EARTHQUAKE SEISMOLOGY I (2023)

introduction
Seismology is the study of the passage ofelasticwaves (see below) through the earth. Seismic seismology is the best tool to study the interior of the earth.

When an earthquake or explosion occurs, some of the energy released is transferred in the form of elastic waves that travel through the earth.

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

The information is then used to determine earthquake locations, underground structures, and so on.

This pendulum mounted seismograph records horizontal movements. The mass is attached to the earth by means of a pendulum and a trunnion is attached to a rod to constrain the movement of the mass only in the horizontal direction.

The spring-loaded seismograph records the vertical movement of the ground. A spring is attached to a mass that is connected to a rod. The bar is attached to a pivot to constrain the mass to move only up and down.

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Basic PhysicsThere is some basic physics and terminology that describes the various aspects of waveform and motion.

loswavelength(λ) is the distance between two adjacent points on the wave that have similar displacements, a wavelength is the distance between consecutive wave crests.

Amplitude(A) of the wave is the maximum displacement of the movements of the particles or the height of the wave crest.

Period(T) is the time it takes for two consecutive waves to pass a reference point or move to complete a cycle.

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

f = 1 / T [Unit: Hertz (Hz) or 1/s]

The speed at which the wavefront travels (or the wave crest) can be captured by plotting the time it takes for the wavefront to travel a known distance:

v= distance / time [unit: m/s]

Or if wavelength and frequency are known:

V = f λ

elastic moduliElasticity is the behavior of a material when it aemphasize(force/area), deforms and changes shape (Print), but returns to its original shape when relieved.

The shape and speed of the seismic waves propagating through the material are controlled by its elastic properties.

The linear relationship between the applied stress σ and the resulting strain ε is:

σ = Ee

E is the so-called constant of proportionalityelastic Module.

We are interested in two types of deformation: uniform compression or expansion and shear deformation:

El volume originally (v₀) Change to final volume (V_F) versus the change in pressureVolumenmodul(K). The bulk modulus is a measure of the incompressibility of the material:

K = V₀(PAGES₀)/(V₀-V_F)

When a solid is deformed by simple shear, a shear stress (γ) is induced by applying a shear stress σ. The ratio of these quantities is the stiffness modulus (G):

G= p/z

The units of modulus of elasticity are the same as those of pressure, i.e. H. MPa or GPa.

Seismic Wells

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There are two different types of waves generated by an earthquake: body wavesjsurface waves

body waves

<![yes !support lists]>·<![exit]>Body waves are seismic waves that propagate through the earth's body.

<![yes !support lists]>·<![exit]>Body waves are reflected and transmitted at interfaces where seismic velocity and/or density changes and obeySnell's law.

The two different types of body waves are:

<![yes !support lists]>· <![exit]>P waves (P stands for Primary or Pressure or Push-Pull). These waves are also calledlongitudinal wavesor compressional waves due to the compression of the particles during their transport. These waves involve compression and thinning of the material as the wave passes, but no rotation. The P wave is transmitted by the back and forth motion of particles along the direction of propagation of the wave. The most correct description of P waves is that they are dilatational or irrotational waves.

<![yes !support lists]>· <![exit]>P waves have the highest velocity and appear first on seismograms.

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<![yes !support lists]>· <![exit]>S waves (S stands for Secondary or Shear or Jolt). Also known astransverse waves, because the motions of the particles are transverse to the direction of motion of the wavefront, or perpendicular to the beam. These waves involve shear and rotation of the material as the wave passes through it, but no change in volume.

<![yes !support lists]>· <![exit]>S waves have slower velocities than P waves and appear after P waves on seismograms.

surface waves

<![yes !support lists]>·<![exit]>Surface waves are seismic waves that travel along the earth's surface and near-surface strata.

<![yes !support lists]>·<![exit]>These waves do not penetrate deep into the earth's interior and are usually produced by shallow earthquakes (nuclear explosions do not produce these surface waves).

<![yes !support lists]>·<![exit]>Surface waves have a larger amplitude and longer duration than body waves.

