seismology

The Seismology ( ancient Greek σεισμός SEISMOS "(earth) Shake earthquake" and -logie ) is the study of earthquakes and the propagation of seismic waves in solid bodies . As a branch of geophysics , it is the most important method for researching the internal structure of the earth . The closely related field of seismics , on the other hand, explores the interior of the earth using artificially excited seismic waves and is part of applied geophysics . The measuring instruments for both research areas are located in over 300 seismological measuring stations worldwide .

tasks

The Seismology is preparing to the Earth's interior tomographic imaging in three dimensions. Hot and cold mass flows are made visible through the anomaly of the speed of seismic waves. If the resolution is improved further, it will be possible to display the material flows in the earth's mantle , which are firstly the drive for plate tectonics and secondly part of the geodynamics that generate the earth's magnetic field.

With the help of seismographs (also called seismometers) seismic waves that either traverse the earth or spread along the surface are recorded. Conclusions about the internal structure of the earth can be drawn from the transit times and amplitudes of these waves. The seismic properties of an area are described by seismicity . The spatial location of earthquake centers is shown by diagrams ( beach balls ).

In contrast, seismics uses active sources such as explosions to explore the structure of the earth's crust and the upper mantle.

A related research area is earth spectroscopy , which deals with comparatively long-wave seismic oscillations and examines their frequency spectrum .

history

One of the fathers of seismology is Ernst von Rebeur-Paschwitz , who in 1889 managed to record an earthquake, which was still accidental, and who published his findings. Seismology was introduced as a separate science by the German scientist Emil Wiechert (founder of the earthquake station in Göttingen ), who invented the first horizontal seismograph in 1899 . Other important persons in seismology were the Danish Inge Lehmann , the American Charles Francis Richter , the German-American Beno Gutenberg , the English Harold Jeffreys , the New Zealander Keith Edward Bullen as well as Eric R. Engdahl and Edward A. Flinn, who developed a regionalization scheme for earthquake regions ( Flinn-Engdahl regions ).

A pupil of Wiechert's, Ludger Mintrop , excelled with regard to the introduction of the first applications in oil prospecting .

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

Seismograms

→ Main article: Seismogram

A central point in seismology is the evaluation of seismograms. Seismograms record the movement (physics) relative to the stationary earth. A distinction is made between different types of earthquake. A distinction is made between long-range, regional, local and microquakes and can also be used to assess the maximum distance of the earthquake.

Remote tremors are recorded below 1 Hz. These earthquakes are recorded on global networks and they have a good signal-to-noise ratio . Regional and local earthquakes must be recorded in smaller-scale networks. These are a few 10 to 1000 km from the epicenter . During these quakes, higher-frequency energy up to 100 Hz is recorded. Microquakes can only be recorded by seismic stations in the immediate vicinity, within a few meters of the epicenter. The minimum sampling rate is 1 kHz.

Seismograms are often recorded in three components. The components are orthogonal to each other and are recorded in counts . In the passage area, these are proportional to the vibration speed of the floor.

restitution

The conversion of the counts outside the range into ground displacement is called restitution. This increases the signal-to-noise ratio and improves the possibilities of identifying the phases and arrival times of the waves. Restituted data are particularly important for determining the magnitude .

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 into transverse and radial components. One uses the epicentral distance, the distance of the seismometer from the earthquake and the azimuth , the angle measured on the seismometer of the epicentral route to the north. In addition, the backazimuth is used, which measures the angle between the epicentral line and the north direction at the epicenter. Contrary to mathematical conventions, 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 energy transport in the earth. The direction of propagation of the beam occurs in the direction of the slowness vector or, alternatively, the wavenumber vector . The beam angle is measured between the vertical and the slowness vector. Using Snell's law of refraction , a constant beam parameter p can be derived, where the beam angle, r is the radius of the earth and c is the speed of propagation of the wave. ${\displaystyle p={\frac {r\cdot \sin \varphi }{c}}}$ ${\displaystyle \varphi }$

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

Concept of the beam

The energy flow in a bundle of rays is constant with a varying cross-section of the bundle. This enables the amplitudes of the seismic beams to be estimated. For the concept of the bundle of rays one makes the assumptions that no diffractions occur and that the waves propagate at high frequencies. It follows from this concept that a beam with a large cross-section has small amplitudes and a beam with a small cross-section has large amplitudes.

