LU502410B1

LU502410B1 - Method and System for Simulating Electromagnetic Field in Borehole-Ground Electromagnetic Transmission, and Electronic Device

Info

Publication number: LU502410B1
Application number: LU502410A
Authority: LU
Inventors: Pengfei Liang
Original assignee: Inst Geology & Geophysics Cas
Priority date: 2022-06-29
Filing date: 2022-06-29
Publication date: 2023-09-11

Abstract

Disclosed are a method and system for simulating an electromagnetic field in borehole-ground electromagnetic transmission, and an electronic device. The method includes: when a source and an observation point are located in borehole sections of a borehole-ground portion, determining a total axial current of a drill rod using a moment method based on a pulse basis function; determining an integral kernel function using fast Hankel transform; determining a magnetic field vector potential and an electric field scalar potential on the basis of the total axial current and the integral kernel function; and simulating an electromagnetic field in borehole-ground electromagnetic transmission using an electric field integral equation according to the magnetic field vector potential and the electric field scalar potential. The moment method based on the pulse basis function adopted in embodiments of the present invention has a small amount of calculation and can improve the calculation efficiency. Moreover, an analytical expression of the integral kernel function can be obtained by means of fast Hankel transform, and an integral value can be accurately calculated, so that the problem of inaccurate calculation when the source and the observation point are close to each other is overcome, and the problems of low calculation efficiency and inaccurate calculation of an electromagnetic field in existing moment methods based on a triangular basis function are solved.

Description

BL-5458

Method and System for Simulating Electromagnetic Field in 17508610

Borehole-Ground Electromagnetic Transmission, and Electronic

Device

Technical Field

The present invention relates to the field of electromagnetic fields, in particular to a method and system for simulating an electromagnetic field in borehole-ground electromagnetic transmission, and an electronic device.

Background

The simulation of an electromagnetic field in borehole-ground electromagnetic transmission is generally performed on the basis of an integral equation method and a moment method. In the moment method, a triangular basis function is used to represent current distribution on a drill rod, and the integral equation method is used to obtain an expression of the electromagnetic field to realize the simulation of the electromagnetic field.

In the conventional art, the expression of the electromagnetic field obtained by using the moment method based on the triangular basis function contains a kernel function which is a complex integral and needs to be calculated using a complex numerical method, so as to obtain the expression of the electromagnetic field. Due to the complex calculation process of this numerical method, the calculation efficiency is low, errors will occur in the calculation process, and the obtained expression of the electromagnetic field is inaccurate.

Summary

The main object of the present invention is to provide a method and system for simulating an electromagnetic field in borehole-ground electromagnetic transmission, so as to solve the problems of low calculation efficiency and inaccurate calculation of an electromagnetic field in existing moment methods based on a triangular basis function.

In order to achieve the above object, a first aspect of the present invention provides a method for simulating an electromagnetic field in borehole-ground electromagnetic transmission, which may include the following operations. 1

BL-5458

When a source and an observation point are located in borehole sections of a V502410 borehole-ground portion, a total axial current of a drill rod is determined using a moment method based on a pulse basis function.

An integral kernel function is determined using fast Hankel transform.

A magnetic field vector potential and an electric field scalar potential are determined on the basis of the total axial current and the integral kernel function.

An electromagnetic field in borehole-ground electromagnetic transmission is simulated using an electric field integral equation according to the magnetic field vector potential and the electric field scalar potential.

Optionally, the borehole-ground portion may include a vertical borehole section and a horizontal borehole section, and the drill rod may include a vertical portion and a horizontal portion.

The operation of determining a total axial current of a drill rod using a moment method based on a pulse basis function when a source and an observation point are located in borehole sections of a borehole-ground portion may include the following operations.

When the source and the observation point are located in the same borehole section of the borehole-ground portion, the source and the observation point are located on the same portion of the drill rod.

When the source and the observation point are respectively located in different borehole sections of the borehole-ground portion, the source and the observation point are respectively located on different portions of the drill rod.

Point matching is performed using a pulse basis function ALS(r—r,) and the total axial current of the drill rod is determined, where A=, -n) Al, js à vector from a start point "» of an mth segment of wire to an end point "» , and °-".) is a Dirac function.

Optionally, the operation of determining an integral kernel function using fast

Hankel transform may include the following operations.

An integral value of the integral kernel function is determined using fast Hankel transform according to the following formula:

S, trae, |- 271765) J, (k, lop) k, dk, 2

BL-5458 _ LU502410

S, (rai Fk) where is an n-order Sommerfeld integral, 2/ is an input function,

Ja (, PP ) is an n-order Bessel function of a first type, ky is a wave number, © is a distance from an origin to the observation point, and P' is a distance from the origin to the source.

Optionally, the operation of determining a magnetic field vector potential and an electric field scalar potential on the basis of the total axial current and the integral kernel function may include the following operations.

