Seismology

Seismology (from the Greek σεισμός SEISMOS, earth tremor ' and -logy ) is the science of earthquakes and the propagation of seismic waves in solids. As a branch of geophysics, it is the most important method to investigate the inner structure of the earth.

The closely related field of seismology, however, explored the Earth's interior by means of artificially excited seismic waves and one in Applied Geophysics.

• 4.1 Concept of the beam

• 5.1 Benndorf relationship
• 5.2 beam phase
• 5.3 Theoretical duration curves 5.3.1 Strong increase in speed
• 5.3.2 velocity inversion

• 6.1 Seismic Array
• 6.2 beamforming ( beamforming )
• 6.3 grams Vespa

• 7.1 Herglotz -Wiechert method

• 8.1 Geiger method 8.1.1 Station corrections

Tasks

Seismology is preparing to tomographic image the Earth's interior in three dimensions. Hot and cold mass flows are visualized by the anomaly of the velocity of seismic waves. With further improvement of the resolution, it will be possible to represent the material flows in the mantle, which are, first drive for the plate tectonics and second part of the geodynamo that generates Earth's magnetic field.

With the help of seismographs (also called seismometers ) are seismic waves that pass through either the earth or propagate along the surface is recorded. From the durations and amplitudes of these waves, conclusions can be drawn regarding the internal structure of the Earth. The seismic properties of a domain are described by the seismicity. Through Diagrams ( beachballs ) the spatial location of earthquake foci is shown.

In contrast, the seismic uses active sources such as explosions to explore the structure of the crust and upper mantle.

A related area of ​​research is the Erdspektroskopie, which deals with relatively long-wave seismic vibrations and their frequency range studied.

History

Seismology was introduced by the German scientist Emil Wiechert ( founder of seismological station in Göttingen), who invented the first horizontal seismograph in 1899. Other important people in seismology were the Dane Inge Lehmann, the American Charles Francis Richter, German Americans Beno Gutenberg, the Englishman Harold Jeffreys, the New Zealander Keith Edward Bullen and Eric R. Engdahl and Edward A. Flinn, the regionalization scheme for earthquake regions ( Flinn - Engdahl regions) developed.

For the introduction of the first applications in the oil prospecting has a student Wiechert, Ludger Mintrop, excelled.

Modern methods in seismology include the seismic tomography, the receiver functions analysis, the study of precursor phases or wave field investigations.

Seismograms

→ Main article: Seismogram

A central point of seismology is the analysis of seismograms. Seismograms record the movement ( physics ) relative to the resting ground. A distinction is made between different types of earthquakes. A distinction is made between long-distance, regional, local and micro-earthquakes and it may also assess the maximum distance of the earthquake.

Hz are distant earthquakes recorded below 1. These quakes are recorded on global networks, and they have a good signal -to-noise ratio. Regional and local earthquakes shall be recorded in kleinskaligeren networks. These have a few 10 to 1000 km Distance to the epicenter. At these higher-frequency tremor energy is already recorded up to 100 Hz. Micro-earthquakes can only seismic stations in the immediate vicinity, are recorded in the range of a few meters to the epicenter. The sampling rate is at least 1 kHz.

Seismograms are often recorded in three components. The components are orthogonal to each other and are recorded in counts. These are in the pass band is proportional to the vibration velocity of the bottom.

Restitution

Converting the counts outside the pass band is called offset soil in restitution. This increases the signal -to-noise ratio, and improves the ability to identify the phases and times of arrival of the waves. Especially for Magnitudenbestimmung restituted data are important.

Rotation

The coordinate system of a seismogram can be rotated in the direction of the great circle between the earthquake and the seismometer. This is a coordinate transformation from the horizontal components in transverse and radial components. We used the Epizentraldistanz, the distance of the seismometer from the earthquake and the azimuth, the angle at the seismometer Epizentralstrecke measured to north. In addition, we used the Backazimuth, the Epizentralstrecke and the North direction measures the angle between the epicenter. Opposite mathematical convention the angle is measured clockwise.

Seismic rays

Seismic rays are a high-frequency solution of the equation of motion of an elastic earth. They describe the trajectory of the transportation of energy in the earth. The propagation direction of the beam takes place in the direction of the Langsamkeitsvektors or alternatively of the wave number vector. The beam angle is measured between the vertical and the Langsamkeitsvektor. Applying Snell's law that is, after a constant -ray parameter p derived, wherein the beam angle of the earth's radius r and c is the propagation speed of the shaft.

