what causes the velocity of seismic waves to change

Seismic Waves

Introduction
Seismology is the written report of the passage of elastic waves (see below) through the earth. Earthquake seismology is the best tool to study the interior of the earth.

When an earthquake or explosion occurs, part of the energy released is as rubberband waves that are transmitted through the world.

The waves are then detected and recorded by seismograms, which measure, amplify and record the movement of the ground.

The information is then used to determine earthquake locations, the subsurface structures and etc.

This pendulum-mounted seismograph records horizontal motion. The mass is coupled to the Earth by ways of a pendulum and a pivot is attached to a rod to constrain the mass to movement in the horizontal direction merely.

The spring-mounted seismograph records the vertical ground move. A spring is fastened to the mass which is continued to a rod. The rod is attached to a pin to constrain the mass to move in an upward and down direction only.

Basic Physics There is some bones terminology and physics that draw the diverse aspects of wave course and movement.

The wavelength (λ) is the distance between ii next points on the moving ridge that accept similar displacements, one wavelength is the distance betwixt successive crest.

Aamplitude (A) of the wave is the maximum displacement of the particle motions, or the elevation of the ripple crest.

Period (T) is the fourth dimension it takes for two successive waves to pass a reference betoken or the motion to complete one wheel.

The cycle of seismic waves or repetitions in a given unit of time is called frequency (f). Frequency and period are related by this relationship:

f = 1 / T �� [unit: hertz (Hz) or 1/southward]

The speed in which the wavefront (or ripple crest) travel tin can be detected if the time the wavefront takes to reach a known distance is recorded:

V = distance / fourth dimension [unit of measurement: m/due south]

Or if wavelength and frequency are known:

Five= f λ

Elastic Moduli Elasticity is the behavior of a material that when subjected to a stress (force/area), deforms and changes shape (strain), simply returns to original shape when the stress is removed.

The manner and speed of seismic waves travel through material is controlled by their elastic backdrop.

The linear relationship betwixt applied stress, σ, and resulting strain ε is:

σ = Eε

E is the abiding of proportionality chosen an elastic modulus.

We are concerned with 2 types of deformation � uniform compression or expansion, and shear deformation:

The original volume (Five₀) change to last volume (V_F) when compared to the force per unit area change is called bulk modulus (K). The majority modulus is a measure of the incompressibility of the textile:

K = V₀(P-P₀)/(Five₀-5_F)

When deforming a solid country by uncomplicated shear, a shear strain (γ) is induced by applying a shear stress, σ. The ratio of these quantities is the rigidity modulus (G):

One thousand = σ/ γ

Units of elastic modulus are the same every bit force per unit area � i.east. MPa or GPa.

Seismic Waves

In that location are two different types wave produced by an earthquake: body waves and surface waves.

Trunk Waves

� Body waves are seismic waves that travel through the body of the earth.

� Body waves are reflected and transmitted at interfaces where seismic velocity and/or density alter, and they obey Snell'due south law.

The two unlike types of torso waves are:

� P-Waves (P stands for primary or pressure or push-pull). These waves are also chosen longitudinal waves or compressional waves due to particle compression during their transport. These waves involve compression and rarefaction of the fabric equally the wave passes through is but not rotation. P-wave is transmitted by particle motility back and forth forth the direction of propagation of the wave. The most correct description of P-waves is it is a dilational or irrotational waves.

� P-waves has the greatest speed and appears beginning on seismograms.

� Due south-Waves (S stands for secondary or shear or shake). Also known every bit transverse waves, because particle motions are transverse to the direction of motion of the wavefront, or perpendicular to the ray. These waves involve shearing and rotation of the material as the wave passes through it, simply non volume change.

� S-waves accept speeds less than P-waves, and appear on seismograms later P-waves.

Surface Waves

� Surface waves are seismic waves that are guided along the surface of the World and the layers virtually the surface.

� These waves exercise non penetrate the deep interior of the globe, and are normally generated past shallow earthquakes (nuclear explosions do not generate these surface waves).

� Surface waves are larger in aamplitude and longer in duration than trunk waves.

� These waves get in at seismograph after the arrival of P- and S-waves because of their slower velocities. The two unlike surface waves are:

� Rayleigh waves or descriptively called "basis roll" in exploration seismology. The particle motion of this moving ridge is confined to a vertical aeroplane containing the direction of propagation and retrogrades elliptically. The particle displacements are greatest at the surface and decrease exponentially downwards. Rayleigh waves show dispersion, and its velocity is not constant only varies with wavelength. This wave is like to how bounding main waves propagate.

