CN104100261B - Obtain with boring the azimuthal resistivity logger system away from stratigraphic boundary distance - Google Patents

Abstract

The invention provides a kind of acquisition with boring the azimuthal resistivity logger system away from stratigraphic boundary distance, including the first initial value adjusting module, for adjusting the initial value of current country rock formation resistivity；Second initial value adjusting module, for adjusting the initial value of logger location layer resistivity；Response value computing module, for calculating the response value of logger Rx and Rz corresponding when at a distance of stratigraphic boundary different distance；Matching judgment module, whether the response value of response value with actual Rx and Rz measured for judging Rx and Rz calculated mates；Processing module, for if it does, be defined as the logger distance at a distance of stratigraphic boundary by distance corresponding in multiple mirror image forward model；If do not mated, triggering the first initial value adjusting module and the second initial value adjusting module, making system continue the distance obtaining logger at a distance of stratigraphic boundary.The initial value of logger location layer resistivity can be got in time by the present invention.

Description

Obtain with boring the azimuthal resistivity logger system away from stratigraphic boundary distance

Technical field

The present invention relates to geological exploration field, in particular to one obtain with bore azimuthal resistivity logger away from The system of stratigraphic boundary distance.

Background technology

Geosteering is extremely important to oil-gas exploration in real time.The purpose of geosteering is to keep drill bit at oil reservoir as far as possible Middle traveling.In order to avoid drill bit enters low-resistance country rock, it is desirable to provide the direction of distally bed boundary with boring instrument, and with brill Resistivity logging tool is at a distance of the information of distally bed boundary distance.This is accomplished by resistivity logging while drilling logger and has orientation spy Survey ability.Fig. 1 show currently a popular two kind with the antenna structure view boring azimuthal resistivity logger.Wherein, R1 Represent that receiving coil, T1 and T2 represent transmitting coil with R2；Fig. 1 a show tilt coil antenna structure view.Owing to tilting Coil has the component orthogonal with transmitting coil, therefore has position sensing capability.Also have due to tilt coil again simultaneously with The component that transmitting coil is parallel, therefore measures in signal and further comprises the information unrelated with orientation.In application process, with orientation The method that unrelated information is processed by data is rejected.Fig. 1 b show the structural representation of crossed coil.Due to receiving coil Orthogonal with transmitting coil, therefore reception antenna is zero with the direct-coupling of transmitting antenna, receives signal and only comprises relevant with orientation Formation information.

Fig. 2 show the antenna structure view based on associating coil that a kind of correlation technique provides.This antenna structure Receiving coil be axisymmetric about instrument core by two, orthogonal with transmitting coil coil and one parallel with transmitting coil Coil forms.Three coils are formed by one group of line coiling, therefore receive the response sum that signal is three coils.Due to associating line Circle has crossed coil, therefore has position sensing capability.Simultaneously because associating coil also comprises and the line launching antenna parallel Circle, therefore combines and further comprises the transmitting coil direct-coupling component by stratum in the voltage response of coil, extract this direct Coupled component, it is possible to use the theory of conventional propagation resistivity logging tool, measures with boring azimuthal resistivity logger place The resistivity on stratum.

But based on the associating coil antenna structure shown in Fig. 2 with boring azimuthal resistivity logger, real-time estimation is remote Place's stratigraphic boundary distance is relatively time-consuming with the vertical dimension still ratio boring instrument, and promptness is poor.

Summary of the invention

It is an object of the invention to provide a kind of acquisition with boring azimuthal resistivity logger away from stratigraphic boundary distance is System, to solve above-mentioned problem.

Provide a kind of acquisition with boring azimuthal resistivity logger away from stratigraphic boundary distance in an embodiment of the present invention System, described logger is associating coil antenna structure, including horizontal emission antenna Tz, horizontal reception antenna Rz and vertical Reception antenna Rx；Described system includes: the first initial value adjusting module, calculated for the signal according to Rz previous receipt Propagation resistivity adjusts the initial value of current country rock formation resistivity；Second initial value adjusting module, for currently connecing according to Rz The propagation resistivity that the signal received calculates adjusts the initial value of described logger location layer resistivity；Response value calculates mould Block, the initial value of the country rock formation resistivity after adjusting according to described first initial value adjusting module and described second initial The initial value of the logger location layer resistivity after value adjusting module adjustment, utilizes multiple mirror image forward model to calculate described survey The response value of Rx and Rz that well instrument is corresponding when at a distance of stratigraphic boundary different distance；Matching judgment module, is used for judging described Whether the response value of Rx and Rz that response value computing module calculates mates with the response value of actual Rx and Rz measured；Process mould Block, if the judged result for described matching judgment module is coupling, by the response value of Rx and Rz of described calculating described In multiple mirror image forward model, corresponding distance is defined as the described logger distance at a distance of stratigraphic boundary；If matching judgment mould The judged result of block, for not mate, triggers described first initial value adjusting module and the second initial value adjusting module readjusts institute State initial value and the initial value of described logger location layer resistivity of country rock formation resistivity, make described system continue to obtain Take the described logger distance at a distance of stratigraphic boundary.

