阅读说明：本技术 一种频率域电性源电磁场视电导率计算方法 (Frequency domain electric source electromagnetic field apparent conductivity calculation method ) 是由 周峰 张志勇 陈辉 李勇 李曼 于 2019-11-28 设计创作，主要内容包括：本发明公开了一种频率域电性源电磁场视电导率计算方法,包括如下步骤：(1)在指定的勘探区域布设供电电极和发射电源；(2)布置观测网、选择频率范围以及观测扇形区域。记录由发送机发射电流信息的I,在接收机端一次性观测多频点电磁场切向分量<Image he="71" wi="57" file="DDA0002294202730000011.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>或法向分量E<Sub>r</Sub>；(3)采用二阶差分技术计算相应频点组合的电场切向分量<Image he="70" wi="58" file="DDA0002294202730000012.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>或法向分量E<Sub>r</Sub>对频率f的导数<Image he="138" wi="94" file="DDA0002294202730000013.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>和<Image he="140" wi="115" file="DDA0002294202730000014.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>并对计算后的偏导信息进行存储；(4)利用导数<Image he="140" wi="94" file="DDA0002294202730000015.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>和<Image he="136" wi="90" file="DDA0002294202730000016.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>来计算频率域电偶源视电导率计算。本发明适合在全域进行地下结构电性分布观测。本发明只需要测量一个方向的电场数据,野外采集成本低、观测效率高,同时对观测设备要求低。(The invention discloses a frequency domain electric source electromagnetic field apparent conductivity calculation method, which comprises the following steps: (1) arranging a power supply electrode and a transmitting power supply in a specified exploration area; (2) arranging an observation network, selecting a frequency range and observing a sector area. Recording I of current information transmitted by transmitter, observing tangential component of multi-frequency point electromagnetic field at receiver end in one time Or normal component E r (ii) a (3) Calculating electric field tangential component of corresponding frequency point combination by adopting second-order difference technology Or normal component E r Derivative of frequency f And storing the calculated partial derivative information; (4) using derivatives And to calculate the frequency domain galvanic source apparent conductivity calculation. The invention is suitable for carrying out underground structure electrical distribution observation in the universe. The invention only needs to measure the electric field data in one direction, has low field acquisition cost and high observation efficiency, and has low requirement on observation equipment.)

1. A frequency domain electric source electromagnetic field apparent conductivity calculation method is characterized by comprising the following steps: comprises the following steps of (a) carrying out,

(1) arranging a horizontal galvanic couple source in a designated exploration area, connecting an alternating current transmitting power supply and a transmitter, measuring the length dl of the galvanic couple source, recording the coordinates of power supply points A and B, and simultaneously recording the current I transmitted by the transmitter; in addition, the included angle between the observation point and the forward direction of the dipole moment is calculated

(2) Arranging an observation network, selecting a frequency observation range and observing a sector area according to exploration requirements; observing the sector area in the angle range of 30-150 deg and 210-330 deg, recording the coordinate of each observation point in each observation line, arranging measuring electrodes and receivers at the observation points, and measuring the tangential component of electric field perpendicular to the connection line between the dipole source center and the measurement point

(3) A series of tangential components of multi-frequency point electromagnetic field obtained by a receiver

(4) the recorded and stored data respectively calculate the tangential component of the electromagnetic field based on the observation pointDerivative of frequency f

2. The method of claim 1, wherein the method comprises the following steps: measuring tangential components of observation points of different frequencies

arranging a horizontal electric dipole source with the length dl in the x direction on the uniform ground surface, transmitting current harmonic current I to the ground, obtaining an electromagnetic field component at any observation point under a cylindrical coordinate system according to an electromagnetic field basic theory,

wherein r represents the length between the viewpoint and the center of the couple source,

3. The method of claim 2, wherein the method comprises the following steps: respectively deriving the frequencies f to obtain the following expressions:

the above formula is deduced and simplified as follows:

order to

from the formulas (7) and (8), the equal sign right derivative parts are consistent, and the uniform derivative is carried out, so that

wherein the content of the first and second substances,

then, the formula (7) and the formula (8) are respectively substituted into the formula (10) to obtain

Further simplifying the formulas (11) and (12) to obtain

Wherein, formula e^-ikrAnd (3) converting by adopting an Euler formula to obtain:

taking the absolute value of the formula (15) to obtain

Therefore, taking the absolute values of equations (13) and (14), respectively, and then substituting equation (16) therein, yields:

then, taking the index with e as base for the formulas (17) and (18) respectively to obtain:

the two sides of the formulas (19) and (20) are respectively squared, and the expression is simplified as follows:

thus, in cylindrical coordinates, r and

therefore, only need to obtain r orThe derivative of the directional component with respect to the frequency f.