A ' '

Based on the integral kernel function, a dyadic Green's function G'(p-p,z,z ),

D ' ' — Nn! ' a scalar & (P-P'77) and a scalar P(p- p',2,2) are respectively determined: 1 h

Ls 0 0

JOH,

G“(p-p'z,z")= 0 Los) 0

JOH,

I"-r II H , 4, cosy Sy —— + —psinyS———r ——5, {r;} k, k, JOEE,, © ' ' : y" —V;

K'(p-p',z,z')=-— joe, Sy Up

P

' ' ! Vv) =v;

P(p-p'z,z)= Hoo" 11, So eos]

P y = arctan (2525) where XX /, representing an included angle between a straight line formed by the observation point and the source and an X axis, the coordinate of an observation point r is (XY.7) the coordinate of a source r' is (XYZ) k is the wave number, # is a function about *' and y. representing the distance from the origin to the source, Ho and “ are permeability and a dielectric constant in the vacuum, # is a relative permeability at the observation point, Ex is a relative complex dielectric constant at the source, Su is a 0-order Sommerfeld integral, 5, h is a 1-order Sommerfeld integral, Vi is voltage excited by a current source in a TE 3

BL-5458 7h 1 LU502410 mode, / is current excited by the current source in the TE mode, ‘/ is current excited by the current source in a TM mode, Z is current excited by a voltage source in the TM mode, ‘ is voltage excited by the current source in the TM mode, h e hi is current excited by a voltage source in the TE mode, ‘ is voltage excited by the voltage source in the TM mode, and P(p- p',2,2) is a correction amount.

The magnetic field vector potential is determined on the basis of the total axial ; s function S“(e-0'.2,7) current and the dyadic Green's function Ee)

The electric field scalar potential is determined on the basis of the total axial

D ' ' — Nn! ' current, the scalar KX (P=P.2.2) and the scalar >(P=P42.2)

Further, the operation of determining the magnetic field vector potential on the

A ' ' basis of the total axial current and the dyadic Green's function G'(p-p',z,z) may include the following operations.

A magnetic field vector potential A(r) is determined according to the following formula: ; I(r")

A(r)=u, | G*(r,r) ——dS' (r) m] Lee

A ' A ' ' ' where G(T) is the dyadic Green's function € (P-P,72,7) Wr) js the total axial current, and “(is the radius of the observation point at a drill rod r'.

Further, the operation of determining the electric field scalar potential on the

D 1 ' basis of the total axial current, the scalar K (p-p,z7) and the scalar

P(p- PE2) may include the following operations.

An electric field scalar potential Dir) is determined according to the following formula: (= —_ [K°œr) ve Ogg [per 7 JD ds

JDE, |g 2xa(r") 3 2xa(r") where I" is the total axial current, 7" is the radius of the observation point

D ' D ' ' ' at the drill rod r', Kr) is the scalar KP") and LT) js the scalar 4

BL-5458

P(p-p',z,z") LU502410

Optionally, the operation of simulating an electromagnetic field in borehole-ground electromagnetic transmission using an electric field integral equation according to the magnetic field vector potential and the electric field scalar potential may include the following operations.

An electromagnetic field E'(r) induced in the drill rod and the stratum is simulated according to the following electric field integral equation:

E’'(r)=—-joA(r)-VO(r) where A(r) is the magnetic field vector potential, and Dir) is the electric field scalar potential.

A second aspect of the present invention provides a system for simulating an electromagnetic field in borehole-ground electromagnetic transmission, which may include a first determination unit, a second determination unit, a third determination unit and a simulation unit.

The first determination unit is configured to determine, when a source and an observation point are located in borehole sections of a borehole-ground portion, a total axial current of a drill rod using a moment method based on a pulse basis function.

The second determination unit is configured to determine an integral kernel function using fast Hankel transform.

The third determination unit is configured to determine a magnetic field vector potential and an electric field scalar potential on the basis of the total axial current and the integral kernel function.

The simulation unit is configured to simulate an electromagnetic field in borehole-ground electromagnetic transmission using an electric field integral equation according to the magnetic field vector potential and the electric field scalar potential.

A third aspect of the present invention provides a computer-readable storage medium, which may store a computer instruction for causing a computer to perform the method for simulating an electromagnetic field in borehole-ground electromagnetic transmission provided in any of the items in the first aspect.

A fourth aspect of the present invention provides an electronic device, which may

BL-5458 include: at least one processor; and a memory communicatively connected to the at 4502410 least one processor. The memory may store a computer instruction executable by the at least one processor, and the computer instruction may be executed by the at least one processor to cause the at least one processor to perform the method for simulating an electromagnetic field in borehole-ground electromagnetic transmission provided in any of the items in the first aspect.

In the method for simulating an electromagnetic field in borehole-ground electromagnetic transmission provided in an embodiment of the present invention, when a source and an observation point are located in borehole sections of a borehole-ground portion, a total axial current of a drill rod is determined using a moment method based on a pulse basis function. An integral kernel function is determined using fast Hankel transform. Compared with a moment method based on a triangular basis function in the conventional art, the moment method based on the pulse basis function adopted in the embodiment of the present invention has a small amount of calculation and can improve the calculation efficiency. Moreover, an analytical expression of the integral kernel function can be obtained by means of fast

Hankel transform, and an integral value can be accurately calculated, so that the problem of inaccurate calculation when the source and the observation point are close to each other is overcome.

A magnetic field vector potential and an electric field scalar potential are determined on the basis of the total axial current and the integral kernel function. An electromagnetic field in borehole-ground electromagnetic transmission is simulated using an electric field integral equation according to the magnetic field vector potential and the electric field scalar potential. In the embodiment of the present invention, the integral value in the integral kernel function is directly called, thereby saving the calculation consumption, improving the calculation efficiency, realizing the rapid calculation of the distribution of a borehole-ground electromagnetic field, and solving the problems of low calculation efficiency and inaccurate calculation of an electromagnetic field in existing moment methods based on a triangular basis function.

Brief Description of the Drawings

In order to more clearly illustrate the technical solutions of specific implementations of the present invention or in the conventional art, the drawings that 6

BL-5458 are required to describe the specific implementations or the conventional art will be LUS02410 briefly introduced below. Apparently, the drawings that are described below are merely some implementations of the present invention, and those ordinarily skilled in the art may obtain other drawings according to these drawings without paying creative work.

