Acoustic Waves for Geoscience. Good for students
EminYusifov4
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51 slides
Sep 06, 2024
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About This Presentation
Acoustic Waves
Slide Content
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ACOUSTIC WAVES
ACOUSTIC WAVES
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Elastic wave
•Motion in a medium in which, when particles are displaced, a force proportional to the displacement acts
on the particles to restore them to their original position.
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•Motion in a medium in which, when particles are displaced, a force proportional to the displacement acts
on the particles to restore them to their original position.
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Surface waves
•Travel more slowly through Earth material at the planet's surface and are predominantly lower frequency
than body waves.
•They are easily distinguished on a seismogram.
•Shallow earthquakes produce stronger surface waves; the strength of the surface waves are reduced in deeper
earthquakes.
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•Travel more slowly through Earth material at the planet's surface and are predominantly lower frequency
than body waves.
•They are easily distinguished on a seismogram.
•Shallow earthquakes produce stronger surface waves; the strength of the surface waves are reduced in deeper
earthquakes.
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Body waves
•Aresolutions of the elastic equation of motion that propagate outward from a seismic source in expanding,
quasi-spherical wave fronts, much like the rings seen when a rock is thrown in a pond.
•The trajectory along which the elastic energy propagates is called a ray.
•Body waves are of two types:
oPrimary waves(also called P-waves, or pressure waves) and
oSecondary waves (S-waves, or shear waves). P-waves are compression waves.
oThey can propagate in solid or liquid material.
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•Aresolutions of the elastic equation of motion that propagate outward from a seismic source in expanding,
quasi-spherical wave fronts, much like the rings seen when a rock is thrown in a pond.
•The trajectory along which the elastic energy propagates is called a ray.
•Body waves are of two types:
oPrimary waves(also called P-waves, or pressure waves) and
oSecondary waves (S-waves, or shear waves). P-waves are compression waves.
oThey can propagate in solid or liquid material.
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A P-wave (PPi) propagating through a medium of density, P, P-wave velocity, Vpi, and S-wave velocity, Vs, is
incident upon an interface with a medium of density, p2, P-wave velocity, V.2, and S-wave velocity, Vs at an
angle, 0j.
Mode conversions occur resulting in reflected P-and S-waves (PP, and PS, respectively) and transmitted
(refracted) P-and S-waves (PP, and PS, respectively).6
incident upon an interface with a medium of density, p2, P-wave velocity, V.2, and S-wave velocity, Vs at an
angle, 0j.
Mode conversions occur resulting in reflected P-and S-waves (PP, and PS, respectively) and transmitted
(refracted) P-and S-waves (PP, and PS, respectively).6
P-wave
•AP wave(primary waveorpressure wave) is one of the two main types of elasticbody waves, calledseismic
wavesin 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 aseismograph.
•P wavesmay be transmitted throughgases, liquids, or solids.
•An elastic body wave or sound wave in which particles oscillate in the direction the wave propagates.
•P-waves are the waves studied in conventional seismic data.
•P-waves incident on an interface at other thannormal incidencecan produce reflected and transmitted S-
waves, in that case known as converted waves.
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•AP wave(primary waveorpressure wave) is one of the two main types of elasticbody waves, calledseismic
wavesin 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 aseismograph.
•P wavesmay be transmitted throughgases, liquids, or solids.
•An elastic body wave or sound wave in which particles oscillate in the direction the wave propagates.
•P-waves are the waves studied in conventional seismic data.
•P-waves incident on an interface at other thannormal incidencecan produce reflected and transmitted S-
waves, in that case known as converted waves.
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S-wave
•An elastic body wave in which particles oscillate perpendicular to the direction in which the wave propagates.
•S-waves are generated by most land seismic sources, but not by air guns.
•P-waves that impinge on an interface at non-normal incidencecan produce S-waves, which in that case are known as converted waves.
•S-waves can likewise be converted to P-waves.
•S-waves, or shear waves, travel more slowly than P-waves and cannot travel through fluids because fluids do not support shear.
•Recording of S-waves requires receivers coupled to the solid Earth.
•Interpretationof S-waves can allow determination ofrock propertiessuch as fracture density and orientation, Poisson's ratio androcktype by crossplotting P-wave and S-wave velocities, and by other techniques.
•Inseismologyand other areas involving elastic waves,S waves,secondary waves, orshear waves(sometimes calledelastic S waves) are a type ofelastic waveand are one of the two main types of elasticbody waves, so named because they move through the body of an object, unlikesurface wave
•S waves aretransverse waves, meaning that the direction ofparticlemotion of a S wave is perpendicular to the direction of wave propagation, and the main restoring force comes fromshear stress
•Therefore, S waves cannot propagate in liquidwith zero (or very low)viscosity; however, they may propagate in liquids with high viscosity.
•The namesecondary wavecomes from the fact that they are the second type of wave to be detected by an earthquakeseismograph, after thecompressionalprimary wave, orP wave, because S waves travel more slowly in solids.
•Unlike P waves, S waves cannot travel through the moltenouter coreof the Earth, and this causes ashadow zonefor S waves opposite to their origin.
•They can still propagate through the solidinner core: when a P wave strikes the boundary of molten and solid cores at an oblique angle, S waves will form and propagate in the solid medium.
•When these S waves hit the boundary again at an oblique angle, they will in turn create P waves that propagate through the liquid medium.
•This property allowsseismologiststo determine some physical properties of the Earth's inner core.
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•An elastic body wave in which particles oscillate perpendicular to the direction in which the wave propagates.
•S-waves are generated by most land seismic sources, but not by air guns.
•P-waves that impinge on an interface at non-normal incidencecan produce S-waves, which in that case are known as converted waves.
•S-waves can likewise be converted to P-waves.
•S-waves, or shear waves, travel more slowly than P-waves and cannot travel through fluids because fluids do not support shear.
•Recording of S-waves requires receivers coupled to the solid Earth.
•Interpretationof S-waves can allow determination ofrock propertiessuch as fracture density and orientation, Poisson's ratio androcktype by crossplotting P-wave and S-wave velocities, and by other techniques.
•Inseismologyand other areas involving elastic waves,S waves,secondary waves, orshear waves(sometimes calledelastic S waves) are a type ofelastic waveand are one of the two main types of elasticbody waves, so named because they move through the body of an object, unlikesurface wave
•S waves aretransverse waves, meaning that the direction ofparticlemotion of a S wave is perpendicular to the direction of wave propagation, and the main restoring force comes fromshear stress
•Therefore, S waves cannot propagate in liquidwith zero (or very low)viscosity; however, they may propagate in liquids with high viscosity.
•The namesecondary wavecomes from the fact that they are the second type of wave to be detected by an earthquakeseismograph, after thecompressionalprimary wave, orP wave, because S waves travel more slowly in solids.
•Unlike P waves, S waves cannot travel through the moltenouter coreof the Earth, and this causes ashadow zonefor S waves opposite to their origin.
•They can still propagate through the solidinner core: when a P wave strikes the boundary of molten and solid cores at an oblique angle, S waves will form and propagate in the solid medium.
•When these S waves hit the boundary again at an oblique angle, they will in turn create P waves that propagate through the liquid medium.
•This property allowsseismologiststo determine some physical properties of the Earth's inner core.
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Interface waves
•An interface isa boundary shared by two media.
•To a wave entering a medium with a slower wave speed, the interface is more like a fixed end than a free end.
•To a wave entering a medium with a faster wave speed, the interface is more like a free end than a fixed end.
