Seismic trace

Last updated February 21, 2019

In seismology, a seismic trace refers to the recorded curve from a single seismograph when measuring ground movement. The name comes from the curve plotted by a seismograph as the paper roll rotated and the needle left a trace from which information about the subsurface could be extracted. Today's instruments record the data digitally and the word trace has come to mean the digital curve.

Seismology The scientific study of earthquakes and propagation of elastic waves through a planet

Seismology is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other planet-like bodies. The field also includes studies of earthquake environmental effects such as tsunamis as well as diverse seismic sources such as volcanic, tectonic, oceanic, atmospheric, and artificial processes such as explosions. A related field that uses geology to infer information regarding past earthquakes is paleoseismology. A recording of earth motion as a function of time is called a seismogram. A seismologist is a scientist who does research in seismology.

A seismometer is an instrument that responds to ground motions, such as caused by earthquakes, volcanic eruptions, and explosions. Seismometers are usually combined with a timing device and a recording device to form a seismograph. The output of such a device — formerly recorded on paper or film, now recorded and processed digitally — is a seismogram. Such data is used to locate and characterize earthquakes, and to study the earth's internal structure.

Complex seismic trace

The recorded seismic trace is considered the real part of the complex trace. By phase shifting the recorded trace by 90 degrees, we can obtain the imaginary part of the complex trace. The complex seismic trace is a complex function whose real and imaginary part are the previously mentioned.^[1] From the complex trace, one can now define seismic attributes such as the complex amplitude, phase, instantaneous phase and instantaneous frequency.

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line. The adjective real in this context was introduced in the 17th century by René Descartes, who distinguished between real and imaginary roots of polynomials. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2. Included within the irrationals are the transcendental numbers, such as $π$ (3.14159265...). In addition to measuring distance, real numbers can be used to measure quantities such as time, mass, energy, velocity, and many more.

A complex number is a number that can be expressed in the form $a + bi$ , where $a$ and $b$ are real numbers, and $i$ is a solution of the equation $x 2 = -1$ . Because no real number satisfies this equation, $i$ is called an imaginary number. For the complex number $a + bi$ , $a$ is called the real part, and $b$ is called the imaginary part. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers, and are fundamental in many aspects of the scientific description of the natural world.

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit $i$ , which is defined by its property $i 2 = -1$ . The square of an imaginary number $bi$ is $- b 2$ . For example, $5 i$ is an imaginary number, and its square is $-25$ . Zero is considered to be both real and imaginary.

Related Research Articles

In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis. It can be thought of as a modified Cartesian plane, with the real part of a complex number represented by a displacement along the x-axis, and the imaginary part by a displacement along the y-axis.

A seismogram is a graph output by a seismograph. It is a record of the ground motion at a measuring station as a function of time. Seismograms typically record motions in three cartesian axes, with the z axis perpendicular to the Earth's surface and the x- and y- axes parallel to the surface. The energy measured in a seismogram may result from an earthquake or from