantages. The present invention will be further described in detail with reference to the accompanying drawings.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

构成本申请的一部分的附图用来提供对本发明的进一步理解,本发明的示意性实施例及其说明用于解释本发明,并不构成对本发明的不当限定。在附图中:The drawings constituting a part of this application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

图1是实施例中用于孔洞围岩探测的频率域电磁装置的结构示意图;FIG1 is a schematic structural diagram of a frequency domain electromagnetic device for detecting surrounding rocks of a hole in an embodiment;

图2是图1中频率域电磁装置在两个不同深度记录点进行测量时的示意图;FIG2 is a schematic diagram of the frequency domain electromagnetic device in FIG1 when measuring at two different depth recording points;

图3是图1中频率域电磁装置在单个深度记录点不同旋转角度测量时的示意图;FIG3 is a schematic diagram of the frequency domain electromagnetic device in FIG1 when measuring at different rotation angles at a single depth recording point;

图4(a)是孔洞围岩及异常体在柱坐标系下沿孔洞直轴切面的剖分示意图;Figure 4 (a) is a schematic diagram of the section of the hole surrounding rock and the abnormal body along the vertical axis of the hole in the cylindrical coordinate system;

图4(b)是孔洞围岩及异常体在柱坐标系下垂直孔洞直轴切面的剖分示意图;Figure 4 (b) is a schematic diagram of the section of the hole surrounding rock and the abnormal body perpendicular to the hole axis in the cylindrical coordinate system;

图5是层状介质模型下层状模型与频率域电磁装置的几何位置示意图;FIG5 is a schematic diagram of the geometric positions of a layered model and a frequency domain electromagnetic device under a layered medium model;

图6是半圆形发射线圈T1发射且圆形接收线圈R1接收的归一化二次磁场曲线图。FIG. 6 is a normalized secondary magnetic field curve diagram of the semicircular transmitting coil T1 transmitting and the circular receiving coil R1 receiving.

具体实施方式DETAILED DESCRIPTION

以下结合附图对本发明的实施例进行详细说明,但是本发明可以根据所限定和覆盖的多种不同方式实施。The embodiments of the present invention are described in detail below with reference to the accompanying drawings. However, the present invention can be implemented in many different ways as defined and covered.

实施例Example

一种用于孔洞围岩探测的频率域电磁装置,参见图1,包括具有直轴线L的装置本体;所述装置本体包括偏心发射组件以及接收线圈组件,详情如下:A frequency domain electromagnetic device for detecting surrounding rocks of holes, see FIG1 , includes a device body having a straight axis L; the device body includes an eccentric transmitting assembly and a receiving coil assembly, details of which are as follows:

所述偏心发射组件包括两个半圆形发射线圈,两个半圆形发射线圈的圆心均位于直轴线L上,且两个半圆形发射线圈的中心与直轴线错位设置;所述接收线圈组件位于两个半圆形发射线圈之间,且接收线圈组件包括沿直轴线设置的多个接收线圈,多个所述接收线圈的中心均位于直轴线上,所述接收线圈中存在一个矩形接收线圈。本实施例中:偏心发射组件包括半圆形发射线圈T1和半圆形发射线圈T2,半圆形发射线圈T1的圆心记为TO1,半圆形发射线圈T2的圆心记为TO2;接收线圈组件包括矩形接收线圈R0、圆形接收线圈R1和圆形接收线圈R2。如图1所示,R0、R1、R2位于T1、T2之间,且T1的圆心、T2的圆心、R0的中心、R1的圆心以及R2的圆心都在直轴线L上。半圆形发射线圈与接收线圈之间以及相邻的两个接收线圈之间均间隔设置。直轴线垂直于两个半圆形发射线圈各自所在平面,且两个半圆形发射线圈在垂直于直轴线的同一平面上投影不存在重叠区域。该矩形接收线圈R0的中心点TO与两个半圆形发射线圈的圆心(TO1和TO2)的连线的中点相重合,且两个半圆形发射线圈直径垂直于该矩形接收线圈所在平面。两个半圆形发射线圈的半径和匝数均相等;在全空间均匀背景条件下,两个半圆形发射线圈在该矩形接收线圈产生的初始磁场相等,不同方位异常体所产生的二次磁场不相等。The eccentric transmitting assembly includes two semicircular transmitting coils, the centers of the two semicircular transmitting coils are both located on the straight axis L, and the centers of the two semicircular transmitting coils are staggered with the straight axis; the receiving coil assembly is located between the two semicircular transmitting coils, and the receiving coil assembly includes a plurality of receiving coils arranged along the straight axis, the centers of the plurality of receiving coils are all located on the straight axis, and there is a rectangular receiving coil in the receiving coil. In this embodiment: the eccentric transmitting assembly includes a semicircular transmitting coil T1 and a semicircular transmitting coil T2, the center of the semicircular transmitting coil T1 is marked as TO1, and the center of the semicircular transmitting coil T2 is marked as TO2; the receiving coil assembly includes a rectangular receiving coil R0, a circular receiving coil R1 and a circular receiving coil R2. As shown in FIG1 , R0, R1 and R2 are located between T1 and T2, and the center of T1, the center of T2, the center of R0, the center of R1 and the center of R2 are all on the straight axis L. The semicircular transmitting coil and the receiving coil and the two adjacent receiving coils are spaced apart. The straight axis is perpendicular to the planes where the two semicircular transmitting coils are located, and there is no overlapping area when the two semicircular transmitting coils are projected on the same plane perpendicular to the straight axis. The center point TO of the rectangular receiving coil R0 coincides with the midpoint of the line connecting the centers of the two semicircular transmitting coils (TO1 and TO2), and the diameters of the two semicircular transmitting coils are perpendicular to the plane where the rectangular receiving coil is located. The radius and number of turns of the two semicircular transmitting coils are equal; under the condition of uniform background in the whole space, the initial magnetic fields generated by the two semicircular transmitting coils in the rectangular receiving coil are equal, and the secondary magnetic fields generated by the anomalies in different orientations are not equal.