•For example, Rayleigh’s waves are one of the three types of interface waves, which travel in vacuum-solid surfaces.
•In isotropic solids the particle motion is elliptical and retrograde, for shallow depths, with respect to the direction of propagation Rayleigh.
•Today, many engineering and seismology studies are focused on understanding Rayleigh’s waves.
•Recent research concerning Rayleigh’s waves is also carried out on nondestructive testing for detecting defects.
•Stoneley’s waves occur at the interface between two solids.
•The higher energy, as well as Rayleigh’s waves, is present in the interface and shows an exponential decay away from the interface.
•Scholte’s waves are presented at the interface of fluid-solid media.
•Similarly, most of the energy in this type of wave is presented in the interface and decays exponentially into the solid medium and fluid one.
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•An interface isa boundary shared by two media.
•To a wave entering a medium with a slower wave speed, the interface is more like a fixed end than a free end.
•To a wave entering a medium with a faster wave speed, the interface is more like a free end than a fixed end.
•For example, Rayleigh’s waves are one of the three types of interface waves, which travel in vacuum-solid surfaces.
•In isotropic solids the particle motion is elliptical and retrograde, for shallow depths, with respect to the direction of propagation Rayleigh.
•Today, many engineering and seismology studies are focused on understanding Rayleigh’s waves.
•Recent research concerning Rayleigh’s waves is also carried out on nondestructive testing for detecting defects.
•Stoneley’s waves occur at the interface between two solids.
•The higher energy, as well as Rayleigh’s waves, is present in the interface and shows an exponential decay away from the interface.
•Scholte’s waves are presented at the interface of fluid-solid media.
•Similarly, most of the energy in this type of wave is presented in the interface and decays exponentially into the solid medium and fluid one.
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Seismic Waves
•Seismic waves arecaused by the sudden movement of materials within the Earth, such as slip along a
fault during an earthquake. Volcanic eruptions, explosions, landslides, avalanches, and even rushing rivers
can also cause seismic
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•Seismic waves arecaused by the sudden movement of materials within the Earth, such as slip along a
fault during an earthquake. Volcanic eruptions, explosions, landslides, avalanches, and even rushing rivers
can also cause seismic
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Love waves
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•Inelastodynamics,Love waves, named afterAugustus Edward Hough Love, are horizontallypolarizedsurface waves.
•The Love wave is a result of theinterferenceof many shear waves (S-waves) guided by an elastic layer, which isweldedto
an elastic half space on one side while bordering a vacuum on the other side.
•Inseismology,Love waves(also known asQ waves(Quer: German for lateral)) aresurfaceseismic wavesthat cause
horizontal shifting of the Earth during anearthquake.
•Augustus Edward Hough Love predicted the existence of Love waves mathematically in 1911.
•They form a distinct class, different from other types ofseismic waves, such asP-wavesandS waves(bothbody waves),
orRayleigh waves(another type of surface wave).
•Love waves travel with a lower velocity than P-or S-waves, but faster than Rayleigh waves.
•These waves are observed only when there is a low velocity layer overlying a high velocity layer/ sub–layers.
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•Inelastodynamics,Love waves, named afterAugustus Edward Hough Love, are horizontallypolarizedsurface waves.
•The Love wave is a result of theinterferenceof many shear waves (S-waves) guided by an elastic layer, which isweldedto
an elastic half space on one side while bordering a vacuum on the other side.
•Inseismology,Love waves(also known asQ waves(Quer: German for lateral)) aresurfaceseismic wavesthat cause
horizontal shifting of the Earth during anearthquake.
•Augustus Edward Hough Love predicted the existence of Love waves mathematically in 1911.
•They form a distinct class, different from other types ofseismic waves, such asP-wavesandS waves(bothbody waves),
orRayleigh waves(another type of surface wave).
•Love waves travel with a lower velocity than P-or S-waves, but faster than Rayleigh waves.
•These waves are observed only when there is a low velocity layer overlying a high velocity layer/ sub–layers.
Flexural mode
•A type ofacousticpropagation along theboreholethat is visualized as a shaking of the borehole across
its diameter.
•The flexural mode is excited by adipolesource, andmeasured by dipole receivers oriented in the same
direction.
•Its speed is chiefly a function of theformationshearvelocity, the borehole size and fluid velocity, and
thefrequency.
•It is used to estimate formation shear velocity, andis the only technique available in slow formations
where shear velocity is less than borehole-fluid velocity.
•In this situation, shear head waves are not generated by amonopolesource, so that standard monopole
techniques cannot be used.
•The flexuralwaveis sensitive to properties of the altered zone, as well as to formationanisotropy,
whether intrinsic orstress-induced.
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•A type ofacousticpropagation along theboreholethat is visualized as a shaking of the borehole across
its diameter.
•The flexural mode is excited by adipolesource, andmeasured by dipole receivers oriented in the same
direction.
•Its speed is chiefly a function of theformationshearvelocity, the borehole size and fluid velocity, and
thefrequency.
•It is used to estimate formation shear velocity, andis the only technique available in slow formations
where shear velocity is less than borehole-fluid velocity.
•In this situation, shear head waves are not generated by amonopolesource, so that standard monopole
techniques cannot be used.
•The flexuralwaveis sensitive to properties of the altered zone, as well as to formationanisotropy,
whether intrinsic orstress-induced.
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Scholte wave
•AScholte waveis asurface wave(interface wave) propagating at an interface between a fluid and an elastic
solid medium (such as an interface between water and sand).
•The wave is of maximum intensity at the interface and decreases exponentially away from the interface into
both the fluid and the solid medium.
•It is named after J. G. Scholte, who discovered it in 1947.
•This wave is similar toaStoneley wave, which propagates at a solid-solid interface, and aRayleigh wave,
which propagates at a vacuum-solid interface.
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•AScholte waveis asurface wave(interface wave) propagating at an interface between a fluid and an elastic
solid medium (such as an interface between water and sand).
•The wave is of maximum intensity at the interface and decreases exponentially away from the interface into
both the fluid and the solid medium.
•It is named after J. G. Scholte, who discovered it in 1947.
•This wave is similar toaStoneley wave, which propagates at a solid-solid interface, and aRayleigh wave,
which propagates at a vacuum-solid interface.
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Rayleigh wave
•Rayleigh wavesare a type ofsurface acoustic wavethat travel along the surface of solids.
•They can be produced in materials in many ways, such as by a localized impact or bypiezo-electrictransduction, and
are frequently used innon-destructive testingfor detecting defects.
•Rayleigh waves are part of theseismic wavesthat are produced on theEarthbyearthquakes.
•When guided in layers they are referred to asLamb waves, Rayleigh–Lamb waves, or generalized Rayleigh waves.
Particle motion of a Rayleigh wave.
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•Rayleigh wavesare a type ofsurface acoustic wavethat travel along the surface of solids.
•They can be produced in materials in many ways, such as by a localized impact or bypiezo-electrictransduction, and
are frequently used innon-destructive testingfor detecting defects.
•Rayleigh waves are part of theseismic wavesthat are produced on theEarthbyearthquakes.
•When guided in layers they are referred to asLamb waves, Rayleigh–Lamb waves, or generalized Rayleigh waves.
Particle motion of a Rayleigh wave.
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Lamb waves
•Lamb wavespropagate in solid plates or spheres.
•They areelastic waveswhose particle motion lies in the plane that contains the direction of wave propagation and the direction perpendicular to the plate.
