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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...

Seismic Reflection Imaging

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There is no doubt that most of us know that seismic imaging techniques opened a new way for geoscientists to see the unseen part below the earth. And the method applied back for over 75 years especially in the oil industry, and is still giving the promised results. And with the recent advancement of technology the technique still innovates to give more depth of investigation and detailed images through techniques such as seismic tomography . However we have to be specific that this post is tailored to reflection tomography that applies artificial controlled active sources of seismic energy.  The basic concept of seismic reflection imaging seemed to be simple to grasp, such as sending seismic waves into the subsurface, then recording them on the surface using various seismic receivers after they bounced and modified into subsurface reflectors. It is that simple!  But when it come to reality this method is challenging why? ➤ First it is logistically intensive in acquisition...

Seismic Migration in geophysics

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It is obvious that after the Normal Move Out (NMO) correction and stacking, only a zero-offset section is synthesized, and the fact that the offset dependence of the receiver position with respect to the source has been removed. That means, we have a section as if we did a seismic survey with source and receiver at the same place, thus zero-offset. Migration deals with a further removal of wave phenomena via focussing in order to arrive at a section which is a true representation of the subsurface . Migration is the focussing process which results in a true image of the subsurface from primary-reflection data, assuming the velocity model is correct. Migration is the process of reconstructing a seismic section so that reflection events are repositioned under their correct surface location and at a correct vertical reflection travel time. Equivalently, this mean that migration obtains the true image in (x, y, z) from seismic data that are obtained in (x, y, t), where x, y and z sta...

Electrical Borehole geophysics

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There are many different geophysical investigation techniques, However when there is a need in exploring detailed information about the subsurface, we have to drill the hole and make a detailed collection of subsurface data, this is termed Borehole geophysics . This procedure involves the depth wise sequential record of physical parameters such as resistivity , density, temperature. It is sometimes known as Geophysical Logging or Geophysical well logging. There are many different geophysical logging however this post will let you know about electrical logging which is commonly includes the resistivity log and self-potential (SP) log . geologic log vs geophysical log G eological Log: This displays variation of subsurface geology ( lithology/rock types ) with depth. Such as from dry sand (top) to sand (middle) to clay (bottom). Geophysical Log: This displays variation of subsurface physical parameters with depth. The term well log is more general that includes both geological and ge...

Basics of Borehole Geophysics

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Most surface geophysical techniques provide vast information about subsurfaces. However when it comes to trace detailed information about subsurface in a certain cross section- area, it is highly recommended to deploy these techniques in a drilled hole. This is termed as Borehole geophysics .  What is Borehole Geophysics? Borehole geophysics involves the depth wise sequential record of physical parameters such as resistivity, density, temperature, porosity, etc. It may sometimes be known as Geophysical Logging . Borehole : Is the narrow hole drilled into ground for the purpose either of obtaining subsurface information or extracting fluids such as water, gas, oil, contaminants. It is the same as a well, but they may differ due to the fact that the borehole is drilled at great depth and has small diameter compared to traditional wells. The basic geophysical borehole system is made up of these parts,  Downhole probe : It consists of sensing instruments/equipment that are lower...