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Anelastic Attenuation Factor
In reflection seismology, the anelastic attenuation factor, often expressed as seismic quality factor or Q (which is inversely proportional to attenuation factor), quantifies the effects of anelastic attenuation on the seismic wavelet caused by fluid movement and grain boundary friction. As a seismic wave propagates through a medium, the elastic energy associated with the wave is gradually absorbed by the medium, eventually ending up as heat energy. This is known as absorption (or anelastic attenuation) and will eventually cause the total disappearance of the seismic wave. Quality factor, ''Q'' ''Q'' is defined as :Q = 2\left ( \frac \right ) It looks like reverse is true - see e.g.J. Geophys. Eng. 10 (2013) 045012 (8pp) doi:10.1088/1742-2132/10/4/045012 Attenuation (1/Q) estimation in reflection seismic records Wasiu Raji1,2 and Andreas Rietbrock2 where \frac is the fraction of energy lost per cycle. The earth preferentially attenuates higher frequencies, resulting in the l ...
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Reflection Seismology
Reflection seismology (or seismic reflection) is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflected seismic waves. The method requires a controlled seismic source of energy, such as dynamite or Tovex blast, a specialized air gun or a seismic vibrator. Reflection seismology is similar to sonar and echolocation. This article is about surface seismic surveys; for vertical seismic profiles, see VSP. History Reflections and refractions of seismic waves at geologic interfaces within the Earth were first observed on recordings of earthquake-generated seismic waves. The basic model of the Earth's deep interior is based on observations of earthquake-generated seismic waves transmitted through the Earth's interior (e.g., Mohorovičić, 1910). The use of human-generated seismic waves to map in detail the geology of the upper few kilometers of the Earth's crust followed shortly thereafter and h ...
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Pore Pressure
Pore water pressure (sometimes abbreviated to pwp) refers to the pressure of groundwater held within a soil or rock, in gaps between particles ( pores). Pore water pressures below the phreatic level of the groundwater are measured with piezometers. The vertical pore water pressure distribution in aquifers can generally be assumed to be close to hydrostatic. In the unsaturated ("vadose") zone, the pore pressure is determined by capillarity and is also referred to as tension, suction, or matric pressure. Pore water pressures under unsaturated conditions are measured with tensiometers, which operate by allowing the pore water to come into equilibrium with a reference pressure indicator through a permeable ceramic cup placed in contact with the soil. Pore water pressure is vital in calculating the stress state in the ground soil mechanics, from Terzaghi's expression for the effective stress of a soil. General principles Pressure develops due to: *''Water elevation differenc ...
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Attenuation
In physics, attenuation (in some contexts, extinction) is the gradual loss of flux intensity through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at variable attenuation rates. Hearing protectors help reduce acoustic flux from flowing into the ears. This phenomenon is called acoustic attenuation and is measured in decibels (dBs). In electrical engineering and telecommunications, attenuation affects the propagation of waves and signals in electrical circuits, in optical fibers, and in air. Electrical attenuators and optical attenuators are commonly manufactured components in this field. Background In many cases, attenuation is an exponential function of the path length through the medium. In optics and in chemical spectroscopy, this is known as the Beer–Lambert law. In engineering, attenuation is usually measured in units of decibels per unit length of medium (dB/cm, dB/km, etc.) and is ...
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Acoustic Attenuation
Acoustic attenuation is a measure of the energy loss of sound propagation in media. Most media have viscosity and are therefore not ideal media. When sound propagates in such media, there is always thermal consumption of energy caused by viscosity. This effect can be quantified through the Stokes's law of sound attenuation. Sound attenuation may also be a result of heat conductivity in the media as has been shown by G. Kirchhoff in 1868. The Stokes-Kirchhoff attenuation formula takes into account both viscosity and thermal conductivity effects. For heterogeneous media, besides media viscosity, acoustic scattering is another main reason for removal of acoustic energy. Acoustic attenuation in a lossy medium plays an important role in many scientific researches and engineering fields, such as medical ultrasonography, vibration and noise reduction. Power-law frequency-dependent acoustic attenuation Many experimental and field measurements show that the acoustic attenuation coeffi ...
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Gradient
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradient of a function is non-zero at a point , the direction of the gradient is the direction in which the function increases most quickly from , and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to maximize a function by gradient ascent. In coordinate-free terms, the gradient of a function f(\bf) may be defined by: :df=\nabla f \cdot d\bf where ''df'' is the total infinitesimal change in ''f'' for an infinitesimal displacement d\bf, and is seen to be maximal when d\bf is in the direction of the gradi ...