•In 1917, the English mathematicianHorace Lambpublished his classic analysis and description ofacousticwaves of this type.
•Their properties turned out to be quite complex.
•An infinite medium supports just two wave modes traveling at unique velocities; but plates support two infinite sets of Lamb wave modes, whose velocities depend on the relationship between wavelength and plate thickness.
•Since the 1990s, the understanding and utilization of Lamb waves has advanced greatly, thanks to the rapid increase in the availability of computing power.
•Lamb's theoretical formulations have found substantial practical application, especially in the field of nondestructive testing.
•The termRayleigh–Lamb wavesembraces theRayleigh wave, a type of wave that propagates along a single surface.
•Both Rayleigh and Lamb waves are constrained by the elastic properties of the surface(s) that guide them.
Figure 1: Upper and lower, respectively: Extensional (S0) mode with.
Flexural (A0) mode with.
(This is a simplified graphic.
It is based on thezcomponent of motion only, so it does not render
the distortion of the plate precisely.)
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•Lamb wavespropagate in solid plates or spheres.
•They areelastic waveswhose particle motion lies in the plane that contains the direction of wave propagation and the direction perpendicular to the plate.
•In 1917, the English mathematicianHorace Lambpublished his classic analysis and description ofacousticwaves of this type.
•Their properties turned out to be quite complex.
•An infinite medium supports just two wave modes traveling at unique velocities; but plates support two infinite sets of Lamb wave modes, whose velocities depend on the relationship between wavelength and plate thickness.
•Since the 1990s, the understanding and utilization of Lamb waves has advanced greatly, thanks to the rapid increase in the availability of computing power.
•Lamb's theoretical formulations have found substantial practical application, especially in the field of nondestructive testing.
•The termRayleigh–Lamb wavesembraces theRayleigh wave, a type of wave that propagates along a single surface.
•Both Rayleigh and Lamb waves are constrained by the elastic properties of the surface(s) that guide them.
Figure 1: Upper and lower, respectively: Extensional (S0) mode with.
Flexural (A0) mode with.
(This is a simplified graphic.
It is based on thezcomponent of motion only, so it does not render
the distortion of the plate precisely.)
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Stoneley wave
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•AStoneley waveis a boundary wave (or interface wave) that typically propagates along a
solid-solid interface.
•When found at a liquid-solid interface, this wave is also referred to as aScholte wave.
•The wave is of maximum intensity at the interface and decreases exponentially away
from it.
•It is named after the British seismologist Dr. Robert Stoneley (1894–1976), a lecturer in
theUniversity of Leeds, who discovered it on October 1, 1924.
•A type of large-amplitudeinterface, or surface, wave generated by a sonic tool in
aborehole.
•Stoneley waves can propagate along a solid-fluid interface, such as along the walls of a
fluid-filled borehole and are the main low-frequencycomponent of signal generated by
sonic sources in boreholes.
•Analysis of Stoneley waves can allow estimation of the locations of fractures
andpermeabilityof theformation.
•Stoneley waves are a major source ofnoisein verticalseismicprofiles.
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•AStoneley waveis a boundary wave (or interface wave) that typically propagates along a
solid-solid interface.
•When found at a liquid-solid interface, this wave is also referred to as aScholte wave.
•The wave is of maximum intensity at the interface and decreases exponentially away
from it.
•It is named after the British seismologist Dr. Robert Stoneley (1894–1976), a lecturer in
theUniversity of Leeds, who discovered it on October 1, 1924.
•A type of large-amplitudeinterface, or surface, wave generated by a sonic tool in
aborehole.
•Stoneley waves can propagate along a solid-fluid interface, such as along the walls of a
fluid-filled borehole and are the main low-frequencycomponent of signal generated by
sonic sources in boreholes.
•Analysis of Stoneley waves can allow estimation of the locations of fractures
andpermeabilityof theformation.
•Stoneley waves are a major source ofnoisein verticalseismicprofiles.
Occurrence and use
•Stoneley waves are most commonly generated during boreholesonic loggingandvertical seismic profiling.
•They propagate along the walls of a fluid-filledborehole.
•They make up a large part of the low-frequency component of the signal from the seismic source and their
attenuation is sensitive to fractures and formationpermeability.
•Recent studies have found that Stoneley wave processing in borehole help to distinguish between fractured
versus non-fractured coal seam.
•Therefore, analysis of Stoneley waves can make it possible to estimate these rock properties.
Effects of permeability
•Permeabilitycan influence Stoneley wave propagation in three ways.
•Stoneley waves can be partly reflected at sharp impedance contrasts such as fractures, lithology, or borehole
diameter changes.
•Moreover, as formation permeability increases, Stoneley wavevelocitydecreases, thereby inducing
dispersion.
•The third effect is the attenuation of Stoneley waves.
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•Stoneley waves are most commonly generated during boreholesonic loggingandvertical seismic profiling.
•They propagate along the walls of a fluid-filledborehole.
•They make up a large part of the low-frequency component of the signal from the seismic source and their
attenuation is sensitive to fractures and formationpermeability.
•Recent studies have found that Stoneley wave processing in borehole help to distinguish between fractured
versus non-fractured coal seam.
•Therefore, analysis of Stoneley waves can make it possible to estimate these rock properties.
Effects of permeability
•Permeabilitycan influence Stoneley wave propagation in three ways.
•Stoneley waves can be partly reflected at sharp impedance contrasts such as fractures, lithology, or borehole
diameter changes.
•Moreover, as formation permeability increases, Stoneley wavevelocitydecreases, thereby inducing
dispersion.
•The third effect is the attenuation of Stoneley waves.
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Mud wave
•Fluid compressional wave or mud wave is thecompressional body wave from a monopole source that travels
through the mud in the borehole directly to the sonic log receivers.
•It travels at a constant velocity with relatively high energy.
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•Fluid compressional wave or mud wave is thecompressional body wave from a monopole source that travels
through the mud in the borehole directly to the sonic log receivers.
•It travels at a constant velocity with relatively high energy.
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Slow Formations
•A slow formation refers to a formation in which the compressional wave velocity measured in the borehole fluid exceeds encompassing shear wave velocities.
•This monopole measurement results in compressional and Stoneley arrivals but no detected shear waves.
•Therefore, a dipole measurement is better suited for a slow formation because it can generate flexural or bender waves which produce measurable shear waves.
•An example of a slow formation is a high porosity gas sand layer.
•Aformationin which thevelocityof the compressional wave traveling through theboreholefluid is greater than the velocity of the shear wave through the surrounding formation.
•In such conditions, there is no criticalrefractionof the shear wave and no shear head wave generated, so that standard techniques based onmonopoletransducers cannot be used to measure formation shear velocity.
•Instead, it is necessary to usedipolesources to excite theflexural mode.
•The velocity of the latter is closely related to that of the shear wave.
•In very slow formations, such as in high-porositygas sands, the formation compressional velocity also may be less than the borehole fluid velocity, causing no compressional head wave.
•In such cases, it is possible to estimate the formation compressional velocity from the low-frequencyend of aleaky mode.
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•A slow formation refers to a formation in which the compressional wave velocity measured in the borehole fluid exceeds encompassing shear wave velocities.
•This monopole measurement results in compressional and Stoneley arrivals but no detected shear waves.
•Therefore, a dipole measurement is better suited for a slow formation because it can generate flexural or bender waves which produce measurable shear waves.
•An example of a slow formation is a high porosity gas sand layer.