在应用本实施例的频率域电磁装置进行数值模拟之前,先对频率域电磁装置进行校验,具体包括如下过程:Before using the frequency domain electromagnetic device of this embodiment to perform numerical simulation, the frequency domain electromagnetic device is first calibrated, which specifically includes the following process:

沿孔洞不同深度记录点、不同旋转角度开展数据采集,如图2和图3所示,具体如下:Data collection was carried out at different recording points at different depths and rotation angles along the hole, as shown in Figures 2 and 3. The details are as follows:

如图2所示,M个不同深度记录点位于孔洞中心轴线上,随着深度增加记录点编号增大(图2中示意了m和m+1两个记录)。As shown in FIG2 , M recording points at different depths are located on the central axis of the hole, and the recording point number increases with increasing depth (two records, m and m+1, are illustrated in FIG2 ).

将频率域电磁装置放入孔洞,单个记录点数据采集过程中,保持频率域电磁装置的直轴线L与孔洞中心轴线重合,对孔内M个不同深度记录点进行N个不同旋转角度的测量(图3中示意了两个旋转角度);记录点位于T1、T2中点;The frequency domain electromagnetic device is placed in the hole. During the data collection process of a single recording point, the straight axis L of the frequency domain electromagnetic device is kept coincident with the central axis of the hole. The recording points at M different depths in the hole are measured at N different rotation angles (two rotation angles are shown in FIG3 ); the recording point is located at the midpoint of T1 and T2;

各深度记录点测量过程中保持记录点与圆心TO1和圆心TO2连线的中点TO重合,将频率域电磁装置沿圆心TO1和圆心TO2连线按一定角度转动,直到矩形接收线圈R0旋转180度以上,得到每个记录点N个旋转角度测量数据;During the measurement of each depth recording point, the recording point is kept coincident with the midpoint TO of the line connecting the center TO1 and the center TO2, and the frequency domain electromagnetic device is rotated at a certain angle along the line connecting the center TO1 and the center TO2 until the rectangular receiving coil R0 rotates more than 180 degrees, and N rotation angle measurement data of each recording point are obtained;

每个深度、旋转角度测量过程中,分别使用两个半圆形发射线圈T1和T2发射F个频率的电磁波信号,各接收线圈分别记录所产生的二次磁场实部与二次磁场虚部,获得孔内测量二次磁场实部IP(T,M,N,R,F)与二次磁场虚部OP(T,M,N,R,F)都是2×M×N×R×F维向量,其中:T为发射线圈编号数组,元素t为取值为1时对应半圆形发射线圈T1,元素t为取值为2时对应半圆形发射线圈T2;M为深度记录点编号数组,其元素m取值1至M的自然数;N为单个记录点的旋转编号数组,其元素n取值1至N的自然数;R为接收线圈编号数组,其元素r取值1至R的自然数,当r=1代表矩形接收线圈R0;F为发射频率编号数组,其元素f取值1至F的自然数;In each depth and rotation angle measurement process, two semicircular transmitting coils T1 and T2 are used to transmit electromagnetic wave signals of F frequencies, and each receiving coil records the real part and imaginary part of the secondary magnetic field generated, and the real part of the secondary magnetic field IP (T, M, N, R, F) and the imaginary part of the secondary magnetic field OP (T, M, N, R, F) measured in the hole are obtained. They are both 2×M×N×R×F dimensional vectors, where: T is the transmitting coil number array, and the element t corresponds to the semicircular transmitting coil T1 when the value is 1, and the element t corresponds to the semicircular transmitting coil T2 when the value is 2; M is the depth recording point number array, and its element m takes the value of a natural number from 1 to M; N is the rotation number array of a single recording point, and its element n takes the value of a natural number from 1 to N; R is the receiving coil number array, and its element r takes the value of a natural number from 1 to R, when r=1 represents the rectangular receiving coil R0; F is the transmitting frequency number array, and its element f takes the value of a natural number from 1 to F;