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Y-intercept
In analytic geometry, using the common convention that the horizontal axis represents a variable ''x'' and the vertical axis represents a variable ''y'', a ''y''-intercept or vertical intercept is a point where the graph of a function or relation intersects the ''y''-axis of the coordinate system. As such, these points satisfy ''x'' = 0. Using equations If the curve in question is given as y= f(x), the ''y''-coordinate of the ''y''-intercept is found by calculating f(0). Functions which are undefined at ''x'' = 0 have no ''y''-intercept. If the function is linear and is expressed in slope-intercept form as f(x)=a+bx, the constant term a is the ''y''-coordinate of the ''y''-intercept. Multiple y-intercepts Some 2-dimensional mathematical relationships such as circles, ellipses, and hyperbolas can have more than one ''y''-intercept. Because functions associate ''x'' values to no more than one ''y'' value as part of their definition, they can have at most one ''y''-intercept. x ...
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Linear Relationship
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are ''linearly'' related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. However ...
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Logarithms
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number  to the base  is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of is , or . The logarithm of to ''base''  is denoted as , or without parentheses, , or even without the explicit base, , when no confusion is possible, or when the base does not matter such as in big O notation. The logarithm base is called the decimal or common logarithm and is commonly used in science and engineering. The natural logarithm has the number  as its base; its use is widespread in mathematics and physics, because of its very simple derivative. The binary logarithm uses base and is frequently used in computer science. Logarithms were introduced by John Napier in 1614 as a means of simplifying calculations. They were rapidly adopted by navigators, scientists, engineers, surveyors and others to perform high-accur ...
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Seismic Reflection
Reflection seismology (or seismic reflection) is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflected seismic waves. The method requires a controlled seismic source of energy, such as dynamite or Tovex blast, a specialized air gun or a seismic vibrator. Reflection seismology is similar to sonar and echolocation. This article is about surface seismic surveys; for vertical seismic profiles, see VSP. History Reflections and refractions of seismic waves at geologic interfaces within the Earth were first observed on recordings of earthquake-generated seismic waves. The basic model of the Earth's deep interior is based on observations of earthquake-generated seismic waves transmitted through the Earth's interior (e.g., Mohorovičić, 1910). The use of human-generated seismic waves to map in detail the geology of the upper few kilometers of the Earth's crust followed shortly thereafter and has ...
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Porosity
Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure the "accessible void", the total amount of void space accessible from the surface (cf. closed-cell foam). There are many ways to test porosity in a substance or part, such as industrial CT scanning. The term porosity is used in multiple fields including pharmaceutics, ceramics, metallurgy, materials, manufacturing, petrophysics, hydrology, earth sciences, soil mechanics, and engineering. Void fraction in two-phase flow In gas-liquid two-phase flow, the void fraction is defined as the fraction of the flow-channel volume that is occupied by the gas phase or, alternatively, as the fraction of the cross-sectional area of the channel that is occupied by the gas phase. Void fraction usually varies from location to location in the flow ch ...
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Attenuation
In physics, attenuation (in some contexts, extinction) is the gradual loss of flux intensity through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at variable attenuation rates. Hearing protectors help reduce acoustic flux from flowing into the ears. This phenomenon is called acoustic attenuation and is measured in decibels (dBs). In electrical engineering and telecommunications, attenuation affects the propagation of waves and signals in electrical circuits, in optical fibers, and in air. Electrical attenuators and optical attenuators are commonly manufactured components in this field. Background In many cases, attenuation is an exponential function of the path length through the medium. In optics and in chemical spectroscopy, this is known as the Beer–Lambert law. In engineering, attenuation is usually measured in units of decibels per unit length of medium (dB/cm, dB/km, etc.) and is ...
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Amplitude Versus Offset
In geophysics and reflection seismology, amplitude versus offset (AVO) or amplitude variation with offset is the general term for referring to the dependency of the seismic attribute, amplitude, with the distance between the source and receiver (the offset). AVO analysis is a technique that geophysicists can execute on seismic data to determine a rock's fluid content, porosity, density or seismic velocity, shear wave information, fluid indicators (hydrocarbon indications). The phenomenon is based on the relationship between the reflection coefficient and the angle of incidence and has been understood since the early 20th century when Karl Zoeppritz wrote down the Zoeppritz equations. Due to its physical origin, AVO can also be known as amplitude versus angle (AVA), but AVO is the more commonly used term because the offset is what a geophysicist can vary in order to change the angle of incidence. (See diagram) Background and theory For a seismic wave reflecting off an inte ...
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