•Aformationin which thevelocityof the compressional wave traveling through theboreholefluid is greater than the velocity of the shear wave through the surrounding formation.
•In such conditions, there is no criticalrefractionof the shear wave and no shear head wave generated, so that standard techniques based onmonopoletransducers cannot be used to measure formation shear velocity.
•Instead, it is necessary to usedipolesources to excite theflexural mode.
•The velocity of the latter is closely related to that of the shear wave.
•In very slow formations, such as in high-porositygas sands, the formation compressional velocity also may be less than the borehole fluid velocity, causing no compressional head wave.
•In such cases, it is possible to estimate the formation compressional velocity from the low-frequencyend of aleaky mode.
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Fast Formations
•A fast formation has higher shear wave velocities than compressional wave velocities.
•Shear waves as well as compressional and Stoneley waves can all be observed with a monopole measurement.
•An example of a fast formation would be a low porosity carbonate layer.
•Although both monopole and dipole measurements have advantages for different types of rock layers, modern
sonic logs contain both types of measurements as to most accurately measure the acoustic properties of the
subsurface.
•Aformationwhere thevelocityof the compressionalwavetraveling through theboreholefluid is less than the
velocity of the shear wave through the surrounding formation.
•In such conditions a shear head wave is generated, so that standard techniques based onmonopoletransducers
can be used to measure formation shear velocity.
•In hard formations, several normal modes are excited in addition to the Stoneley and leaky modes.
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•A fast formation has higher shear wave velocities than compressional wave velocities.
•Shear waves as well as compressional and Stoneley waves can all be observed with a monopole measurement.
•An example of a fast formation would be a low porosity carbonate layer.
•Although both monopole and dipole measurements have advantages for different types of rock layers, modern
sonic logs contain both types of measurements as to most accurately measure the acoustic properties of the
subsurface.
•Aformationwhere thevelocityof the compressionalwavetraveling through theboreholefluid is less than the
velocity of the shear wave through the surrounding formation.
•In such conditions a shear head wave is generated, so that standard techniques based onmonopoletransducers
can be used to measure formation shear velocity.
•In hard formations, several normal modes are excited in addition to the Stoneley and leaky modes.
20
Impedance
•Impedanceis the complex-valued generalization ofresistance.
•It may refer to:
•Acoustic impedance, a constant related to the propagation of sound waves in an acoustic medium
•Electrical impedance, the ratio of the voltage phasor to the electric current phasor, a measure of the opposition to time-varying electric current in an electric circuit
•High impedance, when only a small amount of current is allowed through
•Characteristic impedanceof a transmission line
•Impedance (accelerator physics), a characterization of the self interaction of a charged particle beam
•Nominal impedance, approximate designed impedance
•Impedance matching, the adjustment of input impedance and output impedance
•Mechanical impedance, a measure of opposition to motion of a structure subjected to a force
•Wave impedance, a constant related to electromagnetic wave propagation in a medium
•Impedance of free space, a universal constant and the simplest case of a wave impedance
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•Impedanceis the complex-valued generalization ofresistance.
•It may refer to:
•Acoustic impedance, a constant related to the propagation of sound waves in an acoustic medium
•Electrical impedance, the ratio of the voltage phasor to the electric current phasor, a measure of the opposition to time-varying electric current in an electric circuit
•High impedance, when only a small amount of current is allowed through
•Characteristic impedanceof a transmission line
•Impedance (accelerator physics), a characterization of the self interaction of a charged particle beam
•Nominal impedance, approximate designed impedance
•Impedance matching, the adjustment of input impedance and output impedance
•Mechanical impedance, a measure of opposition to motion of a structure subjected to a force
•Wave impedance, a constant related to electromagnetic wave propagation in a medium
•Impedance of free space, a universal constant and the simplest case of a wave impedance
21
Convolution
•Inmathematics(in particular,functional analysis),convolutionis amathematical operationon twofunctions(fandg) that produces a third function ( f *g ) that expresses how the shape of one is modified by the other.
•The termconvolutionrefers to both the result function and to the process of computing it.
•It is defined as theintegralof 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 (seecommutativity).
•The integral is evaluated for all values of shift, producing the convolution function.
•Some features of convolution are similar tocross-correlation: for real-valued functions, of a continuous or discrete variable, convolution ( f*g) differs from cross-correlation (fXg) only in that eitherf(x)org(x)is reflected about the y-axis in convolution; thusit is a cross-correlation ofg(−x)andf(x), orf(−x)andg(x).
•For complex-valued functions, the cross-correlation operator is theadjointof the convolution operator.
•Convolution has applications that includeprobability,statistics,acoustics,spectroscopy,signal processingandimage processing,geophysics,engineering,physics,computer visionanddifferential equations.
•The convolution can be defined for functions onEuclidean spaceand othergroups(asalgebraic structures).
•For example,periodic functions, such as thediscrete-time Fourier transform, can be defined on acircleand convolved byperiodic convolution.•Adiscrete convolutioncan be defined for functions on the set ofintegers.
•Generalizations of convolution have applications in the field ofnumerical analysisandnumerical linear algebra, and in the design and implementation offinite impulse responsefilters in signal processing.
•Computing theinverseof the convolution operation is known asdeconvolution.
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•Inmathematics(in particular,functional analysis),convolutionis amathematical operationon twofunctions(fandg) that produces a third function ( f *g ) that expresses how the shape of one is modified by the other.
•The termconvolutionrefers to both the result function and to the process of computing it.
•It is defined as theintegralof 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 (seecommutativity).
•The integral is evaluated for all values of shift, producing the convolution function.
•Some features of convolution are similar tocross-correlation: for real-valued functions, of a continuous or discrete variable, convolution ( f*g) differs from cross-correlation (fXg) only in that eitherf(x)org(x)is reflected about the y-axis in convolution; thusit is a cross-correlation ofg(−x)andf(x), orf(−x)andg(x).
•For complex-valued functions, the cross-correlation operator is theadjointof the convolution operator.
•Convolution has applications that includeprobability,statistics,acoustics,spectroscopy,signal processingandimage processing,geophysics,engineering,physics,computer visionanddifferential equations.
•The convolution can be defined for functions onEuclidean spaceand othergroups(asalgebraic structures).
•For example,periodic functions, such as thediscrete-time Fourier transform, can be defined on acircleand convolved byperiodic convolution.•Adiscrete convolutioncan be defined for functions on the set ofintegers.
•Generalizations of convolution have applications in the field ofnumerical analysisandnumerical linear algebra, and in the design and implementation offinite impulse responsefilters in signal processing.
•Computing theinverseof the convolution operation is known asdeconvolution.
22
Visual comparison of convolution,cross-correlation, andautocorrelation.
For the operations involving functionf, and assuming the height offis 1.0, the value of the result no at 5
different points is indicated by the shaded area below each point.
The symmetry offis the reasonandare identical in this example.
23
For the operations involving functionf, and assuming the height offis 1.0, the value of the result no at 5
different points is indicated by the shaded area below each point.
The symmetry offis the reasonandare identical in this example.
23
Deconvolution
•Inmathematics,deconvolutionis the operation inverse toconvolution.
•Both operations are used insignal processingandimage 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 theSNR, 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 andtime-series analysiswere largely laid byNorbert Wienerof theMassachusetts Institute of Technologyin his bookExtrapolation, Interpolation, and Smoothing of Stationary Time Series(1949).
•The book was based on work Wiener had done duringWorld War IIbut that had been classified at the time.