At right angles to the beam is the seismic wavefront. The plane of the wave front is defined by a constant phase. These phases of the wavefronts are measured at a seismic station.

Concept of the beam

The flow of energy in a beam of light is constant at varying cross- section of the bundle. This allows the estimation of amplitudes of seismic rays. For the concept of the beam makes it the assumptions that no diffractions occur and the waves propagate at high frequency. From this concept it follows that a beam with a large cross -section small amplitudes and a beam with a small cross section has large amplitudes.

Travel time curve

→ Main article: Run-time curve

Knowing the time when the earthquake occurred, you can calculate the duration of the seismic rays. From the determined times of seismic rays can be determined by Fermat's principle duration curves. For this purpose, the term is applied against the Epizentraldistanz.

Benndorf relationship

The ray parameter is constant for beams with the same beam angle. For Benndorf relationship, we consider two parallel to the surface incident beams.

It is plotted against the change in the change Epizentraldistanz runtime. The following is the relationship between the beam parameters p, c the propagation speed and the beam angle. Since changing the term of the changes only in the horizontal propagation speed we can contact.

,

The apparent horizontal propagation velocity and the horizontal component is the Langsamkeitsvektors. It follows for the Benndorf relationship that the tangent to a maturity curve plotted against the Epizentraldistanz, the beam parameters normalized corresponds to the radius of the earth. It follows that the beam parameters at the epicenter assumes its highest value, and continuously decreases with distance. In an epicentral distance of 180 °, the beam is incident perpendicular to the surface and the beam parameter is zero. The horizontal apparent velocity increases to infinity. Different observations are made ​​for seismic rays through the core in an epicentral distance greater than 90 ° and at the apex with radiation in the transition zone between the crust and mantle.

Beam phase

The seismic rays are labeled according to their beam path. The nomenclature of these phases is broken down in the tables on the right. It can also create complex phases, such as multiple reflections or [ conversion | Wave conversions ] be named. A reflection of a P-wave on the free surface referred to as PP. Wherein corresponding to multiple reflections, the number of reflections of the phase is preceded. A 4-fold reflected S - wave would thus called 4S. It can also be declared phases that earthquake epicenter lies in great depth and radiates toward the surface. This is referred to as a low- stage and referred to as P-waves pp. In case of strong earthquake, the seismic rays can muster enough energy to run through the core and to be measured on the opposite surface of the earth, this would be referred to as PKIKP. A seismic beam through the inner core may undergo conversion to an S-wave and converted at the transition to the outer core back into a P-wave. This PKJKP phase could not be clearly identified so far, because the PS transmission coefficients have very small amplitudes.

Theoretical duration curves

In the Earth's interior, there are areas with strong contrasts of seismic propagation velocities.

Strong increase in speed

At the crust - mantle boundary, the propagation velocity increases sharply. The timing chart of such a zone is two concave branches which are connected by a convex returning branch. The two peaks where the three branches each are defined by the seismic rays at the edge of the transition zone. These peaks are called critical points or cusps, they put the travel time curve continued steadily. Between the critical points of the travel time curve is ambiguous. The beam parameters as a function of the Epizentraldistanz is a continuous monotone decreasing function, also it is ambiguous between the critical points. The inverse function, however, can be determined uniquely.

Velocity inversion

In the transition zone of sheath to core, the velocity decreases with depth. This inversion zone forms a zone to which no seismic rays reach the surface. The shadow zone is generated by the zone at depth, in the rays are no vertices.

Array seismology

Array seismology improves the signal -to-noise ratio and allows the direct measurement of the horizontal slowness. Finally, it allows to determine phase assignments and to distinguish and determine the focal depth.

Seismic array

A seismic array is the spatial arrangement of seismometers with identical characteristics and central data collection. This can be Geophonketten, Refraktionsauslagen or seismic networks. Teleseismic quakes can best be evaluated, since the wave fronts hardly change their signal via the display and thus have a high degree of coherence.