The system that the embodiment of the present invention provides, based on complex image theory, calculates this logger different at a distance of stratigraphic boundary The response value of Rx and Rz corresponding during distance, and by by the response value of Rx and Rz of calculating and actual Rx and Rz measuring and obtaining Response value carry out matching ratio relatively, can determine that at a distance stratigraphic boundary is at a distance of this logger by fast inversion by matching relationship Vertical dimension, solve associating coil antenna structure with boring azimuthal resistivity logger, real-time estimation limit, stratum at a distance Boundary's distance is relatively time-consuming with the vertical dimension ratio boring instrument, the problem that promptness is poor, improves the performance of instrument.

Accompanying drawing explanation

Fig. 1 a and Fig. 1 b shows the antenna structure view with brill azimuthal resistivity logger that correlation technique provides；

Fig. 2 shows the antenna structure view based on associating coil that correlation technique provides；

Fig. 3 shows that what the embodiment of the present invention provided obtains with boring azimuthal resistivity logger away from stratigraphic boundary distance System flow chart；

Fig. 4 shows the structural representation combining coil that the embodiment of the present invention provides；

Fig. 5 shows associating coil that the embodiment of the present invention the provides typical response curve chart when near stratigraphic boundary；

Fig. 6 shows the schematic diagram of the complex image theory that the embodiment of the present invention provides；

Fig. 7 show three layers of earth formation that the embodiment of the present invention provides come the multiple mirror method of comparison and completely solution method it Between difference schematic diagram；

Fig. 8 shows the multiple mirror method of application that the embodiment of the present invention provides and the Rx coil that solution method respectively obtains completely The magnetic field real part of position and imaginary part schematic diagram；

Fig. 9 shows that the result of calculation of the multiple mirror method of application that the embodiment of the present invention provides solves method completely with application The relative error schematic diagram of result of calculation；

Figure 10 shows the algorithm flow chart of the stratigraphic boundary of the inverting real-time distance that the embodiment of the present invention provides.

Detailed description of the invention

Below by specific embodiment and combine accompanying drawing the present invention is described in further detail.

The embodiment of the present invention utilizes complex image theory, and the reflection of electromagnetic wave equivalence of stratigraphic boundary, distant place is become emission source One multiple mirror image scattering in homogeneous space, thus one-dimensional forward model is reduced to homogeneous space model, it is greatly enhanced Calculating speed.Based on this, embodiments provide a kind of acquisition with boring azimuthal resistivity logger away from stratigraphic boundary The system of distance, this logger is associating coil antenna structure (as shown in Figure 2), connects including horizontal emission antenna Tz, level Receive antenna Rz and vertical reception antenna Rx；Shown in Figure 3, this system can be arranged in logger, including with lower module:

First initial value adjusting module 30, adjusts for the calculated propagation resistivity of signal according to Rz previous receipt The initial value of current country rock formation resistivity；

Wherein, the signal of Rz previous receipt can rule of thumb select the quantity of signal, and the embodiment of the present invention is not done specifically Limit；

Second initial value adjusting module 32, adjusts well logging for the propagation resistivity calculated according to the currently received signal of Rz The initial value of instrument location layer resistivity；

Response value computing module 34, the country rock formation resistivity after adjusting according to the first initial value adjusting module 30 The initial value of the logger location layer resistivity after initial value and the adjustment of the second initial value adjusting module 32, utilizes multiple mirror image Forward model calculates the response value of logger Rx and Rz corresponding when at a distance of stratigraphic boundary different distance；

Matching judgment module 36, for judging the response value of Rx and Rz that response value computing module 34 calculates and actual measurement The response value of Rx and Rz whether mate；