Technical Field

The invention relates to a method for measuring apparent conductivity by applying a frequency domain electromagnetic method in the field of geophysical, in particular to a method for measuring normal component E of an observation point_rAnd tangential component

The method for calculating the conductivity can effectively improve the calculation precision of the apparent conductivity.

Background

In the field of exploration by applying geophysical frequency domain electromagnetic method, apparent resistivity (inverse of apparent conductivity) is an important parameter for evaluating the conductivity of underground rock (ore). Generally, the apparent resistivity is related to factors such as the rock (ore) composition, structure and measuring device of the underground medium, and is the comprehensive effect of the underground rock (ore) and ore. For example, the controlled source audio frequency magnetotelluric (CSAMT) is an active frequency domain electromagnetic prospecting technology developed on the basis of the audio frequency magnetotelluric (aod) method, and due to the introduction of artificial field sources, the CSAMT has the advantages of strong anti-interference capability, high working efficiency, high measurement accuracy and the like, and is widely applied to the fields of solid mineral production, hydrology, petroleum and natural gas general investigation, geothermal field exploration, environmental geological survey, environmental and engineering geophysical survey and the like at present. The electromagnetic prospecting method also adopts the method theory of the geoelectromagnetic method, and is characterized in that a group of mutually orthogonal horizontal components E of electric and magnetic fields are measured_x、H_y(orE is_y、H_x) Defining the impedance Z by calculating the ratio between the two_xy＝E_x/H_y(or Z)_yx＝E_y/H_x) And by which the conventional Charpy apparent resistivity is defined

(or

) The purpose of exploring the electrical structure distribution characteristics of the underground medium is achieved. However, an important theoretical basis of the method is to place an observation point in a so-called "far zone", that is, an electromagnetic field propagates in a plane wave, and electromagnetic field data are severely distorted in a non-plane wave zone, so that the application effect of the CSAMT is greatly limited, and the development process of the CSAMT is hindered. In addition, the characteristics need to be considered in actual field data acquisition, the field work efficiency of CSAMT is greatly influenced, and the field data acquisition work cost is improved. Chinese patent 201810435743.X discloses an artificial field source frequency domain electromagnetic apparent resistivity measuring method, firstly, according to detection or exploration requirements, a horizontal electric dipole field source and electric field horizontal component measuring system is arranged, and a transmitting and receiving fixed device is adopted for nondestructive testing. Electromagnetic signals with different frequencies f are used for recording multi-frequency point electromagnetism E of a measuring point_xAnd (4) components. Calculating the electromagnetic field E of the corresponding frequency point combination by adopting an approximation method of first-order difference derivation_xDerivative to frequency pointAnd storing the calculated partial derivative information. Using electromagnetic fields E_xDerivative of component to frequency point

And performing apparent resistivity conversion treatment. The method overcomes the limitation of using the Kanni apparent resistivity definition criterion to solve the apparent resistivity, and simultaneously reduces the risk of unstable calculation results caused by the fact that the conventional all-region apparent resistivity solution needs to be faced with the solution of a nonlinear equation setAnd the calculation efficiency and accuracy of the apparent resistivity are effectively improved.

Currently, research on calculation of all-region apparent resistivity is carried out at home and abroad, and most of all-region apparent resistivity definition modes adopt a rectangular coordinate system to measure an x component E of an electric field_xThe calculation is carried out, and the method can solve most measurement areas, but is based on the tangential component of the observation point in a cylindrical coordinate system

Has an observation area range far larger than E_xAnd (4) components. In addition, by an electric field E_xOr

The method is characterized in that a proper initial value is required to be selected and iterative approximation is carried out by adopting an iterative solution formula to calculate the apparent resistivity parameter under the general condition of defining the whole-area apparent resistivity, and the selection of the initial value and the iterative formula often cause inaccurate calculation of the apparent resistivity (apparent conductivity), thereby bringing numerical value errors and influencing the later data interpretation efficiency and accuracy.