•Some of the early attempts to apply these theories were in the fields ofweather forecastingandeconomics.
Before and after deconvolution of an image of the lunar
crater Copernicus using theRichardson-Lucyalgorithm.
24
•Inmathematics,deconvolutionis the operation inverse toconvolution.
•Both operations are used insignal processingandimage 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 theSNR, 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 andtime-series analysiswere largely laid byNorbert Wienerof theMassachusetts Institute of Technologyin his bookExtrapolation, Interpolation, and Smoothing of Stationary Time Series(1949).
•The book was based on work Wiener had done duringWorld War IIbut that had been classified at the time.
•Some of the early attempts to apply these theories were in the fields ofweather forecastingandeconomics.
Before and after deconvolution of an image of the lunar
crater Copernicus using theRichardson-Lucyalgorithm.
24
Signal-to-noise ratio
•Signal-to-noise ratio(SNRorS/N) is a measure used inscience and engineeringthat compares the level of a
desiredsignalto the level of backgroundnoise.
•SNR is defined as the ratio of signal power to thenoise power, often expressed indecibels.
•A ratio higher than 1:1 (greater than 0dB) indicates more signal than noise.
•SNR,bandwidth, andchannel capacityof acommunication channelare connected by theShannon–Hartley
theorem.
25
•Signal-to-noise ratio(SNRorS/N) is a measure used inscience and engineeringthat compares the level of a
desiredsignalto the level of backgroundnoise.
•SNR is defined as the ratio of signal power to thenoise power, often expressed indecibels.
•A ratio higher than 1:1 (greater than 0dB) indicates more signal than noise.
•SNR,bandwidth, andchannel capacityof acommunication channelare connected by theShannon–Hartley
theorem.
25
Signal processing
•Signal processingis anelectrical engineeringsubfield that focuses on analyzing, modifying and
synthesizingsignals, such assound,images,potential fields,seismic signals,altimetry processing,
andscientific measurements.
•Signal processing techniques are used to optimize transmissions,digital storage efficiency, correcting
distorted signals,subjective video qualityand to also detect or pinpoint components of interest in a measured
signal.
26
•Signal processingis anelectrical engineeringsubfield that focuses on analyzing, modifying and
synthesizingsignals, such assound,images,potential fields,seismic signals,altimetry processing,
andscientific measurements.
•Signal processing techniques are used to optimize transmissions,digital storage efficiency, correcting
distorted signals,subjective video qualityand to also detect or pinpoint components of interest in a measured
signal.
26
•Signal transmission using electronic signal processing.
•Transducersconvert signals from other physicalwaveformsto electriccurrentorvoltagewaveforms, which then are
processed, transmitted aselectromagnetic waves, received and converted by another transducer to final form.
27
•Transducersconvert signals from other physicalwaveformsto electriccurrentorvoltagewaveforms, which then are
processed, transmitted aselectromagnetic waves, received and converted by another transducer to final form.
27
•The signal on the looks like noise, but the signal processing technique known asspectral density
estimationshows that it contains five well-defined frequency components.
28
estimationshows that it contains five well-defined frequency components.
28
Digital image processing
•Digital image processingis the use of adigital computerto processdigital imagesthrough analgorithm.
•As a subcategory or field ofdigital signal processing, digital image processing has many advantages
overanalog image processing.
•It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the
build-up ofnoiseanddistortionduring processing.
•Since images are defined over two dimensions (perhaps more) digital image processing may be modeled in the
form ofmultidimensional systems.
•The generation and development of digital image processing are mainly affected by three factors: first, the
development of computers; second, the development of mathematics (especially the creation and improvement
of discrete mathematics theory); third, the demand for a wide range of applications in environment,
agriculture, military, industry and medical science has increased.
29
•Digital image processingis the use of adigital computerto processdigital imagesthrough analgorithm.
•As a subcategory or field ofdigital signal processing, digital image processing has many advantages
overanalog image processing.
•It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the
build-up ofnoiseanddistortionduring processing.
•Since images are defined over two dimensions (perhaps more) digital image processing may be modeled in the
form ofmultidimensional systems.
•The generation and development of digital image processing are mainly affected by three factors: first, the
development of computers; second, the development of mathematics (especially the creation and improvement
of discrete mathematics theory); third, the demand for a wide range of applications in environment,
agriculture, military, industry and medical science has increased.
29
Reflection seismology
•Reflection seismology(orseismic reflection) is a method ofexploration geophysicsthat uses the principles
ofseismologyto estimate the properties of theEarth's subsurface fromreflectedseismic waves.
•The method requires a controlledseismic sourceof energy, such asdynamiteorTovexblast, a specializedair
gunor a seismic vibrator.
•Reflection seismology is similar tosonarandecholocation.
Seismic Reflection Outlines
Seismic reflection data
30
•Reflection seismology(orseismic reflection) is a method ofexploration geophysicsthat uses the principles
ofseismologyto estimate the properties of theEarth's subsurface fromreflectedseismic waves.
•The method requires a controlledseismic sourceof energy, such asdynamiteorTovexblast, a specializedair
gunor a seismic vibrator.
•Reflection seismology is similar tosonarandecholocation.
Seismic Reflection Outlines
Seismic reflection data
30
Amplitude versus offset
•Ingeophysicsandreflection seismology,amplitude versus offset(AVO) oramplitude variation with offsetis the
general term for referring to the dependency of theseismic attribute,amplitude, with the distance between the
source and receiver (the offset).
•AVO analysis is a technique thatgeophysicistscan execute on seismic data to determine a rock'sfluid
content,porosity,densityorseismic velocity, shear wave information, fluid indicators (hydrocarbon
indications).
•The phenomenon is based on the relationship between thereflection coefficientand theangle of incidenceand
has been understood since the early 20th century whenKarl Zoeppritzwrote down theZoeppritz equations.
•Due to its physical origin, AVO can also be known asamplitude 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)
31
•Ingeophysicsandreflection seismology,amplitude versus offset(AVO) oramplitude variation with offsetis the
general term for referring to the dependency of theseismic attribute,amplitude, with the distance between the
source and receiver (the offset).
•AVO analysis is a technique thatgeophysicistscan execute on seismic data to determine a rock'sfluid
content,porosity,densityorseismic velocity, shear wave information, fluid indicators (hydrocarbon
indications).
•The phenomenon is based on the relationship between thereflection coefficientand theangle of incidenceand
has been understood since the early 20th century whenKarl Zoeppritzwrote down theZoeppritz equations.
•Due to its physical origin, AVO can also be known asamplitude 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)
31
Normal moveout
•Inreflection seismology,normal moveout(NMO) describes the effect that the distance between a seismic
source and a receiver (the offset) has on the arrival time of a reflection in the form of an increase of time with
offset.
•The relationship between arrival time and offset ishyperbolicand it is the principal criterion that
ageophysicistuses to decide whether an event is a reflection or not.
•It is distinguished from dip moveout (DMO), the systematic change in arrival time due to a dipping layer.
32
•Inreflection seismology,normal moveout(NMO) describes the effect that the distance between a seismic
source and a receiver (the offset) has on the arrival time of a reflection in the form of an increase of time with
offset.
•The relationship between arrival time and offset ishyperbolicand it is the principal criterion that
ageophysicistuses to decide whether an event is a reflection or not.
•It is distinguished from dip moveout (DMO), the systematic change in arrival time due to a dipping layer.
32
stack
•A processedseismicrecordthat contains traces that have
been added together from different records to reduce noise
and improve overall data quality.