Because different distances, the response value of Rx with Rz calculated is different, matching ratio relatively time, Rx and Rz calculated Response value compare, simply by the presence of the response value of a group with Rx and Rz of measurement with the response value of Rx and Rz measured respectively Match, matching ratio can be stopped relatively.Certainly, the response value that coupling herein needs not be in absolute sense is completely the same, can To be similar consistent in set point, it is allowed to exist necessarily between response value and the actual response value measured of calculating Deviation, as long as this deviation is in allowed band, i.e. think that the two mates；

Processing module 38, if the judged result for matching judgment module 36 is coupling, by the sound of Rx and Rz of calculating The distance that should be worth in multiple mirror image forward model correspondence is defined as the logger distance at a distance of stratigraphic boundary；If matching judgment The judged result of module, for not mate, triggers the first initial value adjusting module 30 and the second initial value adjusting module 32 is readjusted The initial value of country rock formation resistivity and the initial value of logger location layer resistivity, make this system continue to obtain logging instrument Device is at a distance of the distance of stratigraphic boundary.

The said system of the present embodiment, based on complex image theory, calculates this logger at a distance of stratigraphic boundary different distance Time corresponding Rx and Rz response value, and by the sound by the response value of Rx and Rz of calculating with actual Rx and Rz measuring and obtaining Should be worth and carry out matching ratio relatively, stratigraphic boundary hanging down at a distance of this logger at a distance can be determined by fast inversion by matching relationship Straight distance, solve associating coil antenna structure with boring azimuthal resistivity logger, stratigraphic boundary, real-time estimation distant place away from From relatively time-consuming with the vertical dimension ratio boring instrument, the problem that promptness is poor, improve the performance of instrument.

Concrete, above-mentioned response value computing module 34 may include that

Magnetic field calculation unit, for calculating this logger Rx's and Rz corresponding when at a distance of stratigraphic boundary different distance Magnetic field is respectively as follows:

$H_{Rx}=\frac{M_z}{4\mathrm{\π}}\frac{e^{-{\mathrm{jk}}_{b}r}}{r^3}(k_b^2{r}^2-3{\mathrm{jk}}_{b}r-3)\frac{(2d+2h)L}{r^2}$

$H_{Rz}=\frac{M_z}{4\mathrm{\π}}\[\frac{e^{-{\mathrm{jk}}_{b}r}}{r^3}(k_b^2{r}^2-3{\mathrm{jk}}_{b}r-3){\left(\frac{2d+2h}{r}\right)}^2+\frac{2e^{-{\mathrm{jk}}_{b}r}}{r}({\mathrm{jk}}_{b}r+1)\]+\frac{M_z}{4\mathrm{\π}}\frac{e^{-{\mathrm{jk}}_{b}r}}{r^3}({\mathrm{jk}}_{b}L+1)$

In above-mentioned formula,D is complex displacement,Wherein,It is respectively this stratum, logger place and outside boundaries stratum Wave number, ω is the emission current angular frequency of the Tz of this well instrument；μ is the pcrmeability of medium, ε_nFor image source place medium Dielectric constant, σ_b、σ_nIt is respectively this stratum, logger place and the electrical conductivity (inverse of resistivity) on outside boundaries stratum, also It it is exactly the inverse of the initial value of the inverse of the initial value of instrument location layer resistivity and country rock formation resistivity；J is imaginary number symbol Number, the virtual emission source that this image source is is 2h+2d with described Tz distance；ε_bDielectric for this logger place medium is normal Number；H is this logger arranged in the multiple mirror image forward model distance at a distance of stratigraphic boundary, M_zFor the magnetic moment of Tz, L is that Rz arrives The distance of Tz.

The embodiment of the present invention based on have associating coil antenna structure with bore azimuthal resistivity logger, propose one Fast inversion is with boring the instrument system at a distance of stratigraphic boundary vertical dimension at a distance.This system utilizes complex image theory, will distally The ELECTROMAGNETIC REFLECTION equivalence on layer border becomes the direct scattering in homogeneous space of the multiple mirror image of emission source, thus will one-dimensionally Layer model is reduced to homogeneous space model, drastically increases calculating speed.

Fig. 4 show the structural representation of associating coil.Rx1 and Rx2 represents two lines orthogonal with transmitting coil respectively Circle.Rz represents the coil parallel with transmitting coil.Three coils same single line coiling, the voltage responses therefore combining coil are Three coil voltage response sums.