Beamforming ( beamforming )

In the beamforming any station is monitored and all incoming signals are normalized against the horizontal slowness of the arrival time of the corresponding station. These signals can then be stacked. This improves the signal-to- noise ratio because the noise stochastically occurring are superimposed destructive. In addition, this treatment of the data acts as a wavenumber filter. To this end, we can calculate the power consumption of the tuned to the slowness beam. From this calculation result is a weighting factor that is referred to as array response function:

,

Where N is the number of seismic stations, k is the wave number and r is the distance. Ideally, the array response function of the Dirac delta function is approximated, this weakens signals with different slowness from ideal. This method is related to the Common Midpoint method in applied seismology.

Vespa grams

To locate later arriving phases, Vespa frames can be created. To this end, the weaker phases of the coda of the stronger phases are highlighted. Since both phases of the same source are taken, they differ only in the slowness. It divides the seismogram into several time intervals and determined for each interval the directional beams with varying amount of slowness. Subsequently, the slowness is plotted against time.

Velocity inversion

The running time can be from a given velocity model of the subsurface easily determined. The inverse problem is to determine the velocity model from the measured transit times. For a soil in which the velocity increases with depth, can be solved analytically with the Herglotz -Wiechert equation of this problem. If the velocity model is more complex, a numerical iterative, linearized approach is taken. This is known as velocity or simultaneous tomography inversion. The approach of the velocity tomography, however, is often ill-posed, ambiguous and has poor resolution. Moreover, it converges slowly; some models are similarly good pictures of the velocity model. These reasons make a good starting model of the subsurface irreplaceable.

Herglotz -Wiechert method

The Herglotz -Wiechert method is used to create a 1D velocity model from measured velocity-time curves. A basic requirement for this method is that the velocity increases monotonically with increasing depth. This means that in the subsoil must be no inversion zones or low-speed zones. However, these zones can be identified and excluded. From the formula for the Epizentraldistanz, a change of variables and integration by parts, the following formula results:

And wherein the Epizentraldistanz, the beam parameters as a function of the normalized radius and the Epizentraldistanz are on the propagation speed. This analytical approach solves uniquely the inverse problem. However, some problems can not be solved:

• The relationship between the duration and the beam parameters and the propagation velocity is not linear. Small changes in the propagation velocity thus lead to disproportionate changes in the duration or the beam parameter.
• Triplikationen in running times, especially late arrivals are difficult to measure, but necessary to derive an unambiguous velocity depth function.
• Low velocity zones can not be resolved.
• Since continuous functions for the duration and the beam parameters are required, must be interpolated. However, these results vary with the interpolation method.

Localization

The localization of earthquakes used to determine the epicenter. It is in this case the hypocenter, the epicenter, which is the projection of the hypocenter on the Earth's surface and determined the seismic moment.

Geiger method

The Geiger method is an iterative gradient method for the localization of earthquake foci. For used from seismograms specified arrival time. In this case, it is assumed that more than four times of arrival may be measured at more than two stations. Usually, several stations are considered. It is also assumed that the velocity model of the subsurface is known. The arrival time of seismic waves of the phase is thus a non-linear function of four unknowns, the range of time and the three coordinates. For the Geiger method with a coarse knowledge of the cooker parameters, the inversion problem was linearized:

,

The arrival time residuals, G is the Jacobian matrix and the unknown model vector. This system of equations is generally determined and can be solved by minimizing the error squares. Thus, the improved oven parameters can be corrected or improved by re- use of this method. In the matrices of linear dependencies can arise which can not be independently determined parameters.

The depth of the epicenter can be well PKP or PKiKP phases dissolve, whereas Pn and Sn phases are completely unsuitable for it. The PKP and the PKiKP phases are difficult to demonstrate in seismograms. The epicenter of an earthquake can be best resolved if the Epizentraldistanz 2-5 degrees. From geometrical considerations it follows that the angle is approximately 90 degrees. Simultaneous use of the P- and S- arrival times increases the solubility of the hypocenter enormously since repealed by the dependence of seismic velocity, proportionalities in the Jacobian matrix. The reading error for S -phase is considerably higher.

Station corrections

The velocity model of the subsurface poses particular problems in the surface region, since there strong heterogeneities occur by weathering and sedimentation. The deviations can cause errors in the localization of up to 10 km. At these stations the mean time residuals are determined from a large set of locating earthquakes. It is assumed that phases always have the same runtime error.