提取矩形接收线圈测量数据,对比n角度、f频率,半圆形发射线圈T1不同深度的测量数据IP(1,M,n,1,f)、OP(1,M,n,1,f)与半圆形发射线圈T2不同深度的测量数据IP(2,M,n,1,f)、OP(2,M,n,1,f);Extract the measurement data of the rectangular receiving coil and compare the n angle, f frequency, the measurement data IP (1, M, n, 1, f), OP (1, M, n, 1, f) of the semicircular transmitting coil T1 at different depths with the measurement data IP (2, M, n, 1, f), OP (2, M, n, 1, f) of the semicircular transmitting coil T2 at different depths;

使用二次磁场实部相对偏差evIP和二次磁场虚部相对偏差evOP两个参数的大小评价数据质量,计算公式如下:The data quality is evaluated by using the relative deviation of the real part of the secondary magnetic field evIP and the relative deviation of the imaginary part of the secondary magnetic field evOP. The calculation formula is as follows:

and ;

当evIP<5%且evOP<5%时,认为数据质量合格;否则,调整频率域电磁装置中发射线圈和接收线圈,需要在全空间均匀背景条件下重新校验装置,使得两个发射线圈在矩形接收线圈产生的初始磁场相等,并重新测量。When evIP<5% and evOP<5%, the data quality is considered qualified; otherwise, adjust the transmitting coil and receiving coil in the frequency domain electromagnetic device, and recalibrate the device under uniform background conditions in the entire space so that the initial magnetic fields generated by the two transmitting coils in the rectangular receiving coil are equal, and remeasure.

应用本实施例的频率域电磁装置开展数值模拟,包括以下步骤:The numerical simulation using the frequency domain electromagnetic device of this embodiment includes the following steps:

步骤S1、定义柱坐标z轴、频率域电磁装置中装置本体的直轴线和孔中心轴线三者重合,在柱坐标系下将孔洞围岩进行网格离散;Step S1, define the cylindrical coordinate z-axis, the straight axis of the device body in the frequency domain electromagnetic device and the center axis of the hole to coincide with each other, and discretize the surrounding rock of the hole in the cylindrical coordinate system;

步骤S2、使用磁偶极子在全空间、均匀背景电导率与磁导率条件下电场与磁场格林函数表达式,分别计算半圆形发射线圈在孔洞围岩离散单元所引起的初始电场与接收线圈初始磁场;Step S2, using the electric field and magnetic field Green's function expressions of the magnetic dipole in the whole space and under the conditions of uniform background conductivity and magnetic permeability, respectively calculate the initial electric field caused by the semicircular transmitting coil in the discrete unit of the surrounding rock of the hole and the initial magnetic field of the receiving coil;

步骤S3、使用步骤S2中离散单元初始电场所形成的电偶极子在全空间、均匀背景电导率与磁导率条件下的磁场格林函数表达式,分别乘以电性异常体的剩余电导率与剩余磁导率,分别得到二次磁场虚部和实部。Step S3, using the magnetic field Green's function expression of the electric dipole formed by the initial electric field of the discrete unit in step S2 under the conditions of uniform background conductivity and magnetic permeability in the whole space, multiplying it by the residual conductivity and residual magnetic permeability of the electrical anomaly body, respectively, to obtain the imaginary part and the real part of the secondary magnetic field, respectively.

本实施例优选的,所述步骤S1具体包括:In this embodiment, preferably, step S1 specifically includes:

设定孔洞围岩背景电导率取值、磁导率均匀取值、电性异常体的剩余电导率取值以及电性异常体的剩余磁导率取值分别为c0、u0、ca和ua;定义柱坐标z轴为孔中心轴线、平面极坐标位于孔深为0处,即定义柱坐标系z轴为孔洞中心直线、孔洞顶端(深度为0)所在水平面为柱坐标的极坐标;在柱坐标系下异常体离散单元在z轴、角度、半径的编号分别为Ia~Ib、Ja~Jb、Ka~Kb。详见图4(a)和图4(b)。Set the background conductivity of the hole surrounding rock, the uniform value of the magnetic permeability, the residual conductivity of the electrical anomaly, and the residual magnetic permeability of the electrical anomaly as c0, u0, ca, and ua respectively; define the cylindrical coordinate z axis as the center axis of the hole, and the plane polar coordinate is located at the hole depth of 0, that is, define the cylindrical coordinate system z axis as the center line of the hole, and the horizontal plane where the top of the hole (depth 0) is located as the cylindrical coordinate polar coordinate; in the cylindrical coordinate system, the numbering of the discrete units of the anomaly in the z axis, angle, and radius is Ia~Ib, Ja~Jb, Ka~Kb respectively. See Figure 4 (a) and Figure 4 (b) for details.