<![yes !support lists]>·<![exit]>These waves reach the seismograph after the arrival of the P and S waves due to their slower speed. The two different surface waves are:

<![yes !support lists]>· <![exit]>Rayleigh winktor descriptively called "groundroll" in exploration seismology. The motion of the particles of this wave is confined to a vertical plane containing the direction of propagation and receding elliptically. Particle shifts are greatest at the surface and decrease exponentially downwards. Rayleigh waves show dispersion and their speed is not constant but varies with wavelength.This wave is similar to the propagation of sea waves.

<![yes !support lists]>· <![exit]>v_R<V_S

<![yes !support lists]>· <![exit]>The period is typically ~20 s, at a wavelength of ~100 km

<![yes !support lists]>· <![exit]>waves of love(named after A.E.H. Love, who discovered them) move parallel to the ground surface by a transverse movement of particles. This wave is somewhat similar to the S waves.

<![yes !support lists]>· <![exit]>Love waves cannot exist in a unitary solid and can only occur when S-wave velocity generally increases with depth.

<![yes !support lists]>· <![exit]>Its existence is further evidence of the Earth's vertical inhomogeneity.

<![yes !support lists]>· <![exit]>The motion of the particles is transverse and horizontal.

<![yes !support lists]>· <![exit]>In general, the velocities of Love waves are greater than Rayleigh waves, so Love waves arrive on the seismograph before Rayleigh waves.

seismic Wellengeschwindigkeiten

<![yes !support lists]>·<![exit]>The velocities of the P and S waves are given below in relation to a material's density (ρ) and elastic coefficients:

What is seismic refraction?

<![yes !support lists]>Ö <![exit]>Subsurface imaging applications include:

<![yes !support lists]>1.<![exit]>locate buried archaeological sites,

<![yes !support lists]>2.<![exit]>to assess the geological hazards of the subsoil,

<![yes !support lists]>3.<![exit]>Definition of the aquifer geometry

<![yes !support lists]>4.<![exit]>Exploration of fossil fuels and other natural resources.

Seismic behavior of P-waves

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<![yes !support lists]>·<![exit]>If a ray encounters an inhomogeneity in its journey, such as a lithological contact with another rock, the incident ray is transformed into several new rays. A reflected wave enters and exits at the same angle, measured with respect to the normal to the boundary: the angle of incidence is equal to the angle of reflection.

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<![yes !support lists]>Ö <![exit]>According to Snell's law, the path of a ray depends on the wave velocities through different layers.

<![yes !support lists]>Ö <![exit]>For refractive seismology, thecritical angleis to understand the value of the most important viewpoint. When the angle (r) equals 90 degrees, the refracted wave propagates along the interface.

<![yes !support lists]>Ö <![exit]>If r = 90, then sin(r) = 1 and the critical angle (i.e_C) is given by:

I_C= sin^-1(V₁/V₂)

<![yes !support lists]>Ö <![exit]>According to Huygen's wavelet theory, as the critically refracted wave propagates along the boundary, the primary critically refracted wave acts as a source of new secondary wavefronts and ray paths.

<![yes !support lists]>Ö <![exit]>These secondary rays reappear at the critical angle.

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simple refraction model

<![yes !support lists]>Ö <![exit]>Two horizontal layers: In the ideal (technical) world, the easiest way to understand refractive seismology is through a two-layer horizontal model.

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Seismic waves are generated by a source (e.g. a sledgehammer, an explosion, an air gun...).

<![yes !support lists]>Ö <![exit]>Geophone receivers record seismic signals received along the topographic profile.

<![yes !support lists]>Ö <![exit]>Because P-waves travel at the fastest speeds, the first seismic signal received by a geophone represents the arrival of the P-wave.

<![yes !support lists]>Ö <![exit]>Five P waves are of interest in refractive seismology:

<![yes !support lists]>Ö <![exit]>just

<![yes !support lists]>Ö <![exit]>Dive

<![yes !support lists]>Ö <![exit]>reflected

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<![yes !support lists]>Ö <![exit]>Broken

<![yes !support lists]>Ö <![exit]>losdirect waveit spreads out at the edge of the upper layer of the atmosphere (called layer 1).

<![yes !support lists]>Ö <![exit]>A lower layer of the transmitted wave (layer 2) is calleddiving wave.

