Pinhole exploration of a buried high　pressure　fluid-fill curved pipe.

Introduction

Previously, a pinhole exploration of a straight long pipe was made by using a linear sensor array mounted inside the pipe^1）,2）. In the beam-forming process, the incident acoustic wave from the pipe-axis was found to estimate well the pinhole position. In this case, noise from the soil covering the pipe is of course received, but major acoustic wave propagates through the fluid of pipe where acoustic impedance at both positions of pinhole and array are equal.

How about the case of the curved pipe where acoustic impedance of fluid and soil are nearly equal?  In this research, pinhole exploration inside a curved pipe will be examined by simulation. Here, some assumptions were made in the simulation as follows. 1)acoustic impedance of the soil which cover the pipe is nearly equal to the fluid inside it, but other elastic wave of the soil are considered strictly. This case is regarded as "saturated soil". 2) Apart from the case of straight pipe, acoustic wave field of curved pipe can never be obtained strictly. Because an analytical wave function which corresponds to the curved coordinate system is not existed.

So here, an analytical approximation method named as "Multiple Multipole Expansions" (MME) will be applied^3）. By the way, previously "Multiple Multipole Expansions" were applied to the simulation of cavity exploration in the quasi-homogeneous ground^４）. In that case, in three dimensions, wave field of reflection from the cavity was calculated so correctly, that the received data of the crossed sensor array on the ground was found to estimate the cavity position and approximate shape well.

Simulations by using MME

The configuration of a curved pipe where both pinhole and sensor array are mounted is shown in Fig.1.

 In this figure, multiple　multipole　sources　and reference points　determining　boundary　condition are also shown.　Multipoles' positions　 are spaced　with an　wave length　interval　 along the pipe axis.　Reference point  j and k are  selected  six　points  on  a  circle  line which　is　perpendicular　to the  pipe axis  as  shown　in the figure. Then this circle is equally　placed along the pipe axis.　The number of circle line were adequately　selected to　each region1, 2, and 3　respectively, 　because 　infinite 　number can　never be selected.

Z

 

The frequency point fi used for image reconstruction were selected as fmax×0.99^ｊ−１，where fmax is upper frequency and j=1,2,..,J,　but J implies the number of total sampling points. The pipe is　constitutedof steel whose inside is filled with water and outside is covered with infinite soil. Inside radius of the 　pipe　is 0.4m and thickness is 7mm. Simulation parameters are shown in  Table.1.

In Figure.2, the pinhole image was reconstructed.　Here fmax is 3000Hz, the total frequency points J is 55,and number of sensor of the array is 14. The image was shown in the following area of "-6m≦Ｘ≦10m　and -8m≦Ｚ≦8m". Eight grades' marks were assigned to show image intensity. Zero intensity was indicated as white color ,and the highest intensity was indicated as black color. The resolution of pixel is 20cm.　If the exact image is obtained, the most dark point appears at XZ origin in which the actual pinhole is located.　The cross-section of the curved pipe was shown as a dashed line, and sensor position of the array were indicated as small circle.

From this result, most dark point appears nearly at the origin where pinhole is located. On the other hand, similar dark point also appears at (x,z)=(0, 5.5)[m]. This reason is that beam-forming directivity of the line array has conical shape around the array axis. In general, virtual dark point like this is discarded by mounting another line array.　Because, same dark point each array indicates determines exact point.　However, this time, increasing both bandwidth and frequency points enables pinhole reconstruction correct. Apart from propagation only through the fluid in the straight pipe, elastic wave induced in the soil might affect to　the acoustic wave received by the sensor array , but favorable result was obtained to estimate pinhole position well.

Conclusions

Pinhole exploration inside a curved pipe was examined by simulation. Acoustic impedance of the soil which covers the pipe was assumed nearly equal to the fluid inside it, but other elastic wave of the soil was considered strictly. This case is regarded as "saturated soil". From the results, the received data of the sensor array through the soil outside the pipe was found to estimate pinhole position well.

References

1）Topics5, "Pinhole exploration of a buried high pressure fluid-fill pipe, 1 st study", '01.9.22

2) Topics６, "Pinhole exploration of a buried high pressure fluid-fill pipe, 2nd study", '01.12.27

3）M.G.Imhof, " Multiple　multipole  expansions for acoustic scattering," J.Acoust.Soc.Am97(2),p754-763(1995)

4)Topics17, "Development of a buried object explorationsystem by crossed sensor array",'04.4.29