以z轴为中心在孔深度范围内取柱状围岩,使用柱坐标系将围岩离散为I×J×K个单元。其中,I为z方向离散份数,J为在柱坐标系下按角度离散份数,K为柱坐标系下按半径离散份数。Take the columnar surrounding rock within the hole depth range with the z axis as the center, and use the cylindrical coordinate system to discretize the surrounding rock into I×J×K units. Among them, I is the number of discrete parts in the z direction, and J is the angle in the cylindrical coordinate system. Discrete number, K is the radius in the cylindrical coordinate system Discrete number of copies.

本实施例优选的,所述步骤S2中:In this embodiment, preferably, in step S2:

半圆形发射线圈在孔洞围岩离散单元所引起的初始电场与接收线圈初始磁场包括一次磁场与二次磁场The initial electric field caused by the semicircular transmitting coil in the discrete unit of the surrounding rock of the hole and the initial magnetic field of the receiving coil include the primary magnetic field With the secondary magnetic field ;

一次磁场使用单位强度磁偶极子在均匀全空间背景下产生的磁场格林函数表达式计算,如下:Primary magnetic field The Green function expression of the magnetic field generated by a unit strength magnetic dipole in a uniform full space background The calculation is as follows:

;

其中,t为发射线圈编号,r为接收线圈编号,rt为发射线圈所形成的磁偶极子源位置,rh为接收线圈磁场接收点位置,c0为均匀全空间电导率,f为发射频率,P为发射线圈磁偶极矩强度;Wherein, t is the transmitting coil number, r is the receiving coil number, rt is the magnetic dipole source position formed by the transmitting coil, rh is the magnetic field receiving point position of the receiving coil, c0 is the uniform full-space conductivity, f is the transmitting frequency, and P is the magnetic dipole moment strength of the transmitting coil;

半圆形发射线圈在孔洞围岩离散单元所引起的初始电场,使用磁偶极子在均匀全空间背景下产生的电场格林函数表达式计算,如下:Initial electric field caused by semicircular transmitting coil in discrete units of surrounding rock of hole , using the Green function expression of the electric field generated by a magnetic dipole in a uniform full-space background The calculation is as follows:

;

其中:i为围岩在柱坐标系下z方向离散单元编号,取值1至I的自然数;j为围岩在柱坐标系下按角度离散单元编号,取值1至J的自然数;k为在柱坐标系下按半径离散单元编号,取值1至K的自然数;m为深度记录点编号数组M中的元素,其取值1至M的自然数;n为单个记录点的旋转编号数组N中的元素,其取值1至N的自然数;rt为中发射线圈所形成的磁偶极子发射源位置;re为中离散单元电场接收点位置。Where: i is the discrete unit number of the surrounding rock in the z direction in the cylindrical coordinate system, which is a natural number from 1 to I; j is the angle of the surrounding rock in the cylindrical coordinate system Discrete unit number, a natural number from 1 to J; k is the radius in the cylindrical coordinate system. The discrete unit number is a natural number ranging from 1 to K; m is an element in the depth recording point number array M, which is a natural number ranging from 1 to M; n is an element in the rotation number array N of a single recording point, which is a natural number ranging from 1 to N; rt is The position of the magnetic dipole emission source formed by the transmitting coil in the middle; re is The location of the electric field receiving point of the discrete unit.

计算离散单元初始电场导致的接收线圈二次磁场,接收线圈二次磁场分为虚部与实部,计算公式如下:Calculate the secondary magnetic field of the receiving coil caused by the initial electric field of the discrete unit , receiving coil secondary magnetic field Imaginary part With real part , the calculation formula is as follows:

;

;

其中:为单位强度电偶极子在均匀全空间背景下产生的磁场表达式;当时,则有:;当i、j、k为均匀围岩背景离散单元编号时,则有:in: is the expression of the magnetic field generated by a unit-strength electric dipole in a uniform full-space background; when and and When , we have: , ; When i, j, k are the discrete unit numbers of the uniform surrounding rock background, then: , .

本实施例优选的,所述步骤S3中孔内测量二次磁场实部IP和二次磁场虚部OP采用下式计算:In this embodiment, the real part IP and the imaginary part OP of the secondary magnetic field measured in the hole in step S3 are preferably calculated using the following formula:

;

;

其中:为对数组取绝对值运算符。in: An absolute value operator for arrays.