<![yes !support lists]>Ö <![exit]>Areflected waveoccurs with the same angle of incidence as the angle of emergence.

<![yes !support lists]>Ö <![exit]>If the incident wave hits the critical angle, the critically refracted wave is createdhead shafttravels along the layer 1-layer 2 interface.

<![yes !support lists]>Ö <![exit]>broken wavespropagate from the interface as the head wave propagates, with departure angles equal to the critical angle.

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<![yes !support lists]>Ö <![exit]>With the arrival time data collected, the arrival times of the P waves are noted or calculated from these ismographs.

<![yes !support lists]>Ö <![exit]>Arrival times can be shown ina travel time charto T-X plot, ie P-wave arrival times (usually in milliseconds) as a function of distance (geophone location).

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<![yes !support lists]>Ö <![exit]>This graph shows that at small distances (X) the direct wave comes first from the source.

<![yes !support lists]>Ö <![exit]>At ranges up to the critical distance, only the direct beam and weak (subcritical) reflected beams reach the geophone. The reflected rays are always later than the direct ray.

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<![yes !support lists]>Ö <![exit]>In themcritical distance, direct waves and the first refracted ray arrives. Its amplitude is stronger than the reflected ray, but still later than the direct ray.

<![yes !support lists]>Ö <![exit]>At some distance (thecross the distance), the refracted ray arrives first since it has traveled in V₂long enough at the interface to pick up the direct beam.

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<![yes !support lists]>Ö <![exit]>From the travel time curve we can calculate:

<![yes !support lists]>Ö <![exit]>P-wave propagation velocities through layers 1 and 2 (V₁and V₂)

<![yes !support lists]>Ö <![exit]>layer thickness 1 (H₁).

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<![yes !support lists]>Ö <![exit]>The combination of equations and the interpretation of the T-X diagram are required to obtain these values.

<![yes !support lists]>Ö <![exit]>The transit time of the direct wave is given by:

t_JUST= x/V₁

<![yes !support lists]>Ö <![exit]>Then V1 can be obtained from the slope of direct arrivals passing through the origin.

<![yes !support lists]>Ö <![exit]>The transit time of a reflected ray is given by:

t_{CONSIDERATION}= (x²+ 4 Std₁²)^1/2/V₁

<![yes !support lists]>Ö <![exit]>This is the equation of a hyperbola where H₁is the thickness of the layer.

<![yes !support lists]>Ö <![exit]>The transit time of the broken wave is given by:

t_REVISED= x/V₂+2 Std₁(V₂²–V₁²)^1/2/(V₁v₂)

<![yes !support lists]>Ö <![exit]>See detailed notes and Fowler for full derivations.

<![yes !support lists]>Ö <![exit]>The equation for t_Brokenis that of a straight line ( y = mx + c). The slope is 1/V₂and the t-intercept (i.e. when x = 0) activates H₁to be determined from:

H₁= t_(x=0)(V₁v₂)/2(V₂²–V₁²)^1/2

Two-layer immersion model

<![yes !support lists]>Ö <![exit]>When speaking of immersion layers, one wants to quantify the extent of immersion. For a simple case of two dipping layers, seismic refraction can be used to calculate the dip of the layers.

<![yes !support lists]>Ö <![exit]>For a given survey profile, the sources should be at the beginning of the profile (front shot) and at the end of the profile (back shot).

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<![yes !support lists]>Ö <![exit]>P-wave arrival times for forward and reverse firing can be plotted on a T-X plot.

<![yes !support lists]>Ö <![exit]>By the reciprocal principle, since the ray paths are the same, the time it takes for a ray to traverse the forward and reverse shots must be equal.

<![yes !support lists]>Ö <![exit]>From the T-X diagram, the V1 and V2 velocities for the forward and reverse shots, as well as the time intersection points for the forward and backward broken waves can be calculated.

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Kearey and Brooks (1984) show how this geometry can be analyzed to get h, θ, etc.

Horizontales Mehrschichtmodell
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<![yes !support lists]>Ö <![exit]>Why limit yourself to the interpretation of two horizontal layers?

