CN102426359A - Oil field radar logging imaging method - Google Patents

Abstract

The invention relates to an oil field radar logging imaging method. The method aims at processing and imaging logging data detected by an oil field logging radar at a vertical direction. The method mainly comprises the following steps: collecting the data at the vertical direction of the radar; performing wave number domain transformation; matching filtering; performing an interpolation operation; performing distance domain transformation; detecting a wave field value in an area; imaging a scattered wave field. By using the imaging method, target signals at the vertical direction of an oil well can focus on a correct position, which is convenient for data analysis and interpretation. A signal-to-clutter ratio of the detection signals can be increased. And target detection resolution and detection precision can be improved.

Description

A kind of oil field radar well logging formation method

Technical field

The present invention relates to a kind of oil field radar well logging formation method, belong to technical field of imaging.

Background technology

At present, in the radar of single hole well logging both at home and abroad, mainly concentrate on the measurement and positioning technology of research, mainly contain two kinds of methods perpendicular to the target of wellhole direction:

First kind is, through MUSIC constant power spectrum method of estimation, target is measured and is located, and this method can not generate radar image.Second kind is, multiple receive antenna data fusion formation method, and imaging technique is just carrying out the data fusion imaging perpendicular to the wellhole direction, does not handle but do focusing at vertical direction.

Do not see the report of the focal imaging technology of research vertical direction as yet.Vertical direction is not done and focus on to be handled, and causes that signal to noise ratio is low, echo signal fuzzy, malposition, resolution and the detection accuracy of target image are low.

Summary of the invention

In order to overcome problems such as the technological above-mentioned signal to noise ratio of existing single-hole imaging is low, echo signal fuzzy, malposition, resolution and the detection accuracy of target image are low; The present invention provides a kind of single hole well logging radar vertical direction to carry out method for imaging, and this method can effectively improve the signal to noise ratio of well logging radar detection.

For realizing above-mentioned purpose, the present invention provides a kind of oil field radar well logging formation method, may further comprise the steps:

(1) is put into the emitting antenna and the receiving antenna of well logging radar in the wellhole;

Received data when (2) gathering the well logging radar and on the vertical direction of wellhole, move;

(3) arrive wavenumber domain to the data conversion that is collected;

(4) at frequency-wavenumber domain the well logging radar data is carried out matched filtering;

(5) carry out interpolation arithmetic at frequency-wavenumber domain;

(6) transform to distance domain to resulting data from the wave beam territory;

(7) wave field value of search coverage and forming images.

Described step (3) is to accomplish through the data of search coverage being carried out two-dimension fourier transform, and data are earlier from b (x _M, r=r _M, (x, r=0 ω), arrive b (x, r=0, k again t=0) to transform to b _ω), transform to B (k at last _x, r=0, k _ω); Described step (4) is accomplished through data being carried out convolution algorithm; Used interpolation method can select geometric interpolation, linear interpolation method, linearity to add in cork method of interpolation and the Sinc method of interpolation any one in the described step (5); Described step (6) is to accomplish through the data of wavenumber domain are carried out two dimensional inverse fourier transform.

The invention has the beneficial effects as follows; Carrying out focal imaging through the detection data to well logging radar in the vertical direction handles; Can in the vertical direction improve the signal to noise ratio of well logging radar detection image, make target more clear, and echo signal is focused on the actual position of target; Improve detection accuracy and resolution, help the analysis and the explanation of data.

Description of drawings

Fig. 1 is a single hole well logging radar arrangement synoptic diagram;

Fig. 2 is a single hole well logging radar detection synoptic diagram;

Fig. 3 is a single hole well logging radar focal imaging process flow diagram flow chart;

Fig. 4 is an interpolation mapping synoptic diagram.

Embodiment

Below in conjunction with accompanying drawing embodiment of the present invention is further specified.

Fig. 1 is a single hole well logging radar arrangement synoptic diagram, and among the present invention, the dual-mode antenna of single hole well logging radar all is in the same wellhole, and emitting antenna or receiving antenna can be respectively single antenna, also can be array antennas.Fig. 2 is the detection synoptic diagram of radar, and in detection process, radar can vertically move, also can be along rotating perpendicular to the wellhole direction, perhaps move image data in motion process along this both direction simultaneously.Among the present invention, the data of only radar being gathered when vertical direction moves are carried out focal imaging, and the process of this focal imaging is as shown in Figure 3.