Fig. 1 is a flowchart of a method for simulating an electromagnetic field in borehole-ground electromagnetic transmission according to an embodiment of the present invention;

Fig. 2 is a block diagram of a system for simulating an electromagnetic field in borehole-ground electromagnetic transmission according to an embodiment of the present invention; and

Fig. 3 is a block diagram of an electronic device according to an embodiment of the present invention.

Detailed Description of the Embodiments

In order to make those skilled in the art better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. It is apparent that the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments. On the basis of the embodiments of the present invention, all other embodiments obtained on the premise of no creative work of those ordinarily skilled in the art should fall within the scope of protection of the present invention.

It is to be noted that the specification and claims of the present invention and the terms "first", "second" and the like in the drawings are used to distinguish similar objects, and do not need to describe a specific sequence or a precedence order. It will be appreciated that data used in such a way may be exchanged under appropriate conditions, in order that the embodiments of the present invention described here can be implemented. In addition, terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusions. For example, it is not limited for processes, methods, systems, products or devices containing a series of steps or units to clearly list those steps or units, and other steps or units which are not clearly listed or are inherent to these processes, methods, products or devices may be included instead. 7

BL-5458

It is to be noted that the embodiments of the present invention and the features LUS02410 of the embodiments may be combined with each other without conflict. The present invention is described below with reference to the drawings and in conjunction with the embodiments in detail.

In order to solve the above problem, an embodiment of the present invention provides a method for simulating an electromagnetic field in borehole-ground electromagnetic transmission. As shown in Fig. 1, the method includes the following steps S101 to S104.

In step S101, when a source and an observation point are located in borehole sections of a borehole-ground portion, a total axial current of a drill rod is determined using a moment method based on a pulse basis function. The source is an excitation source, which may be a voltage source and a current source. A pulse function is taken as a basis function. The total axial current of the drill rod is determined by the moment method.

The parameters regarding the source, such as voltage across the source, current flowing through the source, and the length of the source, may be set or measured in advance according to the properties of a circuit where the excitation source is located. The length, radius, conductivity, permeability, and dielectric constant of the drill rod may be measured on the ground. In an underground model, stratum parameters, such as the number of layers, thickness and conductivity of each layer, may be measured by means of resistivity logging.

The borehole-ground portion includes a vertical borehole section and a horizontal borehole section, and the drill rod includes a vertical portion and a horizontal portion.

Step S101 includes the following operations.

When the source and the observation point are located in the same borehole section of the borehole-ground portion, the source and the observation point are 8

BL-5458 located on the same portion of the drill rod. LUS02410

Point matching is performed using a pulse basis function ALS(r—r,) and the total axial current of the drill rod is determined, where A=, =r.) An is a vector from a start point "= of an mth segment of wire to an end point "», and Ÿ-"n) is a Dirac function.

Compared with a moment method based on a triangular basis function in the conventional art, the moment method based on the pulse basis function adopted in the embodiment of the present invention has a small amount of calculation and can improve the calculation efficiency.

Specifically, with boundary conditions that electric field tangential components of the electric field integral equation are continuous, the following formula may be obtained: [E'(r)+E (r) |. =ZJ » where E(r) is a field excited by a voltage source within a preset range near a drill bit, E'(r) is an electromagnetic field induced in the drill rod and the stratum, A is the surface impedance of the drill rod, J, is the surface current density on the drill rod, and E'(r) may be represented by the values of the magnetic field vector potential and the electric field scalar potential at r:

E'(r)=-— jwœA(r)-V®(r) 2) where A(r) is the magnetic field vector potential, and Dir) is the electric field scalar potential, which is also referred to as a Mixed Potential Electric Field Integral

Equation (MPEFIE).

Further, when the source and the observation point are both located in the vertical borehole section, the source and the observation point are both located in the vertical portion of the drill rod, and a first current of the drill rod is determined. Point matching is performed on the vertical borehole section using a function AL„Ö(r ra) 9

BL-5458 to obtain: LUS02410 <Al 6(r—r,), E'(r)>=< A/,6(r—r,), ZF —E’(r)> =<Al 6(r-r,), ZI, > +<A/,,6(r—r,), joA(r) > +<A/,6(r—r,), V®(r)> (3) where Mn = Fu) is a vector from a start point "» of an m segment of wire to an end point "», Ÿ-"n) is a Dirac function, and !+ is current on each segment of drill rod. According to the property of the Dirac function, the left side of formula (3) may be further represented as: <Al 6(r—r,), EF (r)>=A/, E'(r,) (4)

The right side of formula (3) may be respectively represented as: <A o(r—-r,), ZI >= AI, ZT...

CAS —r1). joA(r) >= AL Hot Ls roo Fre ae y , n), JOA(r) >= AL DE = NI) [| [X dz" | J, (k,| p= p) k, dk,

E98, 27 = 0 \Az (6) <Al 5(r-r,), VO(r) > 1 & _ 1 ueo'u À =A/,*— > 1(n) op, —69; | Al, *—— > [(n)P, 72 L J jog, 277 2 (7) and 1 |T 0 0 1 op, =—— —V" =v de | J, (k |p—p|) —dk 9, | | 2 2" °) à o(k, lop) Fr ; 1 Ir 0 0 1 op =— —V" ——V" de | J, (k |p—p|) — dk

Or wl 1 2 a ) 7 ok lp=r) k, ;

OT O 1h Oe , nl

P, 0 j (Zu 4 Ja: ZC lo-o') Lan ’ (8) where # and ® are permeability and a dielectric constant in the vacuum, # is a relative permeability at the observation point, Ex is a relative complex dielectric constant at the source, 1@) is current on the drill rod, Z is current excited by a voltage source in a TM mode, Jo (kp =p ) is a O-order Bessel function of a first