� V_R < V_S

� Period is typically ~ twenty s, with wavelength or ~ 100km

� Beloved waves (named for A.Due east.H. Love, who discovered them) travel past a transverse move of particles that is parallel to the ground surface. This moving ridge is somewhat similar to South-waves.

� Love waves cannot be in a uniform solid, and can merely occur when in that location is a full general increase of S- wave velocity with depth.

� Their being is some other proof of the Earth�s vertical inhomogeneity.

� The particle move is transverse and horizontal.

� Generally, Dear wave velocities are greater than Rayleigh waves, so Love waves make it earlier Rayleigh waves on seismograph.

Seismic Wave Velocities

� The velocities of P- and South-waves are given below in terms of the density (ρ) and rubberband coefficients of a textile:

Vp = √((K+4/3G)/ρ)

Vs =√(Chiliad/ρ)

� If we notation that the bulk modulus (K) and the rigidity modulus (Thousand) are always positive, then evidently the velocity of P-waves must always be greater than S-waves.

� Shear waves (S-waves) cannot propagate through liquid. This is evident when nosotros substitute M = 0 for liquids, so the velocity of S-waves goes to nada.

� This is how information technology was determined that the outer core consists of liquid.

� Some times yous will come up beyond the majority sound velocity:

V_Φ =√(One thousand/ρ)

�������������������� = √(Vp^two -4/3Vs²)

� Also, Vp and Vs are related via Poisson�south ratio (r).

� When a rod is stretched information technology becomes longer but narrower, the ratio to the lateral to longitudinal strain is Poisson�south ratio.

� The ratio of Vp to Vs is given past:

Vp/Vs = [two(ane-r)/(1-2r)]^1/two

� For near rocks, r ~ 0.25, so Vp ~ i.7 Vs.

There are a few more general rules to the velocity ranges of common materials:

o Unsaturated sediments take lower values than saturated sediments.

o Unconsolidated sediments have lower values than consolidated sediments.

o Velocities are very similar in saturated, unconsolidated sediments.

o Weathered rocks take lower values than like rocks that are unweathered.

o Fractured rocks take lower values than like rocks that are unfractured.

Below is a list of velocity estimation of common waves:

For rocks can plot V v. density:

More generally, Birch observed a general relationship betwixt density and seismic moving ridge velocity which helps us constitute the composition of the Globe:

Now see more detailed notes on seismic waves, and you lot might like as well like to expect at the associated practical (optional).

�

Seismic Ray Theory

� When seismic rays travel through the Earth, they encounter changes in M, G and ρ. This causes the rays to be reflected and refracted .

� When seismic energy travels, information technology ideally would do and then in an approximately spherical way:

� The energy at the wave forepart gets weaker as information technology moves from its source. This geometrical spreading of the free energy causes the amplitude to drop. The energy drops off as 10^-2, and the aamplitude as x^-one � this is chosen attenuation .

Layered Media - Normal Incidence

� When a ray hits an interface with normal incidence (ie at right angles to the boundary), some free energy is reflected, while the rest is passed through into the lower purlieus.

� The reflection coefficient (R) is the ratio of the ratio of the reflected ray amplitude to the incident ray amplitude:

R= A_i/A₀

� For normal incidence this is given by:

R= (Z_two-Z_i)/(Z_two+Z_ane)

Where Z is the audio-visual impedance , and given past

Z = ρV

� The transmission coefficient (T) is:

T = A₂/A₀

���������� = 2Z₁/Z₂+Z₁

Oblique Incidence

� When a P-moving ridge is obliquely incident, in that location is a reflected P moving ridge, and the transmitted ray is refracted in accordance with Snell�s Law.

� In improver, some of the compressional energy is converted into shear energy, and a reflected and refracted S-wave is generated besides.

Refraction & Reflection Seismology

Reflection seismology is used mostly in exploration methods, while refraction seismology is apply more in whole Earth studies. Here nosotros will beginning focus on Refraction Seismology

What is Seismic Refraction?

o One can written report subsurface velocity and layer interface structure by analyzing the first arrival times of P-waves (longitudinal or compressional waves) at the surface of the world. This technique is termed seismic refraction.

o Applications of subsurface imaging include:

1. �locating buried archeological sites,

2. assessing subsurface geological hazards,

3. defining aquifer geometry

4. exploring for fossil fuel and other natural resource.