At first set up the two-dimentional rectangular coordinate system shown in Fig. 2 the right, this coordinate system is the x axle with the vertical direction, is the r axle with the direction perpendicular to wellhole.If the position coordinates of well logging radar antenna be (x, 0), one group of data of establishing the vertical direction of the radar record of logging well be b (x, r=0, t), the data behind Fourier transform on the t axle be b (x, r=0, ω).Be located at the scattering point that has any some M around the wellhole in the search coverage, the coordinate of this scattering point is (x _M, r), the scattered wave field at this scattering point place is b (x _M, r=r _M, t=0).

At first, we do following processing to the data at M point place:

$b(x_M,r=r_M,t=0)=\underset{X}{\∫}\frac{r^3}{R^3}b(x,r=0,t=\frac{R}{v_1})\mathrm{dx}---\left(1\right)$

R=r wherein _M, R is the distance of a M to the well logging radar:

X represent the to log well focus data of radar, v ₁Be the half the of the aerial velocity of wave of radar wave.Following formula can be rewritten into:

$b(x_M,r=r_M,t=0)=\underset{X,W}{\∫\∫}\frac{r^3}{R^3}b(x,r=0,w)\exp \left(\mathrm{j\ω}\frac{R}{v_1}\right)\mathrm{dxd\ω}---\left(2\right)$

If k _wBe wave number: k _w=ω/v ₁, following formula can be write as following form:

$b(x_M,r=r_M,t=0)=\underset{k_{\mathrm{\ω}},X}{\∫\∫}b(x,r=0,k_{\mathrm{\ω}})\frac{r^3{v}_1}{{\left(\sqrt{{(x_M-x)}^2+r^2}\right)}^3}\exp \left(j{k}_{\mathrm{\ω}}\sqrt{{(x_M-x)}^2+r^2}\right)\mathrm{dxd}{k}_{\mathrm{\ω}}---\left(3\right)$

(3) be the form of a convolution, this convolution can be calculated through the product of Fourier transform.As long as therefore know the Fourier transform of second factor in this convolution, just can calculate this convolution.(3) Fourier transform of second of convolution factor is in the formula:

$E\left(k_{\mathrm{\ω}}\right)=\∫\frac{r^3{v}_1}{{\left(\sqrt{x^2+r^2}\right)}^3}\exp \left({\mathrm{jk}}_{\mathrm{\ω}}\sqrt{x^2+r^2}\right)\exp (-j{k}_{\mathrm{\ω}}x)\mathrm{dx}---\left(4\right)$

Integration type (4) has following form: when α → ∞, this integration can be with approximate the finding the solution of method in the phase:

$I\left(\mathrm{\α}\right)\≈\sqrt{\frac{2\mathrm{\π}}{\mathrm{\α}\left|h^{\′\′}\left(x_0\right)\right|}}f\left(x_0\right)\mathrm{Exp}\left[\mathrm{J\α}(h\left(x_0\right)+\mathrm{Sign}(h^{\′\′}\left(x_0\right)\frac{\mathrm{\π}}{4}\right],$ X wherein ₀Be point, that is: the h ' (x mutually of staying of h (x) ₀)=0.In formula (4), have: α=k _x, $h\left(x\right)=\frac{k_{\mathrm{\ω}}}{k_x}\sqrt{x^2+r^2}-x,$ $f\left(x\right)=\frac{r^3{v}_1}{{\left(\sqrt{x^2+r^2}\right)}^3}$ $x_0=\frac{r\·k_x}{\sqrt{k_{\mathrm{\ω}}^2-k_x^2}},$ So: $I\left(\mathrm{\α}\right)\≈\sqrt{\frac{2\mathrm{\π}{k}_{\mathrm{\ω}}}{k_{\mathrm{\ω}}^2-k_x^2}}\·\mathrm{Exp}\left(\mathrm{Jr}\sqrt{k_{\mathrm{\ω}}^2-k_x^2}\right).$ If $k_r=\sqrt{k_{\mathrm{\ω}}^2-k_x^2},$ Then:

$I\left(\mathrm{\α}\right)=E\left(k_{\mathrm{\ω}}\right)\≈v_1\sqrt{2\mathrm{\π}{k}_{\mathrm{\ω}}}\frac{k_r^2}{k_{\mathrm{\ω}}^3}\·\exp \left(\mathrm{jr}{k}_r\right)---\left(5\right)$

The inverse transformation of being write the convolution in (3) formula as the Fourier product, and with (5) formula substitution:

$b(x_M,r=r_M,t=0)\≈\underset{K}{\∫\∫}B(k_x,r=0,k_{\mathrm{\ω}})\·v_1\sqrt{2\mathrm{\π}{k}_{\mathrm{\ω}}}\frac{k_r^2}{k_{\mathrm{\ω}}^3}\exp ({\mathrm{jrk}}_r+{\mathrm{jk}}_{x}x){\mathrm{dk}}_x{\mathrm{dk}}_{\mathrm{\ω}}---\left(6\right)$

Here B (k _x, r=0, k _w) be b (x, r=0, k _w) one dimensional fourier transform on the x axle.With the variable dk in the following formula _ωUse dk _rInterpolation is carried out in replacement simultaneously, obtains:

$b(x_M,r=r_M,t=0)\≈\underset{K}{\∫\∫}B(k_x,r=0,k_r)v_1\sqrt{2\mathrm{\π}{k}_{\mathrm{\ω}}}\frac{k_r^3}{k_{\mathrm{\ω}}^4}\exp ({\mathrm{jrk}}_r+{\mathrm{jk}}_{x}x){\mathrm{dk}}_x{\mathrm{dk}}_r---\left(7\right)$

Following formula shows, the data that the well logging radar receives are carried out convolution algorithm, and the data behind the convolution algorithm are carried out interpolation, and after the interpolation, carrying out two dimensional inverse fourier transform can be to realizing the (x more arbitrarily in the search coverage around the single hole well logging radar _M, r) carry out focal imaging.Wherein Δ t be the well logging radar equivalent time sampling at interval, (7) formula is exactly the resulting result of focal imaging method of the single hole well logging radar that proposes among the present invention.

According to (6) formula, be r=r apart from the radar motion aperture _MThe wave field of the frequency-wavenumber domain at place is:

$B(k_x,r=r_M,k_{\mathrm{\ω}})=v_1\sqrt{2\mathrm{\π}{k}_{\mathrm{\ω}}}\frac{k_r^2}{k_{\mathrm{\ω}}^3}B(k_x,r=0,k_{\mathrm{\ω}})\exp \left({\mathrm{jr}}_M{k}_r\right)---\left(8\right)$

Here, the interpolation method of using is as shown in Figure 4, and interpolation is exactly will

From

Spatial alternation is to (k _x, k _z) space.Fig. 4 is

The territory is to (k _x, k _z) the mapping relations synoptic diagram in territory.

The interpolation arithmetic here, can adopt following interpolation formula:

How much interpolation formulas are:

lnU′ _n+δn＝(1-δn)lnU _n+δnlnU _n+1 (9)

The linear interpolation formula is:

U′ _n+δn＝(1-δn)U _n+δnU _n+1 (10)

Linearity adds the cork interpolation formula:

U′ _n+δn＝exp(-iπδn)[(1-δ _n)U _n+δnU _n+1] (11)

The Sinc interpolation formula is:

U′ _n+δn＝sinc(δn)exp(-iπδn)[(1-δn)U _n]+δnU _n+1 (12)

Claims (5)

1. oil field radar well logging method for imaging, it is characterized in that: described method step is following:

(1) is put into the emitting antenna and the receiving antenna of well logging radar in the wellhole;

Received data when (2) gathering the well logging radar and on the vertical direction of wellhole, move;

(3) arrive wavenumber domain to the data conversion that is collected;

(4) at frequency-wavenumber domain the well logging radar data is carried out matched filtering;

(5) carry out interpolation arithmetic at frequency-wavenumber domain;

(6) transform to distance domain to resulting data from wavenumber domain;

(7) wave field value of search coverage and forming images.

2. oil field according to claim 1 radar well logging formation method is characterized in that: described step (3) is to accomplish through the data of search coverage being carried out two-dimension fourier transform, data earlier from B (x _M , r=r _M , t=0)Transform to B (x, r=0, ω), arrive again B (x, r=0, k _ω ), transform at last B (k _x , r=0, k _ω )

3. radar well logging formation method in oil field according to claim 1 is characterized in that: described step (4) is accomplished through data being carried out convolution algorithm.

4. oil field according to claim 1 radar well logging formation method is characterized in that: used interpolation method can select geometric interpolation, linear interpolation method, linearity to add in cork method of interpolation and the Sinc method of interpolation any one in the described step (5).

5. oil field according to claim 1 radar well logging formation method, it is characterized in that: described step (6) is to accomplish through the data of wavenumber domain are carried out two dimensional inverse fourier transform.

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