Maturity curve

Seismic rays of different phases in the earth's interior

Global phases	nomenclature
P wave through crust and mantle	P
P wave through outer core	K
P wave through inner core	I.
S-wave through the crust and mantle	S.
S-wave through inner core	J
Tertiary wave (partial propagation through ocean)	T

Surface wave	nomenclature
Long-period surface wave (indefinite)	L.
Rayleigh wave	R.
Love wave	Q
Long-period coat love wave	G
Long-period Rayleigh wave (generally Airy phase)	LR
Long-period love wave (usually Airy phase)	LQ

Sky wave phase	nomenclature
P wave apex in upper crust (granitic)	G
P-wave apex in upper crust (basaltic)	b
Refraction in the upper mantle	n
External reflection on the Moho	m
External reflection external core	c
External reflection, inner core	i
Reflection on a discontinuity	z
Diffracted wave	diff

→ Main article: maturity curve

Knowing the time when the earthquake occurred, one can calculate the duration of the seismic rays. From the determined transit times of the seismic rays, transit time curves can be determined according to Fermat's principle . For this purpose, the running time is plotted against the epicentral distance.

Benndorf relationship

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

${\displaystyle {\frac {{\text{d}}\tau }{{\text{d}}x}}={\frac {r_{E}\cdot \sin \varphi }{c(z)}}=p}$

The change in the running time is plotted against the change in the epicentral distance. The following is the relationship between the beam parameter p , the propagation speed c and the beam angle . Since the term of the changes only changes in the horizontal velocity of propagation, we can set. ${\displaystyle {\text{d}}\tau }$ ${\displaystyle {\text{d}}x}$ ${\displaystyle \varphi }$ ${\displaystyle \varphi =90^{\circ }}$

${\displaystyle {\frac {{\text{d}}\tau }{{\text{d}}x}}={\frac {1}{c_{\mathrm {hor} }}}=s_{\mathrm {hor} }={\frac {p}{r_{E}}}}$,

where is the apparent horizontal velocity of propagation and the horizontal component of the slowness vector. From this it follows for the Benndorf relationship that the tangent on a runtime curve, plotted against the epicentral distance, corresponds to the ray parameter normalized to the earth's radius. It follows that the beam parameter in the epicenter assumes its highest value and continuously decreases with distance. At an epicentral distance of 180 °, the ray is incident perpendicular to the surface and the ray parameter becomes zero. The horizontal apparent speed increases to infinity. Deviating observations are made for seismic rays through the core at an epicentral distance of over 90 ° and for rays with the apex in the transition zone between the crust and mantle . ${\displaystyle {\frac {1}{c_{\mathrm {hor} }}}}$ ${\displaystyle s_{\mathrm {hor} }}$

Jet phases

The seismic rays are named according to their path. The nomenclature of these phases is broken down in the tables on the right. Complex phases such as multiple reflections or wave conversions can also be named. A reflection of a P-wave on the free surface is called PP . In the case of corresponding multiple reflections, the number of reflections precedes the phase. A quadruple reflected S wave would thus be referred to as 4S . Phases can also be declared that the earthquake focus lies at great depth and radiates towards the surface. This is called the depth phase and for P waves it is called pP . During strong earthquakes, the seismic rays can generate enough energy to run through the core and be measured on the opposite surface of the earth, this would be referred to as PKIKP . A seismic beam through the inner core can be converted into an S-wave and converted back into a P-wave at the transition to the outer core. This PKJKP phase could not yet be clearly identified because the PS transmission coefficients have very small amplitudes .

Theoretical runtime curves

In the interior of the earth there are zones with strong contrasts in the seismic propagation speeds.