Seismic P-Wave Beliefs

� When a ray encounters an inhomogeneity in its travels, for example a lithological contact with another stone, the incident ray transforms into several new rays. A reflected moving ridge enters and exits at the same bending measured to the normal of the boundary - angle of incidence equals angle of reflection.

o From Snell's Law, a ray path is dependent on the wave velocities through different layers.

o For refraction seismology, the critical bending is the most important angle value to understand. If angle (r) equals 90 degrees, then the refracted wave propagates along the purlieus interface.

o If r = 90, then sin(r) = i, and the critical angle (i_c) is given by:

i_c = sin^-1(5₁/V₂)

o As the critically refracted wave propagates forth the boundary, according to Huygen's Theory of Wavelets, the primary critically refracted wave acts as a source for new secondary moving ridge fronts and ray paths.

o These secondary ray paths exit dorsum to the surface at the critical bending.

Simple Refraction Model

o Ii Horizontal Layers - In the ideal world (of engineering science), refraction seismology is most easily understood through a horizontal ii layer model.

Seismic waves are generated from a source (e.1000. a sledge hammer, explosion, air gun�.).

o Geophone receivers record seismic signals received forth the survey profile.

o Since P-waves travel at the fastest speeds, the offset seismic betoken received by a geophone represents the P-wave inflow.

o Five P-waves are of involvement in refraction seismology:

o direct

o diving

o reflected

o caput

o refracted

�

o The direct wave propagates forth the temper-upper layer (called layer1) boundary.

o A transmitted wave through lower layer (layer 2) is termed a diving wave .

o A reflected wave enters with the aforementioned angle of incidence every bit go out bending.

o If the incident wave hits at the critical bending, the critically refracted caput moving ridge travels along the layer 1-layer 2 interface.

o Refracted waves propagate from the interface as the head moving ridge progresses, with leave angles equal to the critical bending.

o With arrival fourth dimension data collected, arrival times for P-waves are noted or computed from the seismographs.

o Arrival times can be represented on a travel-time graph or T-X plot, that is P-wave arrival times (normally in milliseconds) verses distance (geophone location).

o This plot shows that at small distances (x) from the source, the direct moving ridge arrives starting time.

o At distances upwardly to the critical distance only the direct ray, and weakly (sub-critically) reflected rays arrive at the geophone. The reflected rays are e'er afterwards than the direct ray.

o At the critical distance, directly waves and the commencement refracted ray arrives. Its amplitude is stronger than the reflected ray, but is notwithstanding later on than the direct ray.

o At some altitude (the cross over distance), the refracted ray arrives start, since it has traveled at V₂ for long enough in the interface so as to take hold of upwardly the directly ray.

o From the travel-time curve we tin calculate:

o velocities of P-moving ridge propagation through layers one and 2 (V_one and V₂)

o thickness of layer 1 (H_one).

o To obtain these values, combination of equations and interpretation from the T-X plot is required.

o The travel time of the direct wave is given by:

t _DIRECT = ten/V₁

o So V1 can be obtained from the slope of the directly arrivals, which passes through the origin.

o The travel time for a reflected ray is given by:

t_REFLECTION = (x² + 4H₁ ^two)^i/ii/V_one

o This is the equation for a hyperbola, where H₁ is the layer thickness.

o The travel fourth dimension for the refracted wave is given past:

t_REFACTED = x/5₂ + 2H₁(Five_two ² �V_ane ⁱⁱ)^ane/2/(5₁V₂)

o Run across detailed notes and Fowler for full derivations.

o The equation for t _REFRACTED is that of a straight line ( y = mx + c). The slope gives ane/Five₂ and the intercept on the t axis (i.e. when x=0) enables H_ane to be determined from:

H_i = t_(ten=0)(V_aneV_ii)/2(V₂ ² �V_i ²)^1/ii

Two Layer Dipping Model

o When discussing dipping layers, i wants to quantify the amount of dip. For a simple instance of two dipping layers, seismic refraction can be utilized to calculated dip of the layers.

o For a given survey profile, sources must be located at the beginning of the profile (forward shot) and at the stop of the profile (reverse shot).

o P-wave inflow times for both frontwards and contrary shots can be plotted on a T-10 plot.

o From the Principle of Reciprocity, time required for a ray to travel forth the forrad and contrary shot should exist the same, since the ray pathways are the aforementioned.

o From the T-10 plot, V1 and V2 velocities for forward and reverse shots tin can be calculated, besides as the time-intercepts for forward and reverse refracted waves.