BL-5458 k LU502410 type, ” is the wave number, the coordinate of an observation point r is (x.3,2) the coordinate of a source r' is (*>Y>7), P is a function about * and >, representing the distance from an origin to the observation point, P' is a function about *' and y. representing a distance from the origin to the source, H is a relative permeability at the source, M, is the length of the lower half of the nth segment of drill rod, M, is the length of the upper half of the nth segment of drill rod, h

M, is the length of the nth segment of drill rod, V, is voltage excited by a current source in a TE mode, ‘ is voltage excited by the current source in the TM mode, h e hi is voltage excited by the voltage source in the TE mode, and ‘ is voltage excited by the voltage source in the TM mode.

For a difference format of formula (7), there is the following expression: <Al 6(r-r,), VO(r) > —1 y LL 1 1 peony [& _ -_ = I ++ _ + _ + _ = ome Mr I P — pt

AI, * 27 > @)[ ei Pn +P Pan Ife 2 > | mn 5) (9) where + I h + ' er + ' ' ' 1 om = ern) det | Jy(k, |p - 2) —4k, 0 AL, k, = T RAT ' ef ' ' ' 1

P, fe ) Vir" | Tok, =p) dk, 0 Al, P _ I = ' e = ' ' ' 1

P, fe )-V; (6,1, ") | de Toko = pl) dk, 04 Al, P (10)

In formula (10), N is the position of the nth segment of source, and 11

BL-5458

JT çÇ LU502410 ( plp=p ) is an n-order Bessel function of the first type.

Thus, by combining formulas (3) to (7), a gradient format may be obtained:

ALE (r,)=Al ZI (r=r,)

HH, 1 ; T e ' ' +Al —=—> I(n I°dz' | Jk |p— k dk "es. 27 ( I] J v J o >|P p\) p 1 N —Al *— > I(n) 6p, — 60, vol )| de, — 60, 244 N ~Al, « 1 MEL S 1)

JDE, 27 n=l (11)

The expression of each component in formula (11) is shown in formula (8), and for a difference format of formula (11), there is the following expression:

A, E(r,)=M,Z1,e=r,)

HoH, 1 SZ f e ' ' +A ES 1 Id | Jk, |p— k dk "EE, 27 À |; | ’ 3 o ole el) ’ —1 N + J tt +o — +

Tm al (0) Gr = Pos + Pam 7 Pr } 2 er N

LAE enfer:

JDE, 277 n=l (12)

The expression of each component in formula (12) is shown in formula (10).

According to formula (11) or (12), a first current L@=r,) of the drill rod may be obtained.

Further, when the source and the observation point are both located in the horizontal borehole section, the source and the observation point are both located in the horizontal portion of the drill rod, and a second current of the drill rod is determined. Point matching is performed on the horizontal borehole section using a function M1.) to obtain according to formulas (1) and (2). < Al 6(r—r,), E'(r)>=< A/,6(r—r,), ZF —E’(r)> =<Al 6(r-r,), ZI, > +<A/,,6(r—r,), joA(r)> +<A/,6(r—r,), VO(r) > where Al, = Fu) is a vector from a start point "» of an m segment of wire 12

BL-5458 + LU502410 to an end point Tn and according to the property of the Dirac function, the left side of formula (13) may be represented as: <Al 6(r-r,), E(r)>=A/, E'(r,) (14)

The right side of formula (13) may be respectively represented as: <ALO(r-v,), ZI >= A1, Z|, (15)

N oo <ALS(r-t,), joA(r)>= Al So | | MACAU dk = 2% A 5 15 (16) and in the case of difference, <Al 6(r-r,), VO(r) > —1 > ++ + —— —+

AL, * 2m n=l (1 7) where

Om = | Hi Re 0 nal oo) at, dx’

Ld p* — 1 _Je = '

Pur = | Hi [Phen 0 (ts } bo rh dk, | de: on = | Hi [renin Al et, >= pt}, | de om =] Hi Re 0 2s loo) at, | dx’

ALY 0 P (18) and an expression of formula (17) in a gradient format: <Al 8(r-r,), VO(r) > = , T e ! x=x' !

SG) (k,l p—p) dk, a 1A Aly 0 P 27 ® . X—x' \

Jr) aloo) ak, [ae

ALY 0 (1 9) where Ji(k, |p =p ) is a 1-order Bessel function of the first type.

By combining formulas (13) to (19), a second current I, rs, of the drill rod may be obtained.

Further, when the source is located in the horizontal borehole section and the 13

BL-5458 observation point is located in the vertical borehole section, the source is located in LUS02410 the horizontal portion of the drill rod, the observation point is located in the vertical portion of the drill rod, and a third current of the drill rod is determined. Similarly, point matching is performed using a function ALo(r—r,) to obtain according to formulas (1) and (2): <Al 6(r—r,), E'(r)>=< A/,6(r—r,), ZF —E’(r)> =<Al 6(r-r,), ZI, > +<A/,,6(r—r,), joA(r) > +<A/,6(r—r,), V®(r)> (20) where Mn = Fu) is a vector from a start point "» of an m segment of wire to an end point r. and according to the property of the Dirac function, the left side of formula (20) may be further represented as: <Al 6(r-r,), E(r)>=A/, E'(r,) (21)

The right side of formula (20) may be respectively represented as: <A,6(r-r,), ZI >= A1, Z|, 22) <Al 6(r-r,), joA(r)> —jo cos T e ' ' ' = AI, IMIS 1) f i (I'@2)~ I: (2.2) J, (k, |p - 1) dk, dx 27 n=1 Ax LO (23) and in the case of difference: <Al 6(r-r,), VO(r) > —1 N — Im ++ +4 -— Tt

AL *27 Ë Lom Fon = Con = Fm } (24) y = arctan (2525) where XX /, representing an included angle between a straight line formed by the observation point and the source and an * axis. 14

BL-5458

LU502410 + © V, r,.r' Vr r,.r' ! !