进一步优选的,本实施例中各线圈沿装置直轴线距离d(T1,R1)= d(R1,R0) = d(R0,R2)= d(R2,T2)=1m、各线圈直径或边长=0.2m;层状围岩模型参数:第一层厚度为无穷大,电导率为c0=0.01S/m、磁导率u0=4π×107H/m;第二层为电性异常层厚度2米,剩余电导率为ca=0.09S/m、剩余磁导率ua=4π×106H/m;第三层厚度为无穷大,电导率为0.01S/m、磁导率u0=4π×107H/m。使用具体测量参数:M=100各记录点等间距2米、N=4每个测点总共旋转180度、线圈发射频率为10000Hz。参见图1-图5。Further preferably, in this embodiment, the distance between each coil along the straight axis of the device is d(T1, R1) = d(R1, R0) = d(R0, R2) = d(R2, T2) = 1m, and the diameter or side length of each coil is 0.2m; the parameters of the layered surrounding rock model are: the thickness of the first layer is infinite, the conductivity is c0 = 0.01S/m, and the magnetic permeability is u0 = 4π×107H/m; the second layer is an electrical abnormal layer with a thickness of 2 meters, the residual conductivity is ca = 0.09S/m, and the residual magnetic permeability is ua = 4π×106H/m; the thickness of the third layer is infinite, the conductivity is 0.01S/m, and the magnetic permeability is u0 = 4π×107H/m. Specific measurement parameters are used: M = 100, each recording point is equally spaced 2 meters, N = 4, each measuring point rotates a total of 180 degrees, and the coil transmission frequency is 10000Hz. See Figures 1-5.

基于以上参数进行数值模拟,结果如图6所示。Numerical simulation is carried out based on the above parameters, and the results are shown in Figure 6.

以上所述仅为本发明的优选实施例而已,并不用于限制本发明,对于本领域的技术人员来说,本发明可以有各种更改和变化。凡在本发明的精神和原则之内,所作的任何修改、等同替换、改进等,均应包含在本发明的保护范围之内。The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims (10)

