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Seismic Inversion
In geophysics (primarily in oil-and-gas exploration/development), seismic inversion is the process of transforming seismic reflection data into a quantitative rock-property description of a reservoir. Seismic inversion may be pre- or post- stack, deterministic, random or geostatistical; it typically includes other reservoir measurements such as well logs and cores. Introduction Geophysicists routinely perform seismic surveys to gather information about the geology of an oil or gas field. These surveys record sound waves which have traveled through the layers of rock and fluid in the earth. The amplitude and frequency of these waves can be estimated so that any side-lobe and tuning effects introduced by the wavelet may be removed. Seismic data may be inspected and interpreted on its own without inversion, but this does not provide the most detailed view of the subsurface and can be misleading under certain conditions. Because of its efficiency and quality, most oil and gas compani ...
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Geophysics
Geophysics () is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. The term ''geophysics'' sometimes refers only to solid earth applications: Earth's shape; its gravitational and magnetic fields; its internal structure and composition; its dynamics and their surface expression in plate tectonics, the generation of magmas, volcanism and rock formation. However, modern geophysics organizations and pure scientists use a broader definition that includes the water cycle including snow and ice; fluid dynamics of the oceans and the atmosphere; electricity and magnetism in the ionosphere and magnetosphere and solar-terrestrial physics; and analogous problems associated with the Moon and other planets. Gutenberg, B., 1929, Lehrbuch der Geophysik. Leipzig. Berlin (Gebruder Borntraeger). Runcorn, S.K, (editor-in-chief), 1967, In ...
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Bandwidth-limited Pulse
A bandwidth-limited pulse (also known as Fourier-transform-limited pulse, or more commonly, transform-limited pulse) is a pulse of a wave that has the minimum possible duration for a given spectral bandwidth. Bandwidth-limited pulses have a constant phase across all frequencies making up the pulse. Optical pulses of this type can be generated by mode-locked lasers. Any waveform can be disassembled into its spectral components by Fourier analysis or Fourier transformation. The length of a pulse thereby is determined by its complex spectral components, which include not just their relative intensities, but also the relative positions (spectral phase) of these spectral components. For different pulse shapes, the minimum duration-bandwidth product is different. The duration-bandwidth product is minimal for zero phase-modulation. For example, \mathrm pulses have a minimum duration-bandwidth product of 0.315 while gaussian pulses have a minimum value of 0.441. A bandwidth-limited pu ...
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Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm can be expressed within a finite amount of space ...
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Lithology
The lithology of a rock unit is a description of its physical characteristics visible at outcrop, in hand or core samples, or with low magnification microscopy. Physical characteristics include colour, texture, grain size, and composition. Lithology may refer to either a detailed description of these characteristics, or a summary of the gross physical character of a rock. Examples of lithologies in the second sense include sandstone, slate, basalt, or limestone. Lithology is the basis of subdividing rock sequences into individual lithostratigraphic units for the purposes of mapping and correlation between areas. In certain applications, such as site investigations, lithology is described using a standard terminology such as in the European geotechnical standard Eurocode 7. Rock type The naming of a lithology is based on the rock type. The three major rock types are igneous, sedimentary, and metamorphic. Igneous rocks are formed directly from magma, which is a mixture ...
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Reservoir Petrophysics
A reservoir (; from French ''réservoir'' ) is an enlarged lake behind a dam. Such a dam may be either artificial, built to store fresh water or it may be a natural formation. Reservoirs can be created in a number of ways, including controlling a watercourse that drains an existing body of water, interrupting a watercourse to form an embayment within it, through excavation, or building any number of retaining walls or levees. In other contexts, "reservoirs" may refer to storage spaces for various fluids; they may hold liquids or gasses, including hydrocarbons. ''Tank reservoirs'' store these in ground-level, elevated, or buried tanks. Tank reservoirs for water are also called cisterns. Most underground reservoirs are used to store liquids, principally either water or petroleum. Types Dammed valleys Dammed reservoirs are artificial lakes created and controlled by a dam constructed across a valley, and rely on the natural topography to provide most of the basin of the ...
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Seismic Attribute
In reflection seismology, a seismic attribute is a quantity extracted or derived from seismic data that can be analysed in order to enhance information that might be more subtle in a traditional seismic image, leading to a better geological or geophysical interpretation of the data. Examples of seismic attributes can include measured time, amplitude, frequency and attenuation, in addition to combinations of these. Most seismic attributes are post-stack, but those that use CMP gathers, such as amplitude versus offset (AVO), must be analysed pre-stack.Young, R. & LoPiccolo, R. 2005. AVO analysis demystified. E&P. http://www.e-seis.com/white_papers/AVO%20Analysis%20Demystified.pdf They can be measured along a single seismic trace or across multiple traces within a defined window. The first attributes developed were related to the 1D complex seismic trace and included: envelope amplitude, instantaneous phase, instantaneous frequency, and apparent polarity. Acoustic impedance ...