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<![yes !support lists]>Ö <![exit]>Calculating velocities and layer thicknesses for multiple layers requires patience with many equations full of algebra and trigonometry.

<![yes !support lists]>Ö <![exit]>See Kearey & Brooks (1984), Fowler (1990) for these equations. The interpretation of the T-X graphs remains the same.

<![yes !support lists]>Ö <![exit]>Each slice produces an interpolated refracted wave slowness and time slice that are used to calculate the thickness of the slice.

<![yes !support lists]>Ö <![exit]>This approach leads to an understanding of why seismic rays are reflected back to the earth's surface when V generally increases with depth:

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problems and limitations
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<![yes !support lists]>Ö <![exit]>previous modelsAdopt flat outline interfacesMalleable sequences of sedimentary rocks can form shallow boundaries. However, erosion and uplift produce slightly irregular boundary contacts. More sophisticated algorithms can handle refraction queries when irregular interfaces are expected.

<![yes !support lists]>Ö <![exit]>profile length andPower source limits penetration depththe refractive method. Typically, a profile can only detect features in adepth of one fifth of the length of the survey.

Therefore, refractive imaging of Moho would require profile lengths in excess of a hundred kilometers; a difficult attempt.

<![yes !support lists]>Ö <![exit]>Larger sources could be used for greater depth detection, but certain sources (e.g.explosives) can cause problemsin urban areas.

<![yes !support lists]>Ö <![exit]>The refraction depends on the layers to increase their speed with depth. In whichhidden slow layerSenario, a buried layer is being overlaid by a faster layer. No critical refraction occurs along the interface.

Hence,the refraction will not easily detect the slow layer. All is not lost as reflection seismology could detect the slower layer.

<![yes !support lists]>Ö <![exit]>Seismograms require careful analysisto choose the first arrival times for the shifts. If a thin layer produces first arrivals that cannot be easily identified on a seismogram, the layer may never be identified. Therefore, another layer can be misinterpreted as containing the hidden layer. As a result, the layer thicknesses can increase.

Reflection seismology began to gain traction in the 1920s to begin locating salt domes, an indication of where oil would be found.

The reflection method soon replaced that of refraction after having been tried with numerous successes, the most visible in the petroleum industry.

Let's start with a SingleSubsurface interface

The key is to come up with an equation that represents the time it takes for a given ray to traverse that single layer. First, the seismic velocity through the layer of material propagating the wave must be less than that of the layer directly below, which we assume is infinitely thick.

Hence, by simple time-velocity relationship and geometry:

This can be rewritten (deleting the indices) as:

v²t²= x²+4 Std²

Also

v²t²/4h²- X²/4h²= 1

which has a hyperbolic form:

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What does this arrival time even mean?

Well, the first thing to think about is what you can do with the hyperbola.

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

Therefore, the asymptote of the transit time curve has a slope equal to the reciprocal of the velocity.

Another approach to analyzing the data is toelocity and thickness of ax-Plot²vt²_.Now remember:

By squaring both sides, the equation looks very much like the equation of a straight line.

The slope of the line is the reciprocal of the square of the velocity. The points of intersection result in h by:

seismology exploration

There are many ways in the exploration industry to process reflectance data to provide more information about nearby subsurface. This is beyond this course, but you can read moreMaterial not testable, and also in the following text taken from the Signalworks Pty.Ltd website.

Introduction to data processing in reflection seismology
(de Signalworks Pty. Ltd)
introduction
RReflection seismology is a technique for imaging the geological structure beneath the Earth's surface using sound energy. The technique is mainly used for oil exploration. A source of acoustic energy at the surface sends an acoustic signal to the ground, reflecting some of the energy back to the surface at each geologic interface. A series of geophones or hydrophones detect faint signals bouncing off the surface, which are recorded for further processing. The raw data is very noisy and impossible to interpret, requiring extensive processing to create a picture of Earth's interior.