V_total=V_Rz+V_Rxcos(φ) (1)

V_Rx=V_Rx1+V_Rx2 (2)

Wherein, V_totalRepresent the response of associating coil total voltage, V_RzRepresent the voltage response of Rz coil, V_RxRepresent cross line The voltage response sum of circle；φ is the azimuth of flash tool-face.

Instrument, in drilling process, in order to detect the orientation of stratigraphic boundary at a distance, needs instrument rotating 360 degrees.At instrument In device rotary course, orthogonal antenna R_x1And R_x2Response, along with instrument rotation angles degree is varies with cosine, parallel antenna R_zResponse Constant.

Fig. 5 show associating coil typical response curve chart when near stratigraphic boundary.This curve rotates with instrument to be pressed The component of varies with cosine is the V in formula (1)_RxComponent, the meansigma methods of curve is the V of formula (1)_RzComponent.The extreme value pair of curve The orientation answered contains the azimuth information of stratigraphic boundary, the amplitude of variation of curve reflect with bore instrument at a distance of stratigraphic boundary away from From.The meansigma methods of curve contains instrument location layer resistivity information (similar conventional propagation resistivity measurement).Therefore have This associating coil antenna structure both there is formation azimuth detectivity with boring azimuthal resistivity logger, have again with conventional The ability of the Formation Resistivity Measurement that propagation resistivity logger is similar.

In view of the response curve estimation from the associating coil antenna shown in Fig. 5 with the distance boring instrument stratigraphic boundary apart Belong to the category of inverting.The core of inversion algorithm is by continuous iteration forward model, finds with actual measurement data at optimum The forward model parameter combination of coupling in meaning.Therefore, the arithmetic speed of forward model is the heaviest of decision inversion algorithm speed Want factor.Owing to boring azimuthal resistivity logger when detecting frontier distance, corresponding is one-dimensional multi-layered earth model.This Inventive embodiments utilizes complex image theory, is homogeneous space model by one-dimensional multi-layered earth model conversation, is just accelerating greatly Drill the calculating speed of model, such that it is able to meet real time inversion with boring the instrument distance at a distance of stratigraphic boundary.

Complex image theory is that the electromagnetic wave that transmitting antenna reflects in stratigraphic boundary is equivalent to a virtual image source all The electromagnetic wave that even space produces.The schematic diagram of complex image theory as shown in Figure 6, wherein, dotted line represents the fictitious line after translation Boundary；A horizontal magnetic dipole Tz can be equivalent to the transmitting antenna boring azimuthal resistivity logger, combine coil conduct Reception antenna can be equivalent to a horizontal magnetic dipole Rz and the combination of vertical magnetic dipole Rx.Stratigraphic boundary is at a distance of sending out The distance penetrating antenna Tz is h, according to complex image theory, launches the antenna reflection in stratigraphic boundary and can be equivalent to image source Tz ' At the ground wave that homogeneous space produces.Its image source Tz ' is 2h+2d at a distance of the distance of real source Tz, is equivalent to true stratum Border is shifted distance d, and wherein d is a plural number, and expression formula is:

$d=\frac{\sqrt{k_b^2-k_n^2}}{-k_n^2}$

Wherein:

$k_b^2={\mathrm{\ω}}^2{\mathrm{\μ\ϵ}}_b-{\mathrm{j\ω\μ\σ}}_b,k_n^2={\mathrm{\ω}}^2{\mathrm{\μ\ϵ}}_n-{\mathrm{j\ω\μ\σ}}_n,$ It is respectively stratum, instrument place and at a distance stratum Wave number.

The magnetic field that image source Tz ' produces at associating coil Rx and Rz quickly can be obtained by the analytic expression of homogeneous space

$H_{Rr}=\frac{M_z}{4\mathrm{\π}}\frac{e^{-{\mathrm{jk}}_{b}r}}{r^3}(k_b^2{r}^2-3{\mathrm{jk}}_{b}r-3)\frac{(2d+2h)L}{r^2}$

$H_{Rz}=\frac{M_z}{4\mathrm{\π}}\[\frac{e^{-{\mathrm{jk}}_{b}r}}{r^3}(k_b^2{r}^2-3{\mathrm{jk}}_{b}r-3){\left(\frac{2d+2h}{r}\right)}^2+\frac{2e^{-{\mathrm{jk}}_{b}r}}{r}({\mathrm{jk}}_{b}r+1)\]+\frac{M_z}{4\mathrm{\π}}\frac{e^{-{\mathrm{jk}}_{b}r}}{r^3}({\mathrm{jk}}_{b}L+1)$

In above-mentioned formula, r is the distance that image source arrives associating coil.M_zFor actual transmission sky The magnetic moment of line, L is the receiving coil distance to transmitting coil, and the physical significance that remaining parameter is specified is same as above, here step Repeat.