On = | I HRD op) a | dx

AI, (0 p -- © Ver DV 01, ') ' ! 0m = | I [fener Toko p= pl) dk, dx

AI, LD p ++ Tr.) Vi, ' '

Pon = | I en) en Jo (kolo =p) dk, dx

AI; LO p _+ ARAN DRA) ' ' 0m = I CS ln Jo(kalp=p1) dk, | dr

ALY 0 p (25)

By combining formulas (20) to (25), a third current I, rs, of the drill rod may be obtained.

Further, when the source is located in the vertical borehole section and the observation point is located in the horizontal borehole section, the source is located in the vertical portion of the drill rod, the observation point is located in the horizontal portion of the drill rod, and a fourth current of the drill rod is determined. Similarly, point matching is performed using a function ALo(r—r,) to obtain according to formulas (1) and (2): <Al 6(r—r,), E'(r)>=< A/,6(r—r,), ZF —E’(r)> =<Al 6(r-r,), ZI, > +<A/,,6(r—r,), joA(r) > +<A/,6(r—r,), V®(r)> (26) where Mn = Fu) is a vector from a start point "» of an m segment of wire to an end point r. and according to the property of the Dirac function, the left side of formula (26) may be represented as: <Al 6(r-r,), E(r)>=A/, E'(r,) (27)

The right side of formula (26) may be respectively represented as: <A,6(r-r,), ZI >= A1, Z|, (28) there is a formula in a gradient format:

BL-5458 <Al 5(r-r,), VO(r) > LU502410 x jog, vive X=x' jog, V"_V° ,x-x'

I 7% yg dle Ti Lop LIDO ped Ti Lr _ Sr As k | CP n°15 k 177 =A *

JDE, N , p' _ye )

I) [mew S, pe dz‘ n=l A, p P

N | x—x' | x—x'

Im) +154; dE | Sat de

Betis SEAS a 2 h e ' +A EE? He Sion" =v fart

JOE, n=1 Al, k, pP (29) where 5, is a 1-order Sommerfeld integral.

There is a formula in a difference format: —1 N < A 6(r-r,), VO(r)>=—— In) —p +o -0,, ,S(r=,), V(r) ra 0) 0s = Pan + Pan ou} 2 44 N

Ma fy]

JDE, 2 nel (30) where © 1 + p* + 1 —V° + ' d ' J ke _ " — dk

Pi Ii (re) AR) 3 (k,|P-P}) ph © 1

Pn = | | ACC) | J, (kuo= pl) 4, 0 \ Al, Pp © 1 = Van NV ar) dz' | J (k |p—p|)—dk

Pn [foe „DV ar) | (k,\p A, > © 1

Pr = | | ern ar) | J.(k, lo - 01) 4, 0 \ a; Pp + i: + ‘ e + 1 1 ' 1

P*, À fées )-V°(ri,r, Je Jo (ky p= pl) = dk, 04 Al, P © 1

P, =| | en] | Toko =p) = dk, 0

Al p (31)

By combining formulas (26) to (31), a fourth current I, rs, of the drill rod may be obtained.

The total axial current of the drill rod is determined according to the first current, the second current, the third current, and the fourth current. 16

BL-5458

In step S102, an integral kernel function is determined using fast Hankel 4502410 transform. An integral value of the integral kernel function is determined using newly developed Hankel filter coefficients. The newly proposed Hankel filter coefficients can accurately and rapidly perform fast Hankel transform, an analytical expression of the integral kernel function can be obtained by means of the fast Hankel transform, and an integral value can be accurately calculated, so that the problem of inaccurate calculation when the source and the observation point are close to each other is overcome.

Specifically, step S102 includes the following operations.

An integral value of the integral kernel function is determined using fast Hankel transform according to the following formula: ~ 1 © 5, (FF J (&, p-p ) k, dk, 0

S, (rai Fk) where is an n-order Sommerfeld integral, 2/ is an input function,

In step S103, a magnetic field vector potential and an electric field scalar potential are determined on the basis of the total axial current and the integral kernel function. The integral kernel function is a Sommerfeld integral. In the embodiment of the present invention, the integral value in the integral kernel function is directly called, thereby saving the calculation consumption, improving the calculation efficiency, realizing the rapid calculation of the distribution of a borehole-ground electromagnetic field, and solving the problems of low calculation efficiency and inaccurate calculation of an electromagnetic field in existing moment methods based on a triangular basis function.

Specifically, step S103 includes the following operations.