Kearey & Brooks (1984) prove how this geometry can exist analyzed to get h, θ, etc.

Horizontal Multi-Layer Model

o Why only stop with interpretation of two horizontal layers?

o Calculation of layer velocities and thicknesses for multi-layers requires patience with many equations chock full of algebra and trigonometry.

o Delight refer to Kearey & Brooks(1984), Fowler (1990) for these equations. Interpretation of T-Ten plots remains the same.

o Each layer yields an interpolated refracted moving ridge slowness, and time intercept used to calculate layer thickness.

o This approach leads to understanding why seismic rays are reflected back to the surface on Globe every bit V increases generally with depth:

Problems and Limitations

o The preceding models presume planar purlieus interfaces. Conformable sequences of sedimentary rock may form planar boundaries. However, erosion and uplift easily produce irregular boundary contacts. More sophisticated algorithms tin can process refraction surveys where irregular interfaces might be expected.

o Profile length and source free energy limit the depth penetration of the refraction method. Typically, a profile can but detect features at a depth of one-5th survey length.

Thus, refraction imaging of the Moho would require profile lengths of over one hundred kilometers; an difficult experiment.

o Larger sources could be utilized for greater depth detection, but certain sources (e.g. explosives) may cause problems in urban areas.

o Refraction depends on layers to increase in velocity with depth. In the hidden slow layer senario, a buried layer is overlain by a faster layer. No critical refraction will occur along the boundary interface.

Thus, refraction volition not easily detect the slow layer. All is non lost since reflection seismology could detect the slower layer.

o Seismograms crave careful analysis to selection get-go arrival times for layers. If a thin layer produces first arrivals which cannot easily be identified on a seismogram, the layer may never be identified. Thus, another layer may be misinterpreted every bit incorporating the hidden layer. As a effect, layer thicknesses may increase.

Reflection Seismology

Reflection seismology began to accept prominence in the 1920s to brainstorm to locate common salt domes, an indication where oil would be found.

The reflection method soon replaced the refraction after it was proved with numerous successes, the most visible in the petroleum manufacture.

Lets Showtime With a Unmarried Subsurface Interface

The key is to develop an equation which represents the time it takes for a particular ray to travel through this single layer. Get-go, the seismic velocity through the layer of fabric that the wave is propagating needs to exist lower than the layer direct below, which we will assume is infinitely thick.

Therefore, just past simple time-velocity relation and geometry:

This can be re-written (dropping the subscripts) as:

Five²t² = 10ⁱⁱ +4h^two

and then

Vⁱⁱtⁱⁱ/4h² � x²/4h^two = one

which has a hyperbolic grade:

Now, What Does That Arrival Time Mean Anyhow?

Well, the first thing to note is what you tin practice with the hyperbola.

A hyperbola has an asymptote along which the hyperbola approaches. The equation of this line is

Therefore, the asymptote for the travel time curve has a gradient of the reciprocal of the velocity.

Another approach to analysing the data is to get 5elocity and thickness from a plot of 10² v t² _. Now recall:

By squaring both sides, the equation resembles closely the equation of a direct line.

The gradient of the line is the reciprocial of the square of the velocity. The intercepts gives h via:

Exploration Seismology

In the exploration industry there are many ways of processing reflection information then equally to provide more than information nigh the nearly sub-surface. This is beyond this class, but you may read more non-examinable material, and also in the following text taken from the Signalworks Pty. Ltd web site.

An Introduction to Reflection Seismology Information Processing

(from Signalworks Pty. Ltd)

Introduction

R eflection seismology is a technique for imaging the geological structure below the earth's surface using sound free energy. The technique is used primarily for oil exploration. An acoustic energy source at the surface transmits an acoustic bespeak into the world, which reflects some of the energy back toward the surface at each geological interface. An array of geophones or hydrophones detects the faint signals reflected back to the surface, which are recorded for later on processing. The raw data is very noisy and uninterpretable, requiring all-encompassing processing to produce an epitome of the earth'south interior.

Figure ane. Marine Seismic Data Acquisition.

Seismic Information Acquisition.

F igure 1 illustrates the process of marine seismic data conquering. The survey ship trails an audio-visual source (usually compressed air 'guns') and a cord of hydrophones, chosen a streamer. The streamer is usually nearly 4000m in length and contains groups of hydrophones spaced typically every 15m. When the air guns are fired, releasing a pulse of compressed air, a pressure pulse radiates in an approximately spherical wavefront through the h2o and into the globe. The semi-circles in figure 1 point the position the wavefront at regular intervals in time (say every 100mS). When the wavefront reaches a reflecting geological purlieus, some of the wavefront energy is reflected back towards the surface (calorie-free grey semi-circles). This echoed acoustic energy is sensed by the hydrophones and recorded on the ship for later processing.