In order to verify the accuracy of complex image theory, three shown in the present embodiment Fig. 7 layer earth formation carrys out the multiple mirror of comparison Difference schematic diagram between image space method and completely solution method.Owing to being mainly manifested in water with the distance boring instrument stratigraphic boundary apart The voltage response amplitude of variation of plane antenna Rx, the most only compares Tz and launches, the situation that Rx receives.Consider three layers of stratum conductance Rate is respectively the situation of 1S/m, 0.01S/m and 1S/m.Now corresponding intermediate layer is high resistant oil reservoir, upper and lower two-layer correspondence low-resistance mud Rock or water-bearing layer.Instrument is parallel to bed boundary and translates gradually downward, through two borders.Fig. 8 show the multiple mirror image of application The magnetic field real part of method and completely the Rx coil position that solution method respectively obtains and imaginary part schematic diagram.Band circle solid line is for answering Result of calculation with multiple mirror image fast method.Dotted line is the result of calculation that application solves method completely.Two kinds of methods as shown in Figure 8 Result of calculation is closely.

Fig. 9 show the result of calculation of the multiple mirror method of application and the relative error applying the result of calculation solving method completely Schematic diagram, the result of calculation of the multiple mirror method of application when connector for logging while drilling is respectively at a distance of 1 foot and 2 feet, stratigraphic boundary, Under bed boundary up and down layer resistivity difference different situations, relative relative to the result of calculation that application solves method completely is missed Difference.It can be seen that the resistivity contrasts on upper and lower stratum, stratigraphic boundary is the biggest, the multiple mirror method of application and application solve method completely Difference is the least.When connector for logging while drilling place beyond 2 feet, stratigraphic boundary, the differential resistivity on upper and lower stratum, stratigraphic boundary Different when 100 times, relative error is less than 10%.

Table 1 show the multiple mirror image fast algorithm of application and application solves method completely in different forward model iterations time institute With the contrast of CPU time.Test model is three layers of stratigraphic model shown in Fig. 7, and tranmitting frequency is 2MHz, launches and reception antenna Distance is 19 inches.It can be seen that forward model iterations is the most, the advantage of multiple mirror image fast algorithm is the most obvious.When just drilling Model iterations is more than 1000 times, and when iteration comprises 600 measuring point each time, the arithmetic speed of multiple mirror method is to solve completely 160 times of method, the time used is only 5.37 seconds, therefore can in geosteering is applied real time inversion with boring instrument at a distance of ground The distance on layer border.

Table 1

Based on above-mentioned multiple mirror image quick calculation method, for having surveying with brill azimuthal resistivity of associating coil antenna structure Amount instrument, the algorithm of inverting stratigraphic boundary distance can be summarized as flow chart shown in Figure 10 real-time, comprises the following steps:

Step S102, according to previously obtained by Rz coil signal calculated propagation resistivity data, select country rock The initial value of formation resistivity.

Step S104, selects currently to be calculated the propagation resistivity electricity as stratum, instrument place of acquisition by Rz coil signal Resistance rate initial value.

Step S106, utilizes the multiple quick forward modeling method of mirror image, and computing equipment is (example when the different distance of stratigraphic boundary As ,-6 meters to 6 meter scopes), Rx coil and the response of Rz coil in associating coil.

Step S108, compares whether actual measured results mates with forward model result of calculation, if it does, perform step S110；When actual measured results all cannot be mated in whole distance range with forward model result of calculation, return step S102, adjusts country rock and the resistivity on stratum, instrument place, reenters step S106, until finding and actual measured results phase The forward model result of calculation of coupling.

Step S110, using parameter (i.e. distance) corresponding for forward model as instrument at a distance of the distance of stratigraphic boundary.

Above example utilizes complex image theory, and the reflection of electromagnetic wave equivalence of stratigraphic boundary, distant place is become the one of emission source Individual multiple mirror image scattering in homogeneous space, thus one-dimensional forward model is reduced to homogeneous space model, drastically increase Calculate speed.By fast inversion algorithm based on complex image theory is electric with boring orientation with have associating coil antenna structure Resistance rate logger combines, and can meet in geosteering is applied, and real-time estimation stratigraphic boundary at a distance is at a distance of with boring instrument Vertical dimension.