•The number of traces that have been added together during
stacking is called the fold.
•To sum traces to improve thesignal-to-noise ratio, reduce
noise and improveseismicdata quality.
•Traces from different shot records with a
commonreflectionpoint, such as commonmidpoint(CMP)
data, are stacked to form a single trace duringseismic
processing.
•Stacking reduces the amount of data by a factor called the
fold.
Diagram of the stacking process.
33
•A processedseismicrecordthat contains traces that have
been added together from different records to reduce noise
and improve overall data quality.
•The number of traces that have been added together during
stacking is called the fold.
•To sum traces to improve thesignal-to-noise ratio, reduce
noise and improveseismicdata quality.
•Traces from different shot records with a
commonreflectionpoint, such as commonmidpoint(CMP)
data, are stacked to form a single trace duringseismic
processing.
•Stacking reduces the amount of data by a factor called the
fold.
Diagram of the stacking process.
33
Stacking velocity
•Inreflection seismology,stacking velocity, orNormal Moveout(NMO) velocity, is the value of the seismic
velocity obtained from the best fit of the traveltime curve by a hyperbola.
•The hyperbolic approximation to the traveltime curve (two-way travel time versus offset) is known as
Normal moveout (NMO).
•The procedure of finding the best fit on common midpoint (CMP) seismic gathers is known as NMO velocity
analysis.
34
•Inreflection seismology,stacking velocity, orNormal Moveout(NMO) velocity, is the value of the seismic
velocity obtained from the best fit of the traveltime curve by a hyperbola.
•The hyperbolic approximation to the traveltime curve (two-way travel time versus offset) is known as
Normal moveout (NMO).
•The procedure of finding the best fit on common midpoint (CMP) seismic gathers is known as NMO velocity
analysis.
34
CMP stacking
•CMP stacking simply meansthe summation of a collection of seismic traces from different records into a
single trace.
•It can be considered as the simplest way for improving the SNR inprestackseismic data processing.
•It can help quickly obtain a meaningful poststack seismic image without wavefield continuation.
35
•CMP stacking simply meansthe summation of a collection of seismic traces from different records into a
single trace.
•It can be considered as the simplest way for improving the SNR inprestackseismic data processing.
•It can help quickly obtain a meaningful poststack seismic image without wavefield continuation.
35
PRE-STACK MIGRATION
•Pre-stack migration is essentially when seismic data isadjusted before the stacking sequence occurs.
•Thepopular form of pre-stack migration is depth migration(PDM).
•PDM requires the user to know more aboutvelocities of the layers.
•Once the user inputs these intothe data with velocity analysis methods, there will besome error in the image.
•This error is caused by dippingreflectors or diffractions.
•The PDM will adjust the pictureaccording to the velocities given.
•Pre-stack migration is often applied only when the layersbeing observed have complicated velocity profiles, orwhen the structures are just too complex to see withpost-stack migration.
•Pre-stack is an important tool inmodeling salt diapirs because of their complexity andthis has immediate benefits if the resolution can pick upany hydrocarbons trapped by the diapir.
•Overall, pre-stack migration, depth and time, is a valuabletool in better imaging seismic data, but it is limited bythe amount of time and money required to conduct apre-stack migration.
•Most of the pre-stack migration will be run when post-stacking has failed to resolve the layersor structures.
•However, with advances in computers,pre-stack migration will eventually become more economical.
36
•Pre-stack migration is essentially when seismic data isadjusted before the stacking sequence occurs.
•Thepopular form of pre-stack migration is depth migration(PDM).
•PDM requires the user to know more aboutvelocities of the layers.
•Once the user inputs these intothe data with velocity analysis methods, there will besome error in the image.
•This error is caused by dippingreflectors or diffractions.
•The PDM will adjust the pictureaccording to the velocities given.
•Pre-stack migration is often applied only when the layersbeing observed have complicated velocity profiles, orwhen the structures are just too complex to see withpost-stack migration.
•Pre-stack is an important tool inmodeling salt diapirs because of their complexity andthis has immediate benefits if the resolution can pick upany hydrocarbons trapped by the diapir.
•Overall, pre-stack migration, depth and time, is a valuabletool in better imaging seismic data, but it is limited bythe amount of time and money required to conduct apre-stack migration.
•Most of the pre-stack migration will be run when post-stacking has failed to resolve the layersor structures.
•However, with advances in computers,pre-stack migration will eventually become more economical.
36
POST-STACK MIGRATION
•Post stack migration is the process of migration in whichthe data is stacked after it has been migrated.
•Thisprocess is for many reasons, mainly because of itsreasonable cost compared to pre-stack migration.
•As inpre-stack migration, post stack migration is based on theidea that all data elements represent either primaryreflections or diffractions.
•This is done by using anoperation involving the rearrangement of seismicinformation so that reflections and diffractions areplotted at their true locations.
•The reason that migrationis needed is due to the fact thatvariable velocities anddipping horizons cause the data to record surfacepositions different from their sub-surface positions.
•Thestacking is accomplished by making a composite recordby combining traces from different records.
•Filtering isinvolved with stacking because of timing errors orwave-shape difference among the data being stacked.
•A disadvantage of using post stack migration comparedto pre-stack migration is that it does not give as clearresults as pre-stack.
•Post stack usually gives good results though, when the dip is small and where events withdifferent dips do not interfere on the migrated section.
37
•Post stack migration is the process of migration in whichthe data is stacked after it has been migrated.
•Thisprocess is for many reasons, mainly because of itsreasonable cost compared to pre-stack migration.
•As inpre-stack migration, post stack migration is based on theidea that all data elements represent either primaryreflections or diffractions.
•This is done by using anoperation involving the rearrangement of seismicinformation so that reflections and diffractions areplotted at their true locations.
•The reason that migrationis needed is due to the fact thatvariable velocities anddipping horizons cause the data to record surfacepositions different from their sub-surface positions.
•Thestacking is accomplished by making a composite recordby combining traces from different records.
•Filtering isinvolved with stacking because of timing errors orwave-shape difference among the data being stacked.
•A disadvantage of using post stack migration comparedto pre-stack migration is that it does not give as clearresults as pre-stack.
•Post stack usually gives good results though, when the dip is small and where events withdifferent dips do not interfere on the migrated section.
37
UPPER) PRE-STACK DEPTH MIGRATION, (LOWER) POST-STACK DEPTH MIGRATION38
Wave laws
39
39
Snell's law
•The mathematical description ofrefraction, or the physical change in the direction of awavefrontas it travels from one medium to another with a change invelocityand partial conversion andreflectionof aP-waveto anS-waveat the interface of the two media.
•Snell's law, one of two laws describing refraction, was formulated in the context of light waves, but is applicable toseismicwaves.
•It is named for Willebrord Snel (1580 to 1626), a Dutch mathematician.
•Snell's law can be written as:
•n1sini=n2sinr,
•wheren1= refractive index of first mediumn2= refractive index of second mediumsini= sine of the angle of incidencesinr= sine of the angle of refraction.
40
•The mathematical description ofrefraction, or the physical change in the direction of awavefrontas it travels from one medium to another with a change invelocityand partial conversion andreflectionof aP-waveto anS-waveat the interface of the two media.
•Snell's law, one of two laws describing refraction, was formulated in the context of light waves, but is applicable toseismicwaves.
•It is named for Willebrord Snel (1580 to 1626), a Dutch mathematician.
