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Concept of Hilbert transform explained

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It is obvious that in the field of mathematics the term Hilbert transform can be defined as a transform that takes a function of a real variable and produces another function of a real variable.  Concept of Hilbert transform The fast and easily way to grasp the concept regarding this transform is that, let's say we have the signal constructed by a cosine function, then we can extract the waveform of the sine function from our cosine function, simply create a sine wave out of cosine wave through the Hilbert transform. The Hilbert transform is important in signal processing , at which the analytic representation of a real-valued signal, say x(t) , is produced.  The Hilbert transform was first introduced by David Hilbert in 1905 for the purpose that a special case of the Riemann–Hilbert problem for analytic functions can be solved. The analytic signal produced by the Hilbert transform is useful in many signal analysis applications, while implementing the Hilbert transform enabl...

3 Types of Seismic Reflection Surveys in geophysics

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Seismic data acquisition is the systematic process at which the modified seismic waves from seismic reflectors are recorded by various seismic receivers such as geophones or hydrophones . That is simple to define, however to know the way through which this process occurs is very important as this will give you an idea  when dealing with seismic interpretation tasks. And this is why I have written this piece of article to help you to have an idea on how seismic surveys can be carried out. There are two common techniques at which field seismic data acquisition can be conducted, these are 2-D and 3-D techniques. Due to advancing in technology there is another term known as 4D - seismic technique especially in oil and gas industry , However deciding which one you can deploy will depend on various factors such as geophysical seismic objectives, budget, size of survey area, nature of geological terrain being surveyed. Let's start to describe these terms in more convenient man...

Self-potential (SP) method in geophysics

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Self potential (SP) method is the one of passive form amongst electrical geophysical techniques. This is because self-potential signals originate naturally in the ground. This means that the SP signals are recorded with no need of applying electrical signals into the subsurface. The self- potential is generated itself within the Earth's ground due to various electrochemical processes such as electrical filtration , diffusion , adsorption and others as I will describe later in details. However the technique is based on a simple model where the generated natural ground potential difference (P.d) is measured in millivolts (mV) between two (2) points. Origin  (mechanism) of self - potential  1. Electrokinetic (Ek) potential Flowing of fluid (electrolyte) through a capillary or porous medium generates potentials along the flow path. The potentials are alternatively called electrofiltration , electromechanical or streaming potentials . The effect is believed to be due to electro...

Convolution in geophysics

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Convolution is one among operations that is utilized in geophysical signal processing . However the term seems to not be clearly understood among us due to its formal similarity with other functions such as cross - correlation . Let's try to discuss in a simplified way through this post, how this term is really about in digital signal processing .  First of all, It would be a good approach in order to understand this term, we have to focus on a system that can feed (input) a certain variable and then produce the result as output variable. In digital signal processing, a linear system can change the signal feed into it and then give out another signal as output. The input signal can be decomposed into a set of impulses , each of which can be viewed as a scaled and shifted delta function , while the output signal resulting from each impulse is a scaled and shifted version of the impulse response . Then you see the overall output signal can be found by adding these scaled and shifte...