Strong increase in speed

At the crust-mantle boundary, the speed of propagation increases sharply. The transit time diagram of such a zone shows two concave branches that are connected by a convex returning branch. The two tips on which the three branches are each defined by the seismic rays at the edge of the transition zone. These peaks are called critical points or cusps; they continue the runtime curve. The runtime curve is ambiguous between the critical points. The beam parameter as a function of the epicentral distance is a continuously monotonically decreasing function; it is also ambiguous between the critical points. The inverse function, however, can be clearly determined.

Velocity inversion

In the transition zone from mantle to core , the speed decreases with depth. This inversion zone forms a zone in which no seismic rays reach the surface. The shadow zone is generated by the zone in the depth in which there are no ray peaks.

Array seismology

Array seismology improves the signal-to-noise ratio and enables direct measurement of horizontal slowness. It also makes it possible to determine and differentiate between phase inserts and to determine the depth of the focus.

Seismic array

A seismic array is the spatial arrangement of seismometers with identical characteristics and central data acquisition . These can be geophone chains, refraction displays or seismic networks. Teleseismic earthquakes can be evaluated best, since the wave fronts hardly change their signal over the display and thus have a high level of coherence .

Beamforming

Any station is observed during the directional beam formation and all incoming signals are normalized to the arrival time of the corresponding station based on the horizontal slowness. These signals can now be stacked . This improves the signal-to-noise ratio, as the stochastically occurring interference signals are destructively superimposed. This processing of the data also acts as a wavenumber filter . To do this, one calculates the energy consumption of the directional beam adjusted to the slowness. This calculation results in a weighting factor called the array response function:

${\displaystyle \left|{\frac {1}{N}}\sum \limits _{m=0}^{N-1}e^{i\left({\vec {k}}-{\vec {k}}_{0}\right){\vec {r}}_{m}}\right|^{2}}$,

where N is the number of seismic stations, k is the wave number and r is the distance. In the ideal case, the array response function is approximated to Dirac's delta function , this ideally attenuates signals with a different slowness. This method is related to the common midpoint method in applied seismics.

Vespagramm

Vespagrams can be created to locate phases that arrive later. For this purpose, the weaker phases from the coda of the stronger phases are emphasized. Since both phases come from the same source, they only differ in the slowness. The seismogram is divided into several time intervals and the directional rays with varying amounts of slowness are determined for each interval. Then the slowness is applied against the time.

Velocity inversion

The running time can easily be determined from a given speed model of the subsurface. The inverse problem is to determine the speed model from the measured transit times. For an earth in which the speed increases with depth, this problem can be solved analytically with the Herglotz-Wiechert equation . If the speed model is more complex, a numerically iterative , linearized approach is used. This is known as velocity tomography or simultaneous inversion. The speed tomography approach, however, is often poorly placed , ambiguous and has poor resolution . It is also slowly converging ; some models are similarly good pictures of the speed model. These reasons make a good starting model of the underground irreplaceable.

Herglotz-Wiechert method

The Herglotz-Wiechert method is used to create a 1D speed model from measured runtime curves. A basic prerequisite for this method is that the speed increases monotonically with increasing depth . This means that no inversion zones or low-speed zones may occur in the subsurface. However, these zones can be identified and excluded. The following formula results from the formula for the epicentral distance, a variable change and partial integration:

${\displaystyle \pi \ln {\frac {R}{r_{1}}}=\int \limits _{\Delta =0}^{\Delta _{1}}\cosh ^{-1}\left({\frac {p(\Delta )}{\eta _{1}}}\right){\text{d}}\Delta }$

and , wherein the epicentral distance, the beam parameter as a function of the epicentral distance and the radius are normalized to the velocity of propagation. This analytical approach clearly solves the inverse problem. However, some difficulties cannot be solved: ${\displaystyle p(\Delta _{1})=\eta _{1}}$ ${\displaystyle \Delta }$ ${\displaystyle p(\Delta )}$ ${\displaystyle \eta _{1}={\frac {r_{1}}{c(r_{1})}}}$

• The relationship between the transit time or the beam parameter and the propagation speed is non-linear . Small changes in the speed of propagation thus lead to disproportionate changes in the transit time or the beam parameter.
• Triplications in transit times, especially late arrival times, are difficult to measure, but they are necessary in order to derive a clear speed depth function.
• Low speed zones cannot be resolved.
• Since continuous functions are required for the transit time and the beam parameters, interpolation must be carried out. However, these results vary with the interpolation method.