Figure 1. Collection of marine seismic data.
Seismic data collection.
FFigure 1 illustrates the marine seismic data collection process. The survey boat tows an acoustic source (usually air guns) and a series of hydrophones called streamers. The streamer is typically about 4,000m long and contains arrays of hydrophones typically spaced every 15m. When air guns are fired and release a pulse of compressed air, a pulse of pressure radiates through the water and onto land in a roughly spherical wavefront. The semicircles in Figure 1 show the position of the wavefront at regular time intervals (e.g. every 100 ms). When the wavefront reaches a reflective geological boundary, some of the energy from the wavefront is reflected back to the surface (light gray semicircles). Hydrophones capture this reflected acoustic energy and record it for further processing on the ship.
To simplify seismic acquisition models, energy received at a hydrophone can be assumed to have traveled along a linear ray path from the source to the ground and then reflected off the boundary back to the hydrophone. The optical paths from the source to four hydrophones are shown in Figure 1. The beam paths run perpendicular to the wave fronts.
Principles of the acoustic image.
AAcoustic imaging in its simplest form consists of measuring the time it takes for a pulse to travel from a source to a reflector and back to a receiver. Repeating these measurements over a range of positions allows an image of the reflective surface to be formed. Figure 2 shows the structure of a simple imaging system. In practice, image noise and distortions require more sophisticated data acquisition setups and data processing techniques to obtain accurate images.

Figure 2. Simple acquisition setup.
Ideally, the simple acquisition setup could be used to generate the acoustic image shown in Figure 3. The time delay in the corresponding pulses.

a)..........b)
Figure 3. a) Acoustic image with simple detection and .. b) detail of FirstTrace (ideal case).
Image problems and solutions.
TThe simple imaging technique shown in Figure 2 was used in the early days of seismic imaging but gave poor results. The main problems were:
a sound-- the reflection energy is usually small after traveling a long distance and reflected by a weak reflector. Background noise in the ground, in the air and in the recording electronics can mask the reflection signal.
b) multiples-- the paths of the rays not only traveled from the source to the receiver with a rebound at a reflector, but also followed paths making several intermediate collisions between the reflectors and generating a propagation time that was out of proportion to the depth of the reflector. Events in the image associated with ray paths that produce multiple reflections are called "multiple" and must be removed from the image.
c) Pulse shape of the source-- The source pulse may not be sharp enough to produce a high resolution image and may vary from shot to shot. (Activation of the source to produce a pulse is called a "trigger".)
d) positioning of immersion reflectors-- the acoustic image is created by displaying the trace vertically on the image at each recording location. If a reflector is immersed, the reflection point of the beam path is not vertically below the recording location, but offset to the side. Additional processing is required to correctly position the acoustic image.

a)..........b)
Figure 4. a) Noisy image and ... b) detail of the first trace.
Figure 4 shows the effect of noise on the image. Reflected sound pulses with a maximum amplitude of 1 mV are recorded by the hydrophones. The noisy image shown in the figure contains random noise with a normal amplitude distribution, a mean of 0 mV and a standard deviation of 0.5 mV. The noise has almost completely masked the reflection energy. Reflections cannot be detected in the extracted trace shown in Figure 4(b).
The sum of the repeated recordings taken at the same location can be used to improve the signal-to-noise ratio. Figure 5 shows a set of 32 replicated records. The reflected energy at 156 mS and 416 mS can be vaguely distinguished on this screen, but with a single trace it would be difficult. This figure also shows the result of "stacking" these records. Stacking involves adding each trace and normalizing the resulting summed trace. The reflection energy is amplified and random noise tends to be canceled in the stacked trace (Figure 5(b)), resulting in a higher signal-to-noise (S/N) ratio.

a)..........b)
Figure 5. a) Repeated seismic recordings and ... b) resulting stacked trace.

a)..........b)
Figure 6 a) Trajectory of 'multiple' energy beams and .. b) Trace recorded with multiples at 312 mS.
FFigure 6(a) shows the path of the acoustic energy beam causing two reflections from the reflector 1 between the source and the receiver. The recorded pulse of this energy is called a "multiple" and is seen at 312 mSo in the recorded trace of Figure 6(b). In order to get an acoustic image that resembles reflective layers, multiples must be removed because they are poorly positioned in the image. Pulses of energy that travel directly from source to receiver with a single bounce from reflectors are called "primaries" and produce proportional images of the geology.