Disclosure of Invention

The invention aims to overcome the problems described in the background art and provide a novel frequency domain electric source electromagnetic field apparent conductivity calculation method. Compared with E_xComponent, tangential component of the invention observation

And the normal component E_rThe observation angles of the measuring device are 30-150 degrees and 210-330 degrees, the measuring area range is remarkably improved, the exploration cost is reduced, and the exploration efficiency is improved. In addition, the conventional all-region apparent resistivity calculation needs to select an initial resistivity value and an iterative algorithm to estimate the apparent resistivity, and the inappropriate selection of the initial resistivity value and the iterative algorithm often brings serious numerical errors to the calculation and solution of the apparent conductivity (the reciprocal of the apparent resistivity), so that the apparent conductivity calculation efficiency is seriously influenced

And the normal component E_rDerivative of frequency f

And

the selection of an initial value and an iterative algorithm is avoided, the accuracy and efficiency of apparent conductivity calculation are obviously improved, and the accuracy of data interpretation is improved.

The invention provides a method for calculating apparent conductivity of a frequency domain electric source by an electromagnetic method, which needs to measure tangential components of observation points with different frequencies

And the normal component E_rMeasuring the forward angle between the transmitting-receiving distance r and the dipole moment

And simultaneously, recording the power supply current I and the length dl between the power supply dipoles A and B, and calculating according to a proposed formula and a proposed method to obtain the full-area apparent resistivity of any observation point position.

Arranging a horizontal electric dipole source with the length dl in the x direction on the uniform ground surface, transmitting current harmonic current I to the ground, obtaining an electromagnetic field component at any observation point under a cylindrical coordinate system according to an electromagnetic field basic theory,

wherein r represents the length between the viewpoint and the center of the couple source,

represents the clip between the connecting line of the observation point and the center of the couple source under the column coordinate and the ox axisAngle, k is the wavenumber, under quasi-static conditions, k²Mu. permeability,. omega. 2. pi.f angular frequency, f frequency, i imaginary unit, E_rRepresenting the r-direction component, namely the normal component of the measuring point, in a cylindrical coordinate system,

expressed under the vermilion coordinate system

The direction component, i.e. the tangential component of the measured point, is shown in fig. 2 below.

Respectively deriving the frequencies f to obtain the following expressions:

the above formula is deduced and simplified as follows:

order to

X is expressed as an intermediate variable, and equations (5) and (6) are further simplified as follows:

from the formula (7) And (8) the right derivative parts with equal signs are consistent, and unified derivative is carried out, so that

The method is further simplified into the following steps of,

wherein the content of the first and second substances,

then, the formula (7) and the formula (8) are respectively substituted into the formula (10) to obtain

Further simplifying the formulas (11) and (12) to obtain

Wherein, formula e^-ikrAnd (3) converting by adopting an Euler formula to obtain:

taking the absolute value of the formula (15) to obtain

Therefore, taking the absolute values of equations (13) and (14), respectively, and then substituting equation (16) therein, yields:

then, taking the index with e as base for the formulas (17) and (18) respectively to obtain:

the two sides of the formulas (19) and (20) are respectively squared, and the expression is simplified as follows:

thus, in cylindrical coordinates, r and

the derivative of the directional component with respect to frequency f is used to calculate the conductivity of the subsurface medium as,

therefore, only need to obtain r or

Derivatives of directional components with respect to frequency f, e.g.And

by combining the formula (23) or (24), the conductivity information of the underground medium can be calculated respectively, and the precision loss caused by the traditional iterative approximation algorithm is avoided. In addition, the conductivity calculation formula obtained by the method improves the capability of acquiring the information of the underground abnormal body to a certain degree, and ensures the data quality of data interpretation.

A frequency domain electric source electromagnetic field apparent conductivity calculation method comprises the following steps:

(1) arranging a horizontal galvanic couple source in a specified exploration area, connecting an alternating current transmitting power supply and a transmitter, measuring the length dl of the galvanic couple source, recording the coordinates of power supply points A and B, and simultaneously recording the current I transmitted by the transmitter. In addition, the included angle between the observation point and the forward direction of the dipole moment is calculated

(2) According to exploration requirements, arranging an observation network, selecting a frequency observation range and observing a sector area. Observing the sector area in the angle range of 30-150 deg and 210-330 deg, recording the coordinate of each observation point in each observation line, arranging measuring electrodes and receivers at the observation points, and measuring the tangential component of electric field perpendicular to the connection line between the dipole source center and the measurement point

Or measuring the normal component E of the connecting line direction of the dipole source center and the measuring point_r. According to the existing transmitting source and the transmitter method, the transmitter can transmit a plurality of frequency current source information, so that the receiver can measure the tangential component of the multi-frequency point electromagnetic field at one time

Or normal component E_r；

(3) A series of tangential components of multi-frequency point electromagnetic field obtained by a receiver

Or normal component E_rGrouping is carried out, and the tangential component of the electromagnetic field is calculated by a second-order difference technology (four adjacent frequencies participate in calculation)