1.一种用于孔洞围岩探测的频率域电磁装置,其特征在于,包括具有直轴线的装置本体;1. A frequency domain electromagnetic device for detecting surrounding rocks of holes, characterized in that it comprises a device body having a straight axis; 所述装置本体包括偏心发射组件以及接收线圈组件;所述偏心发射组件包括两个半圆形发射线圈,两个半圆形发射线圈的圆心均位于直轴线上,且两个半圆形发射线圈的中心与直轴线错开设置;所述接收线圈组件位于两个半圆形发射线圈之间,且接收线圈组件包括沿直轴线并列设置的多个接收线圈,多个所述接收线圈的中心均位于直轴线上;The device body includes an eccentric transmitting assembly and a receiving coil assembly; the eccentric transmitting assembly includes two semicircular transmitting coils, the centers of the two semicircular transmitting coils are both located on the straight axis, and the centers of the two semicircular transmitting coils are staggered with the straight axis; the receiving coil assembly is located between the two semicircular transmitting coils, and the receiving coil assembly includes a plurality of receiving coils arranged in parallel along the straight axis, and the centers of the plurality of receiving coils are all located on the straight axis; 直轴线垂直于两个半圆形发射线圈各自所在平面,且两个半圆形发射线圈在垂直于直轴线的同一平面上投影不存在重叠区域;The straight axis is perpendicular to the planes where the two semicircular transmitting coils are located, and there is no overlapping area when the two semicircular transmitting coils are projected on the same plane perpendicular to the straight axis; 所述接收线圈中存在一个矩形接收线圈,该矩形接收线圈的中心点与两个半圆形发射线圈的圆心的连线的中点相重合,且两个半圆形发射线圈直径垂直于该矩形接收线圈所在平面。There is a rectangular receiving coil in the receiving coil, the center point of the rectangular receiving coil coincides with the midpoint of the line connecting the centers of the two semicircular transmitting coils, and the diameters of the two semicircular transmitting coils are perpendicular to the plane where the rectangular receiving coil is located. 2.根据权利要求1所述的用于孔洞围岩探测的频率域电磁装置,其特征在于,半圆形发射线圈与接收线圈之间以及相邻的两个接收线圈之间均间隔设置。2. The frequency domain electromagnetic device for detecting surrounding rocks of holes according to claim 1 is characterized in that the semicircular transmitting coil and the receiving coil and the two adjacent receiving coils are arranged at intervals. 3.根据权利要求2所述的用于孔洞围岩探测的频率域电磁装置,其特征在于,两个半圆形发射线圈的半径和匝数均相等。3. The frequency domain electromagnetic device for hole surrounding rock detection according to claim 2 is characterized in that the radius and number of turns of the two semicircular transmitting coils are equal. 4.根据权利要求2所述的用于孔洞围岩探测的频率域电磁装置,其特征在于,在全空间均匀背景条件下,两个半圆形发射线圈在该矩形接收线圈产生的初始磁场相等,不同方位异常体所产生的二次磁场不相等。4. The frequency domain electromagnetic device for detecting surrounding rocks of holes according to claim 2 is characterized in that under the condition of uniform background in the entire space, the initial magnetic fields generated by the two semicircular transmitting coils in the rectangular receiving coil are equal, and the secondary magnetic fields generated by abnormal bodies in different orientations are not equal. 5.一种数值模拟方法,其特征在于,采用如权利要求4所述的用于孔洞围岩探测的频率域电磁装置进行数值模拟,包括以下步骤:5. A numerical simulation method, characterized in that the numerical simulation is performed using the frequency domain electromagnetic device for hole surrounding rock detection as claimed in claim 4, comprising the following steps: 步骤S1、定义柱坐标z轴、频率域电磁装置中装置本体的直轴线和孔中心轴线三者重合,在柱坐标系下将孔洞围岩进行网格离散;Step S1, define the cylindrical coordinate z-axis, the straight axis of the device body in the frequency domain electromagnetic device and the center axis of the hole to coincide with each other, and discretize the surrounding rock of the hole in the cylindrical coordinate system; 步骤S2、使用磁偶极子在全空间、均匀背景电导率与磁导率条件下电场与磁场格林函数表达式分别计算半圆形发射线圈在孔洞围岩离散单元所引起的初始电场与接收线圈初始磁场;Step S2, using the magnetic dipole in the whole space, uniform background conductivity and magnetic permeability conditions, the electric field and magnetic field Green's function expressions are used to calculate the initial electric field caused by the semicircular transmitting coil in the discrete unit of the hole surrounding rock and the initial magnetic field of the receiving coil; 步骤S3、使用步骤S2中所得初始电场所形成的电偶极子在全空间、均匀背景电导率与磁导率条件下的磁场格林函数表达式分别乘以电性异常体的剩余电导率与剩余磁导率得到孔内测量二次磁场虚部和实部。Step S3, using the electric dipole formed by the initial electric field obtained in step S2, the magnetic field Green's function expression under the conditions of uniform background conductivity and magnetic permeability in the whole space is multiplied by the residual conductivity and residual magnetic permeability of the electrical anomaly body to obtain the imaginary and real parts of the secondary magnetic field measured in the hole. 6.