A ' '

Based on the integral kernel function, a dyadic Green's function G'(p-p,z,z ),

D ' ' — Nn! ' a scalar & (P-P'77) and a scalar P(p- p',2,2) are respectively determined: 17

BL-5458

LU502410 —s, {7} 0 0

JOH,

G“(p-p'z,z")= 0 Los) 0

JOH,

K'(p-p',z,z')=-— joe, Sy Up

P

' ' ! Vv) =v;

P(p-p'z,z)= Hoo" 11, So eos]

P y = arctan (2525) where XX /, representing an included angle between a straight line formed by the observation point and the source and an X axis, the coordinate of an observation point r is (XY.7) the coordinate of a source r' is (XYZ) k is the wave number, # is a function about *' and y. representing the distance from the origin to the source, Ho and “ are permeability and a dielectric constant in the vacuum, # is a relative permeability at the observation point, Ex is a relative complex dielectric constant at the source, Su is a 0-order Sommerfeld integral, 5, h is a 1-order Sommerfeld integral, Vi is voltage excited by a current source in a TE h e mode, [ is current excited by the current source in the TE mode, [ is current excited by the current source in a TM mode, Z is current excited by a voltage source in the TM mode, ‘ is voltage excited by the current source in the TM mode, h e hi is current excited by a voltage source in the TE mode, ‘ is voltage excited by

D 1 ' the voltage source in the TM mode, the scalar K (p-P,7,7) js related to a vertical well, and the scalar (77,7) is a correction amount.

The magnetic field vector potential is determined on the basis of the total axial

A ' ' current and the dyadic Green's function C (P-P57,7).

The electric field scalar potential is determined on the basis of the total axial 18

BL-5458 ® LU Co LU502410 current, the scalar KX (P=P.2.2) and the scalar >(P=P42.2)

A ' ' basis of the total axial current and the dyadic Green's function G'(p-p',z,z) includes the following operations.

A(r)=u, | G*(r,r) ——dS' (r) m] (re

A ' A ' ' ' where G(T) is the dyadic Green's function € (P-P,72,7) Wr) js the total axial current, and “() is the radius of the observation point at a drill rod r'.

D 1 ' basis of the total axial current, the scalar K (p-p,z7) and the scalar

P(p- P" 2,2) includes the following operations.

D ' D ' ' ' at the drill rod r', Kr) is the scalar KP") and LT) js the scalar

P(p-p'zz)

In step S104, an electromagnetic field in borehole-ground electromagnetic transmission is simulated using an electric field integral equation according to the magnetic field vector potential and the electric field scalar potential.

Specifically, step S104 includes the following operations.

E’ (r)=—-joA(r)-VO(r) where A(r) is the magnetic field vector potential, and Dir) is the electric field 19

BL-5458 scalar potential. The distribution of the electromagnetic field induced in the drill rod LUS02410 and the stratum may be obtained through the magnetic field vector potential and the electric field scalar potential.

The embodiments of the present invention can rapidly calculate the distribution of a borehole-ground electromagnetic field, and provide necessary guidance and assistances for parameter optimization and instrument design during the development of borehole-ground electromagnetic transmission instruments.

In an optional implementation provided by the present invention, it is also possible to determine the distribution of a ground electromagnetic field and to derive a field strength value of the electric field on the ground. Since the current along the vertical drill rod has only a vertical component, the obtained magnetic field vector potential Ar) has only a component in a z direction, independent of the required horizontal component of the electric field, and therefore no derivation is made in the embodiments of the present invention. The current on the horizontal drill rod, along the horizontal direction, is multiplied by an xx component of the dyadic Green's function to obtain an electromagnetic field in the horizontal direction. The xx component of the dyadic Green's function is the 1st-row 1st-column element —s, fr}

JOH, in a matrix of an expression of the dyadic Green's function

Gp pine)

By the same reasoning, the gradient V(r) of the electric field scalar potential is also calculated in a vertical section and a horizontal section, respectively. For the vertical section of drill rod, the correlation calculation process is the same as for the previous vertical section of drill rod, while involving the correlation operation of two quantities K” and P,. For the horizontal section of drill rod, the correlation operation of only K* is involved. Thus, only the solution for horizontal components of V®(r) is listed below.

When calculating the horizontal components of the electromagnetic field on the ground, assuming that the observation point r is located on the top surface of the layer, the following formulas may be obtained: 1 & h

Alr)=— In) | 8, {1} de

JO ma a (32)

BL-5458

N LU502410

Jor) = Eve] | Viz2) Jy (k,|p-p!) k, dk, ae 27 7 15 (33)

For the vertical section of drill rod, —1 N N ®,(r) = Ls Im) 0, - 0; [+2 TP, }

JOE, (VA nal (34) where 0 _ | K®@,r," dz' "A 5 7 oF À | K®@,r," dz'

TON Tr

P, = [Pr de

Al, (35)

Since column coordinates are used in the calculation and are symmetrical about ? the following formulas may be obtained: 0 1 Ÿ 60. 0 _ 1 Ÿ 0 — Or) =-— Im Ze A [ism ln op JOE, n=1 op op JOE, n=1 op (36) . h_ 17 2p doe | s | de

P n AL P (37) . he 2 py dom | s | de

P n AL P (38) h__ qe

Op y(r) dy 1) | [5 }æ" 1,(k,|p-p'|) dk 2% A Aly gat ? ?

Ls 10-1 [7 vd J,(k,|p=p') dk 2% to AL goth ? ? so’ 1 & 7 aN

HHO Le S| [ {1 - det Jy (kop) dk, jon, 2S (40)

For the horizontal section of drill rod, 21

BL-5458 (x LU502410 ®,(r)= > Im) 9, 0)

Since column coordinates are used in the calculation and are symmetrical about ? the following formulas may be obtained: so a [FL GEL (EE) wr 1 t'fren Le , x—x' va JJ ated a [$55 : (43)

According to formulas (40) and (43), the distribution of the ground electromagnetic field can be obtained.

From the above description, it can be seen that the present invention achieves the following technical effects.