Or normal component E_rDerivative of frequency f

And

and storing the calculated derivative information;

(4) the recorded and stored data, respectively, in combination with equations (23) or (24), respectively, allow to calculate the tangential component of the electromagnetic field based on the observation point

Derivative of frequency f

The apparent conductivity obtainedOr based on the normal component E of the electromagnetic field at the observation point_rDerivative of frequency f

The resulting apparent conductivity σ_r。

The invention provides a novel frequency domain electric source electromagnetic field apparent conductivity calculation method, which has the following positive effects:

(1) the method is suitable for observing the electrical distribution of the underground structure in the whole domain, expands the observation range of the traditional CSAMT, makes up for the defects in the prior art, and provides technical support for improving the frequency electromagnetic method data interpretation.

(2) The invention only needs to observe the electromagnetic field data of multiple frequency points and single component, does not need to observe mutually orthogonal electric field and magnetic field, can realize simultaneous acquisition of multiple channels, improves the field observation efficiency, and saves a large amount of field data acquisition cost;

(3) the observed electromagnetic field data is convenient for calculating apparent resistivity information and is very convenient for inversion interpretation of later data;

(4) the invention adopts the calculation of the tangential component of the observation point

Derivative of frequency f

Or normal component E of electromagnetic field_rDerivative of frequency f

The apparent resistivity is defined, so that the precision loss caused by inaccurate solving of the traditional iterative solving algorithm is avoided, the calculation precision of the apparent resistivity (the reciprocal of the apparent conductivity) is improved, and the guarantee is improved for later frequency domain electromagnetic data interpretation.

Drawings

Fig. 1 is a schematic diagram of a field observer for a new method for calculating the apparent conductivity of an electromagnetic field of a frequency domain electrical source according to the present invention.

FIG. 2 shows the observed electric field tangential component under the excitation of a horizontal couple source

And a normal component E_rGeneral schematic.

FIG. 3 is a graph of the horizontal electric dipole three-layer H-shaped curve apparent resistivity definition under the condition of 8000m of transmitting-receiving distance.

FIG. 4 shows the definition of the apparent resistivity of the horizontal electric dipole three-layer H-shaped curve under the condition that the transmitting-receiving distance is 80000 m.

Detailed Description

The invention is further described with reference to the following figures and detailed description:

referring to fig. 1, the method for calculating the apparent conductivity of the electromagnetic field of the frequency domain electrical source provided by the invention comprises the following steps:

(1) arranging a horizontal galvanic couple source in a specified exploration area, connecting an alternating current transmitting power supply and a transmitter, measuring the length dl of the galvanic couple source, recording the coordinates of power supply points A and B, and simultaneously recording the current I transmitted by the transmitter. In addition, the included angle between the observation point and the forward direction of the dipole moment is calculated

(2) Arranging an observation network, selecting a frequency observation range and an observation sector area according to exploration requirements, recording the coordinates of an observation point on each observation line in the observation network, arranging a measuring electrode and a receiver at the observation point, and measuring the tangential component of an electric field perpendicular to the direction of the connecting line of the center of a dipole source and the measurement point

Or measuring the normal component E of the connecting line direction of the dipole source center and the measuring point_r. According to the existing transmission source and transmitter technology, the transmitter can transmit a plurality of frequency current source information, so that the receiver can measure the tangential components of the multi-frequency point electromagnetic field at one time

Or normal component E_r；

(3) A series of tangential components of multi-frequency point electromagnetic field obtained by a receiver

Or normal component E_rGrouping is carried out, and the tangential component of the electromagnetic field is calculated by a second-order difference technology (four adjacent frequencies participate in calculation)

Or normal component E_rDerivative of frequency f

And

and storing the calculated derivative information;

(4) the recorded and stored data are respectively combined with formulas, and the tangential components of the electromagnetic field at the observation points can be respectively calculated

Derivative of frequency f

The apparent conductivity obtained

Or based on the normal component E of the electromagnetic field at the observation point_rDerivative of frequency fThe resulting apparent conductivity σ_r。

The following is a calculation example of the method for calculating the apparent conductivity of the electromagnetic field of the frequency domain electric source according to the invention.

Three layers of H curves, wherein the resistivity of a first layer of the model is 100 omega m, the thickness of the model is 100m, the resistivity of a second layer is 25 omega m, the thickness of the model is 200m, the resistivity of a third layer is 100 omega m, and the thickness of the model is infinite; the transmitting-receiving distance is 8000m,

the transceiving distance is 80000m,

apparent resistivity curves are defined as shown in fig. 3 and 4 below.