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8 June, 2018 00:00 00 AM
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Compressive sensing: Oil and gas exploration

CS theory has had a groundbreaking impact and opened a new avenue of research
Mafijul Bhuiyan
Compressive sensing: Oil and gas exploration
Seismic data acquisition

Imagine, you took a picture with your friends in an event and later noticed that the image resolution is meagre and blurred as well. You found lots of missing pixels in that picture, and it is blended with random noises (i.e., salt and pepper noise). Now you would like to obtain the high-quality and sharp image from that low-quality picture. Unfortunately, there is no silver bullet to solve this problem. Using conventional method, to achieve the high-qualityphotograph you need to satisfy the Nyquist sampling theorem which mentions that the perfect recovery or restoration requires at least twice regularly sampled pixels of the maximum frequency of that image. Linear reconstruction of a picture adds artefacts if the Nyquist condition is violated. In this scenario, Compressive Sensing (CS) comes as great assistance. It is a sophisticated mathematical tool plays a vital role to perform perfect reconstruction of an image with very high probability using far less sampling pixels. It removes the random or incoherent noise too. Luckily, CS theory can also be used extensively in other fields too such as astrophysics, geophysics, and engineering.

CS theory was first proposed by Emmanuel Candes, a professor at Stanford University while working with a corrupted version of “Shepp-Logan Phantom” image. Later, he along with Justing Romberg, and Terry Tao published their first paper regarding this theory in 2009. In conventional image acquisition and processing technique, we generally acquire all the pixels (e.g., millions of pixels) of an image using the camera or other devices. However, all these spatial pixels of the image can be represented using only a few elements in another domain (i.e. Fourier or wavelet) which implies most of the pixels in the picture is redundant and can be discarded. In contrast, based on CS theory, we need to acquire a tiny fraction of randomly sampled pixels of an image which requires reduced storage space, acquisition time and energy for data acquisition. This under sampled image is then fully recovered using  -1minimization algorithm. For example, in traditional imaging, one needs to take a million measurements for a high-resolution image. In compressed sensing, however, only a small fraction — say, 10 percent (i.e. 100,000) pixels are randomly measured from various parts of the image. From that starting point, we can effectively recover the remaining 900,000 pixels to be filled in. To achieve perfect recovery in CS; two following constraints need to be satisfied.

1.    Sparsity – the image should be sparse (i.e. few nonzero elements) in another domain (e.g. Fourier, or wavelet).

2.     Sampling or measurements of the image should be randomly distributed.

CS theory already had a groundbreaking scientific impact and opened a new avenue of the research area. That is because the mostnaturalsignal in our surroundings can be represented sparsely in another domain. Sometimes, the image itself is sparse like in astrophysics. Therefore, it became prevalent among scientists and engineers due to its versatile areas of applications such as image acquisition, radar technology, oil and gas exploration, MRI technology etc. In this article, I will not discuss the details mathematics of CS theory instead I would like to focus on some crucial areas where CS has already been applied successfully. I would suggest interested readers go through the reference materials for further details.

Acquisition of seismic data plays a vital role in exploring oil and gas reservoir. Figure 1 depicts seismic data acquisition for land and marine scenarios. Data acquisition is very important and expensive procedure. Almost $2.5bn had been spent in north America in 2016 just for seismic data acquisition. Proper acquisition of seismic data can ensure not only the longevity of the hydrocarbon reservoir but also allow petroleum engineer to make a better estimation of the volume of hydrocarbon beneath earth’s surface. Nevertheless, it is the most expensive and time-consuming part of the hydrocarbon exploration. Using CS technique, we can reduce the number of sources and receivers required for data acquisition. Therefore, the total time and cost of data acquisition will be drastically reduced. CS technique can be applied both inland and marine environment. It will also reduce adverse effects occurred due to data acquisition. Figure2 shows an example of fully recovered seismic data using CS technique.

Natural gas is the primary source of energy in Bangladesh. Currently, Bangladesh is facing, the scarcity of hydrocarbon energy which, makes an adverse impact, on the rapidly growing, industrialization.Recently Bangladesh acquired a vast area in the Bay of Bengal after settling a longstanding maritime boundary dispute with India and Myanmar. Therefore, the government should take necessary steps, to explore for energy sources in onshore and offshore areas. In most cases, the local government might not afford the total cost of the exploration. In this scenario, CS technique which allows low-costhydrocarbon exploration would be a feasible solutionforsurveying oil and gas in these sizeable navaland inland areas.

Likewise, researchers and engineers of other countries, we should also participate actively in doing research and implementation of CS technique, particularly in oil and gas exploration, and telecommunication. We can also research developing MRI scanner using CS technique in Bangladesh to increase the quality of diagnosis and deduct almost 80% cost of imaging. I hope the government and privately-owned companies will focus on these issues.

The author is currently pursuing his doctoral degree in Computational Physics at University of Alberta, Canada

 

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Editor : M. Shamsur Rahman
Published by the Editor on behalf of Independent Publications Limited at Media Printers, 446/H, Tejgaon I/A, Dhaka-1215.
Editorial, News & Commercial Offices : Beximco Media Complex, 149-150 Tejgaon I/A, Dhaka-1208, Bangladesh. GPO Box No. 934, Dhaka-1000.

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