•Snell's law can be written as:
•n1sini=n2sinr,
•wheren1= refractive index of first mediumn2= refractive index of second mediumsini= sine of the angle of incidencesinr= sine of the angle of refraction.
40
Zoeppritz equations
•A set of equations that describes thepartitioningof energy in a wavefield relative to itsangle of incidenceat a boundary across which the properties of therockand fluid content changes.
•In geophysics and reflection seismology, the Zoeppritz equations area set of equations that describe the partitioning ofseismic wave energy at an interface, typically a boundary between two different layers of rock
•Ingeophysicsandreflection seismology, theZoeppritz equationsare a set of equations that describe the partitioning ofseismic waveenergy at an interface, due tomode conversion.
•They are named after their author, the GermangeophysicistKarl Bernhard Zoeppritz, who died before they were published in 1919.
•The equations are important in geophysics because they relate the amplitude ofP-wave, incident upon a plane interface, and the amplitude ofreflectedandrefractedP-andS-wavesto theangle of incidence.
•They are the basis for investigating the factors affecting the amplitude of a returning seismic wave when the angle of incidence is altered —also known asamplitude versus offsetanalysis —which is a helpful technique in the detection ofpetroleum reservoirs.
•The Zoeppritz equations were not the first to describe the amplitudes of reflected and refracted waves at a plane interface.
•Cargill Gilston Knottused an approach in terms of potentials almost 20 years earlier, in 1899, to deriveKnott's equations.
•Both approaches are valid, but Zoeppritz's approach is more easily understood.
41
•A set of equations that describes thepartitioningof energy in a wavefield relative to itsangle of incidenceat a boundary across which the properties of therockand fluid content changes.
•In geophysics and reflection seismology, the Zoeppritz equations area set of equations that describe the partitioning ofseismic wave energy at an interface, typically a boundary between two different layers of rock
•Ingeophysicsandreflection seismology, theZoeppritz equationsare a set of equations that describe the partitioning ofseismic waveenergy at an interface, due tomode conversion.
•They are named after their author, the GermangeophysicistKarl Bernhard Zoeppritz, who died before they were published in 1919.
•The equations are important in geophysics because they relate the amplitude ofP-wave, incident upon a plane interface, and the amplitude ofreflectedandrefractedP-andS-wavesto theangle of incidence.
•They are the basis for investigating the factors affecting the amplitude of a returning seismic wave when the angle of incidence is altered —also known asamplitude versus offsetanalysis —which is a helpful technique in the detection ofpetroleum reservoirs.
•The Zoeppritz equations were not the first to describe the amplitudes of reflected and refracted waves at a plane interface.
•Cargill Gilston Knottused an approach in terms of potentials almost 20 years earlier, in 1899, to deriveKnott's equations.
•Both approaches are valid, but Zoeppritz's approach is more easily understood.
41
For an incident plane P-wave of unity amplitude, the continuity conditionsyieldthe four
Zoeppritz equations :
42
Zoeppritz equations :
42
Fermat's principle
•The principle that the path taken by a ray of light from one point to another is that which takes the
minimum time (or the maximum time in select cases), named for its discoverer, French mathematician
Pierre de Fermat (1601 to 1665).
•Snell's law and the laws ofreflectionandrefractionfollow from Fermat's principle.
•Fermat's principle also applies toseismicwaves.
43
•The principle that the path taken by a ray of light from one point to another is that which takes the
minimum time (or the maximum time in select cases), named for its discoverer, French mathematician
Pierre de Fermat (1601 to 1665).
•Snell's law and the laws ofreflectionandrefractionfollow from Fermat's principle.
•Fermat's principle also applies toseismicwaves.
43
Shuey approximation
TheAVO equationsare very important to hydrocarbon exploration and
production because they help to estimate some rock properties, reservoir
fluids and alsoenable to mitigate the drilling operations risks.
Zoeppritz expressions give the refraction and reflection coefficients for
different offsets considering a plane interface that separates two
homogeneous and isotropic layers.
Although, as commented by Yilmaz (2001), Avseth et al. (2005)and
Aleardi et al. (2017), theZoeppritzequations are complex.
The expressions comprehend various factors and the recognition of the
practical meaning for each parameter is not intuitive, as reported in
Sheriff and Geldart (1995)and Rosa (2018).
So, in many cases is useful to work with some simplifications such as
Shuey approximation.
Shuey (1985)proposed a new arrangement for theAki-Richards
equation, which is already a linear approximation of Zoeppritz
expressions.
Gholami & Farshad (2019)paper highlighted the relevance of Shuey
(1985)arrangement in AVO studies, that is widely applied in the
industry.
Shuey (1985)paper shows the angle-dependent reflection amplitude with
the following formula known as Shuey’s three-term AVO equation:44
TheAVO equationsare very important to hydrocarbon exploration and
production because they help to estimate some rock properties, reservoir
fluids and alsoenable to mitigate the drilling operations risks.
Zoeppritz expressions give the refraction and reflection coefficients for
different offsets considering a plane interface that separates two
homogeneous and isotropic layers.
Although, as commented by Yilmaz (2001), Avseth et al. (2005)and
Aleardi et al. (2017), theZoeppritzequations are complex.
The expressions comprehend various factors and the recognition of the
practical meaning for each parameter is not intuitive, as reported in
Sheriff and Geldart (1995)and Rosa (2018).
So, in many cases is useful to work with some simplifications such as
Shuey approximation.
Shuey (1985)proposed a new arrangement for theAki-Richards
equation, which is already a linear approximation of Zoeppritz
expressions.
Gholami & Farshad (2019)paper highlighted the relevance of Shuey
(1985)arrangement in AVO studies, that is widely applied in the
industry.
Shuey (1985)paper shows the angle-dependent reflection amplitude with
the following formula known as Shuey’s three-term AVO equation:44
Comparison to other waves
•A number ofwave modes have been predicted based on the fluidity of the medium
45
•A number ofwave modes have been predicted based on the fluidity of the medium
45
Checkshot survey
Vertical seismic profile
46
Vertical seismic profile
46
Checkshot survey
A type ofborehole seismic datadesigned to measure the seismictraveltimefrom the surface to a known depth.
P-wavevelocityof the formations encountered in a wellbore can be measured directly by lowering ageophoneto eachformationof interest, sending out a source of energy from the surface of the Earth, and recording the resultantsignal.
The data can then be correlated to surface seismic data by correcting thesonic logand generating a syntheticseismogramto confirm or modify seismic interpretations.
It differs from avertical seismic profilein the number and density ofreceiverdepths recorded; geophone positions may be widely and irregularly located in the wellbore, whereas a vertical seismic profile usually has numerous geophones positioned at closely and regularly spaced intervals in the wellbore.
47
A type ofborehole seismic datadesigned to measure the seismictraveltimefrom the surface to a known depth.
P-wavevelocityof the formations encountered in a wellbore can be measured directly by lowering ageophoneto eachformationof interest, sending out a source of energy from the surface of the Earth, and recording the resultantsignal.
The data can then be correlated to surface seismic data by correcting thesonic logand generating a syntheticseismogramto confirm or modify seismic interpretations.
It differs from avertical seismic profilein the number and density ofreceiverdepths recorded; geophone positions may be widely and irregularly located in the wellbore, whereas a vertical seismic profile usually has numerous geophones positioned at closely and regularly spaced intervals in the wellbore.
47
Vertical seismic profile
•Ingeophysics,vertical seismic profile(VSP) is a technique
ofseismicmeasurements used for correlation with surface seismic data.
