Seismic Interferometry
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Seismic Interferometry
Interferometry examines the general interference phenomena between pairs of signals in order to gain useful information about the subsurface. Seismic interferometry (SI) utilizes the crosscorrelation of signal pairs to reconstruct the impulse response of a given media. Papers by Keiiti Aki (1957), Géza Kunetz, and Jon Claerbout (1968) helped develop the technique for ''seismic'' applications and provided the framework upon which modern theory is based. A signal at a location A can be crosscorrelated with a signal at a location B to reproduce a virtual source-receiver pair using seismic interferometry. Crosscorrelation is often considered the key mathematical operation in this approach, but it is also possible to use convolution to come up with a similar result. The crosscorrelation of passive noise measured at a free surface reproduces the subsurface response as if it was induced by an impulsive point source, which is, by definition, equal to Green's function. As such, it is po ...
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Interferometry
Interferometry is a technique which uses the ''interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, spectroscopy (and its applications to chemistry), quantum mechanics, nuclear and particle physics, plasma physics, remote sensing, biomolecular interactions, surface profiling, microfluidics, mechanical stress/strain measurement, velocimetry, optometry, and making holograms. Interferometers are devices that extract information from interference. They are widely used in science and industry for the measurement of microscopic displacements, refractive index changes and surface irregularities. In the case with most interferometers, light from a single source is split into two beams that travel in different optical paths, which are then combined again to produce interfer ...
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Surface Wave
In physics, a surface wave is a mechanical wave that propagates along the Interface (chemistry), interface between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occur within liquids, at the interface between two fluids with different densities. Elastic surface waves can travel along the surface of solids, such as ''Rayleigh wave, Rayleigh'' or ''Love wave, Love'' waves. Electromagnetic waves can also propagate as "surface waves" in that they can be guided along with a refractive index gradient or along an interface between two media having different dielectric constants. In radio transmission (telecommunications), transmission, a ''ground wave'' is a guided wave that propagates close to the surface of the Earth. Mechanical waves In seismology, several types of surface waves are encountered. Surface waves, in this mechanical sense, are commonly known as either ''Love waves'' (L waves) or ''Rayleigh ...
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Passive Seismic
Passive seismic is the detection of natural low frequency earth movements, usually with the purpose of discerning geological structure and locate underground oil, gas, or other resources. Usually the data listening is done in multiple measurement points that are separated by several hundred meters, over periods of several hours to several days, using portable seismometers. The conclusions about the geological structure are based on the spectral analysis or on the mathematical reconstruction of the propagation and possible sources of the observed seismic waves. If the latter is planned, data are usually acquired in multiple (in the ideal case - all) points simultaneously, using so called synchronized lines. Reliability of the time reverse modelling can be further increased using results of reflection seismology about the distribution of the sound speed in the underground volume. Passive seismic usually focuses on a low frequency signals (0 to 10 Hz) and is sometimes called the ...
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Hydro-fracing
Fracking (also known as hydraulic fracturing, hydrofracturing, or hydrofracking) is a well stimulation technique involving the fracturing of bedrock formations by a pressurized liquid. The process involves the high-pressure injection of "fracking fluid" (primarily water, containing sand or other proppants suspended with the aid of thickening agents) into a wellbore to create cracks in the deep-rock formations through which natural gas, petroleum, and brine will flow more freely. When the hydraulic pressure is removed from the well, small grains of hydraulic fracturing proppants (either sand or aluminium oxide) hold the fractures open. Hydraulic fracturing began as an experiment in 1947, and the first commercially successful application followed in 1950. As of 2012, 2.5 million "frac jobs" had been performed worldwide on oil and gas wells, over one million of those within the U.S. Such treatment is generally necessary to achieve adequate flow rates in shale gas, tight gas, tig ...
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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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Salt Dome
A salt dome is a type of structural dome formed when salt (or other evaporite minerals) intrudes into overlying rocks in a process known as diapirism. Salt domes can have unique surface and subsurface structures, and they can be discovered using techniques such as seismic reflection. They are important in petroleum geology as they can function as petroleum traps. Formation Stratigraphically, salt basins developed periodically from the Proterozoic to the Neogene. The formation of a salt dome begins with the deposition of salt in a restricted basin. In these basins, the outflow of water exceeds inflow. More concretely, the basin loses water through evaporation, resulting in the precipitation and deposition of salt. While the rate of sedimentation of salt is significantly larger than the rate of sedimentation of clastics, it is recognized that a single evaporation event is rarely enough to produce the vast quantities of salt needed to form a layer thick enough for the formation ...
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Hydrocarbon Exploration
Hydrocarbon exploration (or oil and gas exploration) is the search by petroleum geologists and geophysicists for deposits of hydrocarbons, particularly petroleum and natural gas, in the Earth using petroleum geology. Exploration methods Visible surface features such as oil seeps, natural gas seeps, pockmarks (underwater craters caused by escaping gas) provide basic evidence of hydrocarbon generation (be it shallow or deep in the Earth). However, most exploration depends on highly sophisticated technology to detect and determine the extent of these deposits using exploration geophysics. Areas thought to contain hydrocarbons are initially subjected to a gravity survey, magnetic survey, passive seismic or regional seismic reflection surveys to detect large-scale features of the sub-surface geology. Features of interest (known as ''leads'') are subjected to more detailed seismic surveys which work on the principle of the time it takes for reflected sound waves to travel throu ...
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Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ...
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Geophone
A geophone is a device that converts ground movement (velocity) into voltage, which may be recorded at a recording station. The deviation of this measured voltage from the base line is called the seismic response and is analyzed for structure of the earth. Etymology The term geophone derives from the Greek word "γῆ (ge) " meaning "earth" and "phone" meaning "sound". Construction Geophones have historically been passive analog devices and typically comprise a spring-mounted wire coil moving within the field of a case-mounted permanent magnet to generate an electrical signal. Recent designs have been based on microelectromechanical systems (MEMS) technology which generates an electrical response to ground motion through an active feedback circuit to maintain the position of a small piece of silicon. The response of a coil/magnet geophone is proportional to ground velocity, while MEMS devices usually respond proportional to acceleration. MEMS have a much higher noise level (5 ...
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Drill Bit
Drill bits are cutting tools used in a drill to remove material to create holes, almost always of circular cross-section. Drill bits come in many sizes and shapes and can create different kinds of holes in many different materials. In order to create holes drill bits are usually attached to a drill, which powers them to cut through the workpiece, typically by rotation. The drill will grasp the upper end of a bit called the ''shank'' in the chuck. Drills come in standardized drill bit sizes. A comprehensive drill bit and tap size chart lists metric and imperial sized drills alongside the required screw tap sizes. There are also certain specialized drill bits that can create holes with a non-circular cross-section. Characteristics Drill geometry has several characteristics: *The spiral (or rate of twist) in the drill bit controls the rate of chip removal. A fast spiral (high twist rate or "compact flute") drill bit is used in high feed rate applications under low spindle ...
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Convolution Of Spiky Function With Box
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions ( and ) that produces a third function (f*g) that expresses how the shape of one is modified by the other. The term ''convolution'' refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The choice of which function is reflected and shifted before the integral does not change the integral result (see commutativity). The integral is evaluated for all values of shift, producing the convolution function. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution (f*g) differs from cross-correlation (f \star g) only in that either or is reflected about the y-axis in convolution; thus it is a cross-correlation of and , or and . For complex-valued functi ...
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