Compared with a moment method based on a triangular basis function in the conventional art, the moment method based on the pulse basis function adopted in the embodiment of the present invention has a small amount of calculation and can improve the calculation efficiency. Moreover, an analytical expression of the integral kernel function can be obtained by means of fast Hankel transform, and an integral value can be accurately calculated, so that the problem of inaccurate calculation when the source and the observation point are close to each other is overcome.

In the embodiment of the present invention, the integral value in the integral kernel function is directly called, thereby saving the calculation consumption, improving the calculation efficiency, realizing the rapid calculation of the distribution of a borehole-ground electromagnetic field, and solving the problems of low calculation efficiency and inaccurate calculation of an electromagnetic field in existing moment methods based on a triangular basis function.

The embodiments of the present invention can rapidly calculate the distribution of a borehole-ground electromagnetic field, and provide necessary guidance and assistances for parameter optimization and instrument design during the 22

BL-5458 development of borehole-ground electromagnetic transmission instruments. LUS02410

It is to be noted that the steps shown in the flowchart of the drawings may be executed in a computer system including, for example, a set of computer-executable instructions. Moreover, although a logic sequence is shown in the flowchart, the shown or described steps may be executed in a sequence different from the sequence here under certain conditions.

An embodiment of the present invention also provides a system for simulating an electromagnetic field in borehole-ground electromagnetic transmission, used for performing the method for simulating an electromagnetic field in borehole-ground electromagnetic transmission. As shown in Fig. 2, the system includes a first determination unit 21, a second determination unit 22, a third determination unit 23, and a simulation unit 24.

The first determination unit 21 is configured to determine, when a source and an observation point are located in borehole sections of a borehole-ground portion, a total axial current of a drill rod using a moment method based on a pulse basis function.

The second determination unit 22 is configured to determine an integral kernel function using fast Hankel transform.

The third determination unit 23 is configured to determine a magnetic field vector potential and an electric field scalar potential on the basis of the total axial current and the integral kernel function.

The simulation unit 24 is configured to simulate an electromagnetic field in borehole-ground electromagnetic transmission using an electric field integral equation according to the magnetic field vector potential and the electric field scalar potential.

An embodiment of the present invention also provides an electronic device. As shown in Fig. 3, the electronic device includes one or more processors 31 and a memory 32, as exemplified by one processor 31 in Fig. 3.

The controller may further include: an input apparatus 33 and an output apparatus 34.

The processor 31, the memory 34, the input apparatus 33, and the output apparatus 34 may be connected by a bus or other means, as exemplified by a bus connection in Fig. 3.

The processor 31 may be a Central Processing Unit (CPU). The processor 31 23

BL-5458 may also be another general-purpose processor, a Digital Signal Processor (DSP), LUS02410 an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA) or another programmable logic device, discrete gate or transistor logic device, discrete hardware component, and other chips, or a combination of the above chips. The general-purpose processor may be a microprocessor or any conventional processor.

The memory 32 is used as a non-transitory computer-readable storage medium, and may be configured to store non-transitory software programs, non-transitory computer-executable programs, and modules, such as program instructions/modules corresponding to the control method in the embodiment of the present invention. The processor 31 executes various functional applications of the server and data processing by executing non-transitory software programs, instructions and modules stored in the memory 32, i.e. implementing the method for simulating an electromagnetic field in borehole-ground electromagnetic transmission in the above method embodiments.

The memory 32 may include a storage program area and an storage data area.

The storage program area may store an operating system and an application required for at least one function. The storage data area may store data created according to usage of a processing apparatus operated by a server, and the like. In addition, the memory 32 may include a high-speed random access memory, and may also include a non-transitory memory such as at least one disk storage device, a flash device, or other non-transitory solid storage devices. In some embodiments, the memory 32 optionally includes memories remotely located relative to the processor 31, which may be connected to a network connection apparatus over a network. The examples of such networks include, but are not limited to, the Internet, the Intranet, local area networks, mobile communication networks, and combinations thereof.

The input apparatus 33 may receive input digital or character information and generate a key signal input related to user settings and function control of the processing apparatus of the server. The output apparatus 34 may include a display device such as a display screen.

The one or more modules are stored in the memory 32, and when executed by the one or more processors 31, the method as shown in Fig. 1 is performed.

Those skilled in the art can understand that all or part of the processes in the above method embodiments may be implemented by a computer program to instruct 24

BL-5458 related hardware, and the program may be stored in a computer-readable storage LUS02410 medium. When the program is executed, the flow of the embodiments of the motor control method as described above may be included. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access

Memory (RAM), a Flash Memory (FM), a Hard Disk Drive (HDD) or a Solid-State

Drive (SSD), etc. The storage medium may also include a combination of the memories described above.

Although the implementations of the present invention have been described with reference to the accompanying drawings, various modifications and changes may be made by those skilled in the art without departing from the spirit and scope of the present invention, and such modifications and changes fall within the scope defined by the appended claims.

Claims

BL-5458 What is claimed is: LUS02410

1. A method for simulating an electromagnetic field in borehole-ground electromagnetic transmission, comprising: when a source and an observation point are located in borehole sections of a borehole-ground portion, determining a total axial current of a drill rod using a moment method based on a pulse basis function; determining an integral kernel function using fast Hankel transform; determining a magnetic field vector potential and an electric field scalar potential on the basis of the total axial current and the integral kernel function; and simulating an electromagnetic field in borehole-ground electromagnetic transmission using an electric field integral equation according to the magnetic field vector potential and the electric field scalar potential.