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Stratigraphy
Stratigraphy is a branch of geology concerned with the study of rock layers ( strata) and layering (stratification). It is primarily used in the study of sedimentary and layered volcanic rocks. Stratigraphy has three related subfields: lithostratigraphy (lithologic stratigraphy), biostratigraphy (biologic stratigraphy), and chronostratigraphy (stratigraphy by age). Historical development Catholic priest Nicholas Steno established the theoretical basis for stratigraphy when he introduced the law of superposition, the principle of original horizontality and the principle of lateral continuity in a 1669 work on the fossilization of organic remains in layers of sediment. The first practical large-scale application of stratigraphy was by William Smith in the 1790s and early 19th century. Known as the "Father of English geology", Smith recognized the significance of strata or rock layering and the importance of fossil markers for correlating strata; he created the first geol ...
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Interference (wave Propagation)
In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive interference result from the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves. Etymology The word ''interference'' is derived from the Latin words ''inter'' which means "between" and ''fere'' which means "hit or strike", and was coined by Thomas Young in 1801. Mechanisms The principle of superposition of waves states that when two or more propagating waves of the same type are incident on the same point, the resultant amplitude at that point is equal to ...
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P-wave
A P wave (primary wave or pressure wave) is one of the two main types of elastic body waves, called seismic waves in seismology. P waves travel faster than other seismic waves and hence are the first signal from an earthquake to arrive at any affected location or at a seismograph. P waves may be transmitted through gases, liquids, or solids. Nomenclature The name ''P wave'' can stand for either pressure wave (as it is formed from alternating compressions and rarefactions) or primary wave (as it has high velocity and is therefore the first wave to be recorded by a seismograph). The name ''S wave'' represents another seismic wave propagation mode, standing for secondary or shear wave. Seismic waves in the Earth Primary and secondary waves are body waves that travel within the Earth. The motion and behavior of both P and S waves in the Earth are monitored to probe the interior structure of the Earth. Discontinuities in velocity as a function of depth are indicative of ch ...
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Stochastic
Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselves, these two terms are often used synonymously. Furthermore, in probability theory, the formal concept of a '' stochastic process'' is also referred to as a ''random process''. Stochasticity is used in many different fields, including the natural sciences such as biology, chemistry, ecology, neuroscience, and physics, as well as technology and engineering fields such as image processing, signal processing, information theory, computer science, cryptography, and telecommunications. It is also used in finance, due to seemingly random changes in financial markets as well as in medicine, linguistics, music, media, colour theory, botany, manufacturing, and geomorphology. Etymology The word ''stochastic'' in English was originally used as ...
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Acoustic Impedance
Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system. The SI unit of acoustic impedance is the pascal-second per cubic metre (), or in the MKS system the rayl per square metre (), while that of specific acoustic impedance is the pascal-second per metre (), or in the MKS system the rayl. There is a close analogy with electrical impedance, which measures the opposition that a system presents to the electric current resulting from a voltage applied to the system. Mathematical definitions Acoustic impedance For a linear time-invariant system, the relationship between the acoustic pressure applied to the system and the resulting acoustic volume flow rate through a surface perpendicular to the direction of that pressure at its point of application is given by: : p(t) = * Qt), or equivalently by : Q(t) = * pt), where * ''p'' is the acoustic pressure; * ...
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Deconvolution
In mathematics, deconvolution is the operation inverse to convolution. Both operations are used in signal processing and image processing. For example, it may be possible to recover the original signal after a filter (convolution) by using a deconvolution method with a certain degree of accuracy. Due to the measurement error of the recorded signal or image, it can be demonstrated that the worse the SNR, the worse the reversing of a filter will be; hence, inverting a filter is not always a good solution as the error amplifies. Deconvolution offers a solution to this problem. The foundations for deconvolution and time-series analysis were largely laid by Norbert Wiener of the Massachusetts Institute of Technology in his book ''Extrapolation, Interpolation, and Smoothing of Stationary Time Series'' (1949). The book was based on work Wiener had done during World War II but that had been classified at the time. Some of the early attempts to apply these theories were in the fields of ...
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