•The defining characteristic of a VSP (of which there are many types) is
that either the energy source, or the detectors (or sometimes both) are in
aborehole. In the most common type of VSP,hydrophones, or more
oftengeophonesoraccelerometers, in the borehole record reflected seismic
energy originating from aseismic sourceat the surface.
•There are numerous methods for acquiring a vertical seismic profile
(VSP).
•Zero-offset VSPs (A) have sources close to the wellbore directly above
receivers.
•Offset VSPs (B) have sources some distance from the receivers in the
wellbore.
•Walkaway VSPs (C) feature a source that is moved to progressively
farther offset and receivers held in a fixed location.
•Walk-above VSPs (D) accommodate the recording geometry of a deviated
well, having each receiver in a different lateral position and the source
directly above the receiver.
•Salt-proximity VSPs (E) are reflection surveys to help define a salt-
sediment interface near a wellbore by using a source on top of asalt dome
away from the drilling rig. 48
•Ingeophysics,vertical seismic profile(VSP) is a technique
ofseismicmeasurements used for correlation with surface seismic data.
•The defining characteristic of a VSP (of which there are many types) is
that either the energy source, or the detectors (or sometimes both) are in
aborehole. In the most common type of VSP,hydrophones, or more
oftengeophonesoraccelerometers, in the borehole record reflected seismic
energy originating from aseismic sourceat the surface.
•There are numerous methods for acquiring a vertical seismic profile
(VSP).
•Zero-offset VSPs (A) have sources close to the wellbore directly above
receivers.
•Offset VSPs (B) have sources some distance from the receivers in the
wellbore.
•Walkaway VSPs (C) feature a source that is moved to progressively
farther offset and receivers held in a fixed location.
•Walk-above VSPs (D) accommodate the recording geometry of a deviated
well, having each receiver in a different lateral position and the source
directly above the receiver.
•Salt-proximity VSPs (E) are reflection surveys to help define a salt-
sediment interface near a wellbore by using a source on top of asalt dome
away from the drilling rig. 48
Vertical seismic profile (VSP)
•A class ofboreholeseismicmeasurements used forcorrelationwith surface seismic data, for obtaining images of higher resolution than surface seismic images and for looking ahead of thedrill bit; also called a VSP.
•Purely defined, VSP refers to measurements made in a vertical wellbore using geophones inside the wellbore and asourceat the surface near the well.
•In the more general context, VSPs vary in the well configuration, the number and location of sources and geophones, and how they are deployed.
•Most VSPs use a surface seismic source, which is commonly avibratoron land and an air gun in offshore ormarineenvironments.
•VSPs include the zero-offsetVSP,offset VSP,walkaway VSP,walk-above VSP,salt-proximity VSP,shear-waveVSP, and drill-noiseor seismic-while-drilling VSP.
•A VSP is a much more detailedsurveythan a check-shot survey because the geophones are more closely spaced, typically on the order of 25 m [82 ft], whereas a check-shot survey might include measurements of intervals hundreds of meters apart.
•Also, a VSP uses the reflected energy contained in the recordedtraceat eachreceiverposition as well as the first direct path from source to receiver.
•The check-shot survey uses only the direct pathtraveltime. In addition to tying well data to seismic data, the vertical seismic profile also enables converting seismic data tozero-phasedata and distinguishing primary reflections from multiples.
49
•A class ofboreholeseismicmeasurements used forcorrelationwith surface seismic data, for obtaining images of higher resolution than surface seismic images and for looking ahead of thedrill bit; also called a VSP.
•Purely defined, VSP refers to measurements made in a vertical wellbore using geophones inside the wellbore and asourceat the surface near the well.
•In the more general context, VSPs vary in the well configuration, the number and location of sources and geophones, and how they are deployed.
•Most VSPs use a surface seismic source, which is commonly avibratoron land and an air gun in offshore ormarineenvironments.
•VSPs include the zero-offsetVSP,offset VSP,walkaway VSP,walk-above VSP,salt-proximity VSP,shear-waveVSP, and drill-noiseor seismic-while-drilling VSP.
•A VSP is a much more detailedsurveythan a check-shot survey because the geophones are more closely spaced, typically on the order of 25 m [82 ft], whereas a check-shot survey might include measurements of intervals hundreds of meters apart.
•Also, a VSP uses the reflected energy contained in the recordedtraceat eachreceiverposition as well as the first direct path from source to receiver.
•The check-shot survey uses only the direct pathtraveltime. In addition to tying well data to seismic data, the vertical seismic profile also enables converting seismic data tozero-phasedata and distinguishing primary reflections from multiples.
49
•Drill-noise VSPs (F), also known as seismic-while-drilling (SWD) VSPs, use the noise of the drill bit as the source and receivers laid out along the ground.
•Multi-offset VSPs (G) involve a source some distance from numerous receivers in the wellbore.
•A vertical seismic profile is constructed to identify a value known as a source wavelet.
•This is useful when it comes to a process known as deconvolution.
•Deconvolutionallows for a more readable and more focused VSP.
•The idea is that the VSP reports any abnormal seismic activity and deconvolution allows for a more focused profile on these abnormal activities.
•VSPs are used to measure a seismic signal at depth and with that measurement the wavelength at the source of the seismic activity is easily found.
•With the measurement of the source wavelet, geophysicists can carry out deconvolution on the VSP and decrease the reports of all seismic activity and limit the reports to just abnormal or extreme changes in seismic activity.
•In recent years, using a VSP has become more popular in regards toreducing well placement risks as well as improving the monitoring of such wells.
•The advancement in technology for well monitoring has made VSPs more accurate and more precise with the use ofvery long baseline interferometry(VLBI).
•VLBI is an astronomical radio antenna technique that allows for high resolution imaging on a spatial scale.
•Therefore, using these techniques to create a seismic profile produces incredibly accurate images of wavelets and enhances determination of source wavelets.
•VSPs are more suitable than other seismic profiles to host the equipment for VLBI.
•The long vertical length required to create a borehole for a VSP allows for the equipment of a VLBI to analyze data within a larger region. VLBI can produce high resolution results within a region upwards of 50 km.
50
•Multi-offset VSPs (G) involve a source some distance from numerous receivers in the wellbore.
•A vertical seismic profile is constructed to identify a value known as a source wavelet.
•This is useful when it comes to a process known as deconvolution.
•Deconvolutionallows for a more readable and more focused VSP.
•The idea is that the VSP reports any abnormal seismic activity and deconvolution allows for a more focused profile on these abnormal activities.
•VSPs are used to measure a seismic signal at depth and with that measurement the wavelength at the source of the seismic activity is easily found.
•With the measurement of the source wavelet, geophysicists can carry out deconvolution on the VSP and decrease the reports of all seismic activity and limit the reports to just abnormal or extreme changes in seismic activity.
•In recent years, using a VSP has become more popular in regards toreducing well placement risks as well as improving the monitoring of such wells.
•The advancement in technology for well monitoring has made VSPs more accurate and more precise with the use ofvery long baseline interferometry(VLBI).
•VLBI is an astronomical radio antenna technique that allows for high resolution imaging on a spatial scale.
•Therefore, using these techniques to create a seismic profile produces incredibly accurate images of wavelets and enhances determination of source wavelets.
•VSPs are more suitable than other seismic profiles to host the equipment for VLBI.
•The long vertical length required to create a borehole for a VSP allows for the equipment of a VLBI to analyze data within a larger region. VLBI can produce high resolution results within a region upwards of 50 km.
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