根据权利要求5所述的数值模拟方法,其特征在于,所述步骤S1具体包括:6. The numerical simulation method according to claim 5, characterized in that the step S1 specifically comprises: 设定孔洞围岩背景电导率取值、磁导率均匀取值、电性异常体的剩余电导率取值以及电性异常体的剩余磁导率取值分别为c0、u0、ca和ua;定义柱坐标z轴为孔中心轴线、平面极坐标位于孔深为0处;Set the background conductivity value of the hole surrounding rock, the uniform value of the magnetic permeability, the residual conductivity value of the electrical anomaly body, and the residual magnetic permeability value of the electrical anomaly body to be c0, u0, ca, and ua respectively; define the cylindrical coordinate z axis as the center axis of the hole, and the plane polar coordinate is located at the hole depth of 0; 以z轴为中心在孔深度范围内取柱状围岩,使用柱坐标系将围岩离散为I×J×K个单元,其中:I为z方向离散份数,J为在柱坐标系下按角度ψ离散份数,K为柱坐标系下按半径ρ离散份数。Take the columnar surrounding rock within the hole depth range with the z-axis as the center, and use the cylindrical coordinate system to discretize the surrounding rock into I×J×K units, where: I is the number of discrete portions in the z direction, J is the number of discrete portions according to the angle ψ in the cylindrical coordinate system, and K is the number of discrete portions according to the radius ρ in the cylindrical coordinate system. 7.根据权利要求6所述的数值模拟方法,其特征在于,所述步骤S2中:7. The numerical simulation method according to claim 6, characterized in that in step S2: 接收线圈初始磁场包括一次磁场Hp与二次磁场HSThe initial magnetic field of the receiving coil includes the primary magnetic field H p and the secondary magnetic field HS ; 一次磁场Hp使用单位强度磁偶极子在均匀全空间背景下产生的磁场格林函数表达式GH H计算,如下:The primary magnetic field H p is calculated using the Green's function expression G H H for the magnetic field generated by a unit strength magnetic dipole in a uniform full-space background, as follows: Hp(t,r,f)=GH H(rt,rh,c0,f)×P(t);H p (t, r, f) = G H H (rt, rh, c0, f) × P (t); 其中:t为发射线圈编号,r为接收线圈编号,rt为发射线圈所形成的磁偶极子源位置,rh为接收线圈磁场接收点位置,c0为均匀全空间电导率,f为发射频率,P为发射线圈磁偶极矩强度;Where: t is the transmitting coil number, r is the receiving coil number, rt is the magnetic dipole source position formed by the transmitting coil, rh is the magnetic field receiving point position of the receiving coil, c0 is the uniform full-space conductivity, f is the transmitting frequency, and P is the magnetic dipole moment strength of the transmitting coil; 半圆形发射线圈在孔洞围岩离散单元所引起的初始电场Ep使用磁偶极子在均匀全空间背景下产生的电场格林函数表达式GH E计算,如下:The initial electric field E p caused by the semicircular transmitting coil in the discrete unit of the surrounding rock of the hole is calculated using the Green function expression G H E of the electric field generated by the magnetic dipole in the uniform full space background, as follows: Ep(t,m,n,i,j,k,f)=GH E(rt,re,c0,f)×P(t);E p (t, m, n, i, j, k, f) = G H E (rt, re, c0, f) × P (t); 其中:m为深度记录点编号数组M中的元素,其取值1至M的自然数;n为单个记录点的旋转编号数组N中的元素,其取值1至N的自然数;i为围岩在柱坐标系下z方向离散单元编号,取值1至I的自然数;j为围岩在柱坐标系下按角度ψ离散单元编号,取值1至J的自然数;k为在柱坐标系下按半径ρ离散单元编号,取值1至K的自然数;re为GH E中离散单元电场接收点位置;Wherein: m is an element in the depth recording point number array M, which takes a natural number from 1 to M; n is an element in the rotation number array N of a single recording point, which takes a natural number from 1 to N; i is the discrete unit number of the surrounding rock in the z direction in the cylindrical coordinate system, which takes a natural number from 1 to I; j is the discrete unit number of the surrounding rock according to the angle ψ in the cylindrical coordinate system, which takes a natural number from 1 to J ; k is the discrete unit number according to the radius ρ in the cylindrical coordinate system, which takes a natural number from 1 to K; re is the position of the electric field receiving point of the discrete unit in GHE ; 计算离散单元初始电场导致的接收线圈二次磁场HS,接收线圈二次磁场HS分为虚部与实部HI s,计算公式如下:Calculate the secondary magnetic field HS of the receiving coil caused by the initial electric field of the discrete unit. The secondary magnetic field HS of the receiving coil is divided into the imaginary part and the real part H I s , the calculation formula is as follows: 其中:为单位强度电偶极子在均匀全空间背景下产生的磁场表达式;当Ia≤i≤Ib且Ja≤j≤Jb且Ka≤k≤Kb时,则有:当i、j、k为均匀围岩背景离散单元编号时,则有: in: is the magnetic field expression generated by a unit strength electric dipole in a uniform full-space background; when Ia≤i≤Ib and Ja≤j≤Jb and Ka≤k≤Kb, then: When i, j, k are the discrete unit numbers of the uniform surrounding rock background, then: 8.根据权利要求7所述的数值模拟方法,其特征在于,所述步骤S3中孔内测量二次磁场实部IP和二次磁场虚部OP采用下式计算:8. The numerical simulation method according to claim 7, characterized in that the real part IP and the imaginary part OP of the secondary magnetic field measured in the hole in step S3 are calculated using the following formula: 其中:ABS[]为对数组取绝对值运算符。Among them: ABS[] is the absolute value operator for an array. 9.