2. The method according to claim 1, wherein the borehole-ground portion comprises a vertical borehole section and a horizontal borehole section, and the drill rod comprises a vertical portion and a horizontal portion; the determining a total axial current of a drill rod using a moment method based on a pulse basis function when a source and an observation point are located in borehole sections of a borehole-ground portion comprises: when the source and the observation point are located in the same borehole section of the borehole-ground portion, locating the source and the observation point on the same portion of the drill rod; when the source and the observation point are respectively located in different borehole sections of the borehole-ground portion, respectively locating the source and the observation point on different portions of the drill rod; and performing point matching using a pulse basis function ALo(r—r,) , and determining the total axial current of the drill rod, wherein Mn = —Fn) An is à vector from a start point "” of an m segment of wire to an end point r, and °F.) is a Dirac function.

3. The method according to claim 1, wherein the determining an integral kernel function using fast Hankel transform comprises: determining an integral value of the integral kernel function using fast Hankel transform according to the following formula: 26

BL-5458 _ 1 a- LU502410 5, (FF J (&, l=) k, dk, 0 S, (re) Fr) wherein is an n-order Sommerfeld integral, p” is an input function, Ja (k,|o-p ) is an n-order Bessel function of a first type, ky is a wave number, © is a distance from an origin to the observation point, and Pis a distance from the origin to the source.

4. The method according to claim 1, wherein the determining a magnetic field vector potential and an electric field scalar potential on the basis of the total axial current and the integral kernel function comprises: respectively determining, based on the integral kernel function, a dyadic Green's <A ! ! ® ! ! LA! ! function G (P=P"2.2) a scalar K’(-P'7,7") and a scalar "P-P,7,7". 1 h Ls 0 0 JOH, G“(p-p'z,z")= 0 Los) 0 JOH, I"-r II H , —4,CosyS —— + TM SIMYS NS Es} k, k, JOEE,, © ' ' : y" —V; K'(p-p',z,z')=-— joe, Sy Up P ' ' ! Vv) =v; P(p-p'z,z)= Hoo" 11, So eos] P y =arctan| 2-2 wherein X-X /, representing an included angle between a straight line formed by the observation point and the source and an X axis, the coordinate of an observation point r is (XY.7) the coordinate of a source r' is (X>Y57) k, is the wave number, ©? is a function about X' and y. representing the distance from the origin to the source, Ho and “ are permeability and a dielectric constant in the vacuum, is a relative permeability at the observation point, Ex is a 27

BL-5458 s LU502410 relative complex dielectric constant at the source, “9 is a O-order Sommerfeld h integral, 5, is a 1-order Sommerfeld integral, Vi is voltage excited by a current h e source in a TE mode, [ is current excited by the current source in the TE mode, [ is current excited by the current source in a TM mode, Z is current excited by a voltage source in the TM mode, ‘ is voltage excited by the current source in the h e TM mode, hi is current excited by a voltage source in the TE mode, ‘ is voltage excited by the voltage source in the TM mode, and P(p- p',2,2) is a correction amount; determining the magnetic field vector potential on the basis of the total axial s function G(P—p"2.2). current and the dyadic Green's function >< 2 7; and determining the electric field scalar potential on the basis of the total axial current, D ' ' — Nn! ' the scalar X”(0-0',7,7) and the scalar P-7P)2,7)

5. The method according to claim 4, wherein the determining the magnetic field vector potential on the basis of the total axial current and the dyadic Green's function A ' ' G'(o-P>2,7) comprises: determining a magnetic field vector potential A(r) according to the following formula: ; I(r") A(r)=u, | G*(r,r) ——dS' (r) m] Lee A ' A ' ' ' wherein G (1) is the dyadic Green's function C (P-P57,7) 1" is the total axial current, and “(is the radius of the observation point at a drill rod r'.

6. The method according to claim 4, wherein the determining the electric field D 1 ' scalar potential on the basis of the total axial current, the scalar K (p-P;,,7) and the scalar (792,2) comprises: determining an electric field scalar potential Dir) according to the following formula: 28

BL-5458 ; ‘ LU502410 or [ter Var per) oe as) wherein I(r) is the total axial current, 4") is the radius of the observation point at the drill rod r', K™(r,r) is the scalar K"(P-P"2.2") ana LOT) is the scalar f(P-P,22).

7. The method according to claim 1, wherein the simulating an electromagnetic field in borehole-ground electromagnetic transmission using an electric field integral equation according to the magnetic field vector potential and the electric field scalar potential comprises: simulating an electromagnetic field E'(r) induced in the drill rod and the stratum according to the following electric field integral equation: E’'(r)=—-joA(r)-VO(r) wherein A(r) is the magnetic field vector potential, and Dir) is the electric field scalar potential.

8. A system for simulating an electromagnetic field in borehole-ground electromagnetic transmission, comprising: a first determination unit, configured to determine, when a source and an observation point are located in borehole sections of a borehole-ground portion, a total axial current of a drill rod using a moment method based on a pulse basis function; a second determination unit, configured to determine an integral kernel function using fast Hankel transform; a third determination unit, configured to determine a magnetic field vector potential and an electric field scalar potential on the basis of the total axial current and the integral kernel function; and a simulation unit, configured to simulate an electromagnetic field in borehole-ground electromagnetic transmission using an electric field integral equation according to the magnetic field vector potential and the electric field scalar potential.

9. A computer-readable storage medium, storing a computer instruction for causing a computer to perform the method for simulating an electromagnetic field in 29

BL-5458 borehole-ground electromagnetic transmission according to any one of claims 1-7. LUS02410

10. An electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor, wherein the memory stores a computer instruction executable by the at least one processor, and the computer instruction is executed by the at least one processor to cause the at least one processor to perform the method for simulating an electromagnetic field in borehole-ground electromagnetic transmission according to any one of claims 1-7.