Obviously, those skilled in the art should be understood that each module of the above-mentioned present invention or each step can be with general Calculating device realize, they can concentrate on single calculating device, or be distributed in multiple calculating device and formed Network on, alternatively, they can with calculate the executable program code of device realize, it is thus possible to by they store Performed by calculating device in the storage device, or they are fabricated to respectively each integrated circuit modules, or by them In multiple modules or step be fabricated to single integrated circuit module and realize.So, the present invention be not restricted to any specifically Hardware and software combines.

The foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, for the skill of this area For art personnel, the present invention can have various modifications and variations.All within the spirit and principles in the present invention, that is made any repaiies Change, equivalent, improvement etc., should be included within the scope of the present invention.

Claims (2)

1. one kind obtains with boring the azimuthal resistivity logger system away from stratigraphic boundary distance, it is characterised in that described well logging Instrument is associating coil antenna structure, including horizontal emission antenna Tz, horizontal reception antenna Rz and vertical reception antenna Rx；Described System includes:

First initial value adjusting module, adjusts for the calculated propagation resistivity of signal according to Rz previous receipt and works as front wall The initial value of rock formation resistivity；

Second initial value adjusting module, adjusts described logging instrument for the propagation resistivity calculated according to the currently received signal of Rz The initial value of device location layer resistivity；

Response value computing module, is used for the initial of the country rock formation resistivity after adjusting according to described first initial value adjusting module The initial value of the logger location layer resistivity after value and described second initial value adjusting module adjustment, is just utilizing multiple mirror image Drill model and calculate the response value of described logger Rx and Rz corresponding when at a distance of stratigraphic boundary different distance；

Matching judgment module, the Rx of response value with actual measurement for judging Rx and Rz that described response value computing module calculates Whether mate with the response value of Rz；

Processing module, if the judged result for described matching judgment module is coupling, by the sound of Rx and Rz of described calculating Corresponding distance in described multiple mirror image forward model should be worth and be defined as the described logger distance at a distance of stratigraphic boundary；If The judged result of matching judgment module, for not mate, triggers described first initial value adjusting module and the second initial value adjusting module Readjust initial value and the initial value of described logger location layer resistivity of described country rock formation resistivity, make described System continues the distance obtaining described logger at a distance of stratigraphic boundary.

System the most according to claim 1, it is characterised in that described response value computing module includes:

Magnetic field calculation unit, for calculating the magnetic of described logger Rx and Rz corresponding when at a distance of stratigraphic boundary different distance Field is respectively as follows:

$H_{Rx}=\frac{M_z}{4\mathrm{\π}}\frac{e^{-{\mathrm{jk}}_{b}r}}{r^3}(k_b^2{r}^2-3{\mathrm{jk}}_{b}r-3)\frac{(2d+2h)L}{r^2}$

$H_{Rz}=\frac{M_z}{4\mathrm{\π}}\[\frac{e^{-{\mathrm{jk}}_{b}r}}{r^3}(k_b^2{r}^2-3{\mathrm{jk}}_{b}r-3){\left(\frac{2d+2h}{r}\right)}^2+\frac{2e^{-{\mathrm{jk}}_{b}r}}{r^3}({\mathrm{jk}}_{b}r+1)\]+\frac{M_z}{4\mathrm{\π}}\frac{e^{-{\mathrm{jk}}_{b}r}}{r^3}({\mathrm{jk}}_{b}L+1)$

In above-mentioned formula,D is complex displacement,Wherein,It is respectively described stratum, logger place and outside boundaries Wave number, ω is the emission current angular frequency of the Tz of described logger；μ is the pcrmeability of medium, ε_nFor image source place medium Dielectric constant, σ_b、σ_nIt is respectively described stratum, logger place and the electrical conductivity on outside boundaries stratum, namely instrument institute At the inverse of initial value of formation resistivity and the inverse of the initial value of country rock formation resistivity；J is imaginary symbols, described mirror image The virtual emission source that source is is 2h+2d with described Tz distance；ε_bDielectric constant for described logger place medium；H is multiple The described logger arranged in mirror image forward model is at a distance of the distance of stratigraphic boundary, M_zFor the magnetic moment of Tz, L be Rz to Tz away from From.