根据权利要求5所述的数值模拟方法,其特征在于,采用如权利要求4所述的用于孔洞围岩探测的频率域电磁装置进行数值模拟之前,还包括对频率域电磁装置进行校验,具体包括:9. The numerical simulation method according to claim 5 is characterized in that before the numerical simulation is performed using the frequency domain electromagnetic device for hole surrounding rock detection according to claim 4, the method further comprises calibrating the frequency domain electromagnetic device, specifically comprising: 步骤一、将频率域电磁装置放入孔洞,保持半圆形发射线圈的圆心连线位于孔中心轴线上,对孔内M个不同深度记录点进行N个不同角度测量;其中:半圆形发射线圈T1的圆心记为TO1,半圆形发射线圈T2的圆心记为TO2;接收线圈组件包括矩形接收线圈R0、圆形接收线圈R1和圆形接收线圈R2;Step 1: Place the frequency domain electromagnetic device into the hole, keep the center line of the semicircular transmitting coil on the central axis of the hole, and perform N different angle measurements on M recording points at different depths in the hole; wherein: the center of the semicircular transmitting coil T1 is recorded as TO1, and the center of the semicircular transmitting coil T2 is recorded as TO2; the receiving coil assembly includes a rectangular receiving coil R0, a circular receiving coil R1 and a circular receiving coil R2; 步骤二、各深度记录点测量过程中保持记录点与圆心TO1和圆心TO2连线的中点TO重合,将频率域电磁装置沿圆心TO1和圆心TO2连线进行转动,直到矩形接收线圈R0旋转180度以上,得到每个记录点N个旋转角度测量数据;Step 2: During the measurement of each depth recording point, keep the recording point coincident with the midpoint TO of the line connecting the center TO1 and the center TO2, rotate the frequency domain electromagnetic device along the line connecting the center TO1 and the center TO2 until the rectangular receiving coil R0 rotates more than 180 degrees, and obtain N rotation angle measurement data for each recording point; 步骤三、每个深度、旋转角度测量过程中,分别使用两个半圆形发射线圈T1和T2发射F个频率的电磁波信号,各接收线圈分别记录所产生的二次磁场实部与虚部,获得孔内测量二次磁场实部IP(T,M,N,R,F)与二次磁场虚部OP(T,M,N,R,F)都是2×M×N×R×F维向量,其中:T为发射线圈编号数组,元素t为取值为1时对应半圆形发射线圈T1,元素t为取值为2时对应半圆形发射线圈T2;M为深度记录点编号数组,其元素m取值1至M的自然数;N为单个记录点的旋转编号数组,其元素n取值1至N的自然数;R为接收线圈编号数组,其元素r取值1至R的自然数,当r=1代表矩形接收线圈R0;F为发射频率编号数组,其元素f取值1至F的自然数;Step 3. During each depth and rotation angle measurement process, two semicircular transmitting coils T1 and T2 are used to transmit electromagnetic wave signals of F frequencies, and each receiving coil records the real and imaginary parts of the generated secondary magnetic field, and the real part of the secondary magnetic field IP (T, M, N, R, F) and the imaginary part of the secondary magnetic field OP (T, M, N, R, F) measured in the hole are obtained. They are both 2×M×N×R×F dimensional vectors, where: T is the transmitting coil number array, and the element t corresponds to the semicircular transmitting coil T1 when the value is 1, and the element t corresponds to the semicircular transmitting coil T2 when the value is 2; M is the depth recording point number array, and its element m takes the value of a natural number from 1 to M; N is the rotation number array of a single recording point, and its element n takes the value of a natural number from 1 to N; R is the receiving coil number array, and its element r takes the value of a natural number from 1 to R, and when r=1 represents the rectangular receiving coil R0; F is the transmitting frequency number array, and its element f takes the value of a natural number from 1 to F; 步骤四、提取矩形接收线圈测量数据,对比n角度和f频率条件下半圆形发射线圈T1不同深度的测量数据IP(1,M,n,1,f)、OP(1,M,n,1,f)与半圆形发射线圈T2不同深度的测量数据IP(2,M,n,1,f)、OP(2,M,n,1,f);Step 4: Extract the measurement data of the rectangular receiving coil, and compare the measurement data IP(1,M,n,1,f) and OP(1,M,n,1,f) of different depths of the semicircular transmitting coil T1 under the conditions of angle n and frequency f with the measurement data IP(2,M,n,1,f) and OP(2,M,n,1,f) of different depths of the semicircular transmitting coil T2; 步骤五、使用二次磁场实部相对偏差evIP和二次磁场虚部相对偏差evOP两个参数对数据质量进行评估,计算公式如下:Step 5: Use the two parameters of the relative deviation of the real part of the secondary magnetic field evIP and the relative deviation of the imaginary part of the secondary magnetic field evOP to evaluate the data quality. The calculation formula is as follows: evIP=ABS[(IP(1,M,n,1,f)-IP(2,M,n,1,f))/(IP(1,M,n,1,f)+IP(2,M,n,1,f))];evOP=ABS[(OP(1,M,n,1,f)-(OP(2,M,n,1,f))/(OP(1,M,n,1,f)+OP(2,M,n,1,f))];其中:ABS[]为对数组取绝对值运算符。evIP=ABS[(IP(1,M,n,1,f)-IP(2,M,n,1,f))/(IP(1,M,n,1,f)+IP(2,M,n,1,f))]; evOP=ABS[(OP(1,M,n,1,f)-(OP(2,M,n,1,f))/(OP(1,M,n,1,f)+OP(2,M,n,1,f))]; where: ABS[] is the absolute value operator for an array. 10.根据权利要求9所述的数值模拟方法,其特征在于,所述步骤五中对数据质量进行评估具体是:当evIP<5%且evOP<5%时,认为数据质量合格。10. The numerical simulation method according to claim 9 is characterized in that the data quality is evaluated in step 5 specifically: when evIP<5% and evOP<5%, the data quality is considered to be qualified.
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