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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 enables ...

2 Induced Polarization Methods in Geophysics

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Induced Polarization (IP) applies the same basic operation and array configuration as resistivity method that If you apply the current into the ground via current electrodes , the voltage can be measured at potential electrodes which are non - polarizable in IP method. The Earth accumulates the charges of applied current at some time, but when the applied current is switched off, the overvoltage will tend to decay slightly (slowly) from its peak value to zero after a certain time interval. This is the capacitive property of the Earth's ground. You can measure the IP effect by using either chargeability or apparent resistivity. Let's see through this post how these two (2) measurements can be deployed to describe IP effect. ip measurement methods What are the two (2) commonly applied methods in IP measurements? Here below are two (2) common IP measurement methods,  i/ Time domain (pulse transient) ii/ Frequency domain 1: time domain ip measurement It measures overvoltage as a f...

Concept of Gravity Anomaly

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Concept of Gravity Anomaly  Gravity anomaly can be defined as the differences  between the corrected measured gravity and the theoretical (normal) gravity. In most cases gravity anomaly reading is given in milliGal (mGal). As the definition above describes, there are two terms you must understand related to the gravity anomaly such that normal gravity and the observed gravity . Then these terms are described here below in order to get basic insight on this topic. - Normal (theoretical) gravity This is the value of gravity computed without any geological complication. It is computed by the normal gravity formula of the Geodetic reference system. - Observed gravity This is the gravity reading observed at each gravity station after correction have been made for drift and tides. Factors affecting gravity anomaly - Dimensions When we are talking about the dimension of a body we simply mean the size. As the size of the body increases, the probability of producing great gravity att...

2 Types of Seismic waves in Geophysics

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When the shaking of the Earth's ground (known as earthquake) occurs at several times, then it is due to release and movement of energetic waves called seismic waves. Without ruining time,. I don't want to dig deeper on this topic, but just give you the basics regarding these waves. Stay alerted! Seismology is the study of seismic waves and Earthquakes. This may include the study of vibration, propagation, types and application of these seismic waves through the Earth. The term seismology originated from two Greek words " Seismos " means Earthquake and " Logos " means study of. The study of these waves is important as it gives clues regarding, ➔ It used to study the structure and nature of Earth's interior. ➔ It is used in seismic exploration geophysics. Note: The main source of seismic waves in nature is produced from Earthquakes. However there are man made sources of seismic waves such as dynamites, Vibrators forexample vibroseis. Although due to heter...

Plate Tectonic theory for Earth's dynamics

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Some phenomena like Earthquakes and volcanic eruptions gives us important facts for understanding Earth's dynamics. The Earth have passed through various geological processes over time that shapes amaizing features you can observe out there such as mountains, oceanic basins, just to mention a few. Although these processes have to interact effectively in a way that can be explained through Plate tectonic theory. PLATE TECTONIC MODEL This involves the formation of new lithosphere at the ridge and its destruction at a subduction zones. The theory explained how the Earth is active (dynamic). It proposed by 1960's . Most of geologists accept plate tectonic theory because it ties together many unrelated geologic features and natural phenomena. Also it is through plate boundaries where some phenomenon such as Mountain building, Earthquake , Volcanic eruptions occurs. There are major seven (7) Tectonic plates known, Africa , North America , South America , Pacific , Eurasian , Antarcti...