To simplify seismic acquisition models, the free energy received at a hydrophone can be considered to have travelled along a linear raypath from the source, into the world, and so reflecting from the boundary back to the hydrophone. Raypaths from the source to four hydrophones are shown in effigy 1. The raypaths are perpendicular to the wavefronts.

Principles of Audio-visual Imaging.

A coustic imaging in its simplest form consists of measuring the time taken by a pulse to travel from a source to a reflector and dorsum to a receiver. Repeating these measurements over a range of positions allows an image of the reflecting surface to be formed. Figure ii shows the configuration of a simple imaging system. In practice, racket and imaging distortions crave more elaborate information acquisition configurations and data processing techniques to accomplish authentic imaging.

Figure 2. Simple Conquering Configuration.

Ideally, the simple conquering configuration could be used to produce the audio-visual image shown in figure 3. Each geological interface reflects some of the acoustic signal so that each trace shows a pulse corresponding to each reflector, with an increasing reflector depth resulting in an increasing time delay on the corresponding pulse.

a) ..........b)

Effigy iii. a) Elementary Conquering Acoustic Image and .. b) Detail of First Trace (Ideal case).

Imaging Bug and Solutions.

T he simple imaging technique shown in figure 2 was used in the early days of seismic imaging, just produced poor results. The main bug were:

a) Racket -- the reflection energy is usually small afterward travelling a large distance and bouncing off a weak reflector. Spurious noise in the earth, air and recording electronics can swamp the reflection bespeak.

b) Multiples -- the raypaths non just travelled from source to receiver with ane bounciness off a reflector, but likewise followed paths making several intermediate bounces between reflectors and producing a travel fourth dimension out of proportion to the reflector depth. Events on the prototype associated with raypaths making multiple bounces are chosen 'multiples' and should be removed from the image.

c) Source Pulse Shape -- the source pulse may non be sharp enough to produce a high resolution prototype and may vary in shape from shot to shot. (The activation of the source to produce a pulse is termed a 'shot'.)

d) Positioning of Dipping Reflectors -- the acoustic image is produced by displaying the trace at each record location vertically on the image. If a reflector is dipping, the raypath reflection signal does not prevarication vertically below the tape location, just is get-go to one side. Further processing is required to correctly position the acoustic paradigm.

a) ..........b)

Figure 4. a) Noisy Image and .. b) Detail of Start Trace.

Effigy iv shows the result of racket on the image. The reflected audio-visual pulses are recorded from the hydrophones with a peak aamplitude of 1mV. The noisy image shown in the figure has had random noise added with a normal amplitude distribution, hateful value of 0mV and standard difference of 0.5mV. The dissonance has most completely masked the reflection free energy. The reflections cannot be discerned on the extracted trace shown in figure 4 (b).

Adding together repeated records taken at the same location can be used to meliorate the indicate to noise ratio. Figure 5 shows a series of 32 repeated records. The reflected energy at 156mS and 416mS can be vaguely made out on this display, merely would be hard from a unmarried trace. This figure as well shows the event of 'stacking' these records. Stacking involves summing each trace and normalising the resultant summed trace. The reflection free energy is reinforced and the random noise tends to cancel in the stacked trace (effigy v (b)), resulting in an increased signal to noise ratio (S/North).

a) ..........b)

Figure v. a) Repeated Seismic Records and .. b) Resultant Stacked Trace.

a) ..........b)

Effigy 6 a) Raypath of 'Multiple' Energy and .. b) Recorded Trace with Multiple at 312mS.

F igure 6 (a) shows the raypath of acoustic free energy making two bounces off reflector 1 between the source and receiver. The recorded pulse of this energy is termed a 'multiple' and can be seen at 312mS on the recorded trace of effigy 6 (b). To obtain an acoustic epitome resembling the reflecting layers, multiples must be removed as they are mis-positioned on the image. The pulses of energy that travel directly from source to receiver with a single bounce off the reflectors are termed 'primaries' and produce proportional images of the geology.

a) ..........b)

Figure 7. a) Common Depth Point Acquisition Configuration and .. b) CDP Get together.