Localization

The localization of earthquakes is used to determine the source of the earthquake . It becomes the hypocenter , the epicenter , which represents the projection of the hypocenter on the earth's surface and determines the seismic moment .

Violinist method

The Geiger method is an iterative gradient method for the localization of earthquake sources. For this purpose, certain arrival times are used from seismograms. It is assumed that more than four arrival times can be measured at more than two stations. Usually several stations are considered. It is also assumed that the speed model of the subsurface is known. The arrival time of the phases of the earthquake waves is thus a non-linear function of four unknowns, the hearth time and the three coordinates . For the Geiger method with a rough knowledge of the focus parameters, the inversion problem was linearized:

${\displaystyle \delta t=G\Delta m}$,

where the time of arrival residuals, G is the Jacobi matrix, and the unknown model vector. This system of equations is usually overdetermined and can be solved by minimizing the error squares. The thus improved hearth parameters can be corrected and further improved by applying this method again. Linear dependencies can arise in the matrices , which means that parameters cannot be determined independently of one another. ${\displaystyle \delta t}$ ${\displaystyle \Delta m}$

The depth of the earthquake focus can be easily resolved by PKP or PKiKP phases, whereas Pn and Sn phases are completely unsuitable for this. However, the PKP and PKiKP phases are difficult to identify in seismograms. The epicenter of an earthquake is best resolved when the epicentral distance is between 2 and 5 degrees. From geometric considerations it follows that the radiation angle is approximately 90 degrees. The simultaneous use of P and S arrival times increases the resolvability of the hypocenter enormously, since the dependence of the seismic speed removes proportionalities in the Jacobi matrix. However, the reading error for S phases is much higher. ${\displaystyle c_{P}\approx {\sqrt {3}}c_{S}}$

Station corrections

The speed model of the subsurface harbors problems, especially in the surface area, since there are strong heterogeneities due to weathering and sediment deposits. The deviations can cause errors in the localization of up to 10 km. At these stations, mean runtime residuals are determined from a large set of localized earthquakes. It is assumed that phases always have the same runtime error.

literature

• Monika Gisler: Divine Nature ?: Formations in the earthquake discourse in Switzerland in the 18th century. Dissertation . Chronos, Zurich 2007, ISBN 978-3-0340-0858-7 .
• Friedemann Wenzel (Ed.): Perspectives in modern seismology. (= Lecture notes in earth sciences. Vol. 105). Springer, Berlin 2005, ISBN 3-540-23712-7 . (English)
• Jan T. Kozák, Rudolf Dušek: Seismological Maps - An Example of Thematic Cartography. In: Cartographica Helvetica. Issue 27, 2003, pp. 27-35. (Full text)
• Hugh Doyle: Seismology. Wiley, Chichester 1995, ISBN 0-471-94869-1 . (English)
• Thorsten Dahm: Lecture notes: Seismology I transit times, localization, tomography. Hamburg 2010.
• E. Wiechert, K. Zoeppritz: About earthquake waves. 1907.
• E. Wiechert, L. Geiger: Determination of the path of earthquake waves in the interior of the earth. In: Physikalische Zeitschrift. 11, 1910, pp. 294-311.
• AA Fitch: Seismic reflection interpretation. Borntraeger, Berlin 1976, pp. 139-142.
• S. Rost, C. Thomas: Array seismology: Methods and applications. In: Reviews of Geophysics. 40 (3), 2002, p. 1008. doi: 10.1029 / 2000RG000100
• Peter M. Shearer: Introduction to Seismology. 2., corr. Edition. Cambridge University Press, 2011, ISBN 978-0-521-70842-5

Web links

Commons : Seismology  - collection of images, videos and audio files

• Podcast interview with Prof. Heiner Igel on the basics of seismology accessed on July 15, 2010
• Online lexicon for the Herglotz-Wiechert process