a)..........b)
Figure 7. a) Common setup for acquiring depth points and .. b) CDPGather.
FFigure 7(a) shows the data acquisition setup that allows multiple energies to be identified and removed during processing. This is called the Common Depth Point (CDP) method because data is repeatedly recorded along increasing offsets between the source and receiver, but with the ray paths being reflected from the same depth position on each geologic surface. The CDP collection shown in Figure 7(b) shows the traces recorded for all source/receiver pairs. As the distance between the source and receiver increases, the path length of the beam reflected by a reflector increases and the pulse is recorded with a longer time delay. The curved line of pulses in the array corresponding to a particular reflector is called an "event" and its shape is determined by the depth of the reflector and the speed of sound along the ray paths.
It is the shape of the event that allows to identify and remove multiple events with 2D filtering. The ideal shape of these events is hyperbolic and is called the normal exit curve (NMO). When geological strata are flat and have a constant speed of sound, the events have a precise NMO shape. As the geology becomes more complex with tilting strata and rapid variations in velocity, events deviate from the ideal.

a)..........b)
Figure 8. a) NMO-corrected CDP collection and.. b) trace generated by collection stacking.
TThe process of filtering out multiples is called "stacking". This is a two-step process in which the collection is skewed so that the primary events become flat (referred to as "NMO correction"), and then each trace is summed to produce a single stacked trace. The stacked trace is also rescaled by a factor of 1/N, where N is the number of traces added to the stack.
The flat primary reflector flattened out on the crease, but the NMO correction lengthened the pulse on the long offset tracks. This is called "NMO stretching" and reduces the sharpness of the corresponding stacked pulse. This can be seen in the 156 mS event in Figure 8(b) compared to the ideal event shape in Figure 6(b). To reduce the problem, areas of excessive NMO stretch are zeroed ("muted") prior to stacking.
The multi-event at around 312 ms is not smoothed by the primary NMO correction and has reduced amplitude on the stack trace. Figure 8(b) shows that the multiple amplitude was reduced by approximately 50% while the primary amplitudes were preserved. This performance can be improved by increasing the range of offsets recorded in the collection and by increasing the sharpness (or resolution) of the pulses.

a)..........b)
Figure 9. a) CDP Gather (Sharp Acoustic Pulse) y .. b) Stacked Trace.
Figure 9 shows the NMO-corrected CDP collection and stacked trace generated using a sharper acoustic pulse. The sharp pulse has a dominant period of 25 ms compared to the 51 ms previously used. The multiple of the stacking curve is reduced to about a quarter of the amplitude of the primary events.

a)..........b)
Figure 10. a) Raw seismic wavelet and .. b) Wavelet after modeling.
Seismic sources generally produce non-ideal waveforms (or pulses), often having multiple oscillations on a broad waveform and inconsistent shapes from shot to shot. A raw wavelet like that shown in Figure 10(a) can be filtered to remove oscillations and sharpen the pulse to produce a shaped wavelet shown in Figure 10(b). An ideally sharp wavelet improves the resolution and interpretability of the acoustic image.
Figure 11. The reflection point of an immersion reflector is offset from the center of the source/receiver pair.
Figure 11 shows the optical path from a closely spaced source/receiver pair to an immersion reflector. The reflection point is not below the center of the transceiver where it is plotted on a stacked trace section. The process of repositioning the immersion reflectors is called "migration" and the result of this process is a "migrated section". The migration also corrects "bends", hyperbolic events that occur in sections of the pier and emanate from sharp discontinuities in the geology. The migration can be performed in a stack section by adding amplitudes along a hyperbolic curve and placing the scaled sum at the vertex of the hyperbola. This can also be seen from the fact that inflections have collapsed to a point across the entire section of the stack. The shape of the cumulative hyperbola varies along the section and is a function of depth and the shallowest sound velocities. The velocity distribution obtained from previous batch velocity analysis can be used to control the migration process.

a)..........b)
Figure 12. a) Stacked seismic sections and .. b) Migrated.
Figure 12(a) shows a stacked section with a poorly positioned high-angle reflector. The migrated section (Figure 12(b)) shows the dip reflector offset in the upward direction and with a steeper slope.