F igure 7 (a) shows the data aquisition configuration that allows multiple energy to be identified and removed during processing. This is called the Common Depth Point (CDP) method because the data is repeatedly recorded over increasing source to receiver offsets, but with the raypaths reflecting off the same depth location on each geological surface. The CDP gather shown in figure 7 (b) shows the recorded traces for all source / receiver pairs. Equally the source to receiver starting time increases, the length of the raypath bouncing off a reflector increases and the pulse is recorded at a larger time filibuster. The curved line of pulses on the gather respective to a particular reflector is chosen an 'event', and its shape is determined by the reflector'southward depth and the acoustic velocity along the raypaths.

Information technology is the shape of the event that allows multiple events to be identified and removed past 2d filtering. The platonic shape of these events is hyperbolic and is called a Normal Move Out (NMO) curve. When the geological layers are flat and have constant acoustic velocity, the events have an authentic NMO shape. Equally the geology becomes more circuitous with sloping layers and rapid velocity variations, the events deviate from the platonic shape.

a) ..........b)

Figure eight. a) NMO Corrected CDP Assemble and .. b) Trace Produced past Stacking the Gather.

T he procedure used to filter out the multiples is called 'stacking'. This is a two phase process involving distorting the get together so that the primary events become flat (termed 'NMO correction'), so summing each trace to produce a unmarried stacked trace. The stacked trace is also commonly rescaled past a factor of 1/N, where North is the number of traces added in the stack.

The shallow main reflector has been flattened in the gather, but the NMO correction has stretched out the pulse in the long kickoff traces. This is called 'NMO stretch' and will reduce the sharpness of the corresponding stacked pulse. This is seen in the 156mS issue in effigy 8 (b) when compared to the ideal event shape in figure 6 (b). To reduce the trouble, regions of excessive NMO stretch are zeroed ('muted') before stacking.

The multiple result at about 312mS is not flattened by the master NMO correction and has reduced amplitude on the stack trace. Figure 8 (b) shows that the multiple amplitude has been reduced past near 50% while the chief amplitudes have been preserved. This operation can exist improved by increasing the range of offsets recorded in the gather and increasing the sharpness (or resolution) of the pulses.

a) ..........b)

Effigy ix. a) CDP Gather (Sharp Acoustic Pulse) and .. b) Stacked Trace.

Effigy 9 shows the NMO corrected CDP gather and stacked trace produced using a sharper acoustic pulse. The abrupt pulse has a dominant period of 25mS compared to 51mS used previously. The multiple on the stacked trace is reduced to around a quarter of the aamplitude of the primary events.

a) ..........b)

Effigy 10. a) Raw Seismic Wavelet and .. b) Wavelet later on Shaping.

Seismic sources usually produce non-platonic wavelet (or pulse) shapes, frequently having several oscillations over a broad wavelet and inconsistent shapes from shot to shot. A raw wavelet such as shown in effigy 10 (a) can be filtered to remove oscillations and acuminate the pulse to produce a shaped wavelet shown in figure 10 (b). An ideal abrupt wavelet improves the resolution and interpretability of the acoustic image.

Figure xi. The Reflection Point for a Dipping Reflector is Start from the Middle of the Source / Receiver Pair.

Figure 11 shows the raypath from a almost beginning source / receiver pair downward to a dipping reflector. The reflection bespeak does not lie below the centre of the source / receiver where it is plotted on a stacked trace section. The process of repositioning dipping reflectors is chosen 'migration', and the output of this process is a 'migrated section'. Migration also corrects 'diffractions', which are hyperbola shaped events appearing on stack sections and emanating from sharp discontinuities in the geology. Migration tin can exist performed on a stack department by summing amplitudes along a hyperbolic curve and placing the scaled sum at the apex of the hyperbola. This tin also be viewed equally collapsing diffractions to a betoken over the unabridged stack section. The shape of the summing hyperbolas varies over the section and is a part of the depth and shallower acoustic velocities. The velocity distribution determined from earlier stacking velocity analyses can exist used to control the migration process.

a) ..........b)

Figure 12. a) Stacked and .. b) Migrated Seismic Sections.

Effigy 12 (a) shows a stacked section with a steeply dipping reflector mis-positioned. The migrated department (figure 12 (b)) shows the dipping reflector re-positioned in the up-dip direction and with a steeper gradient.

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Source: https://www.ucl.ac.uk/EarthSci/people/lidunka/GEOL2014/Geophysics4%20-%20Seismic%20waves/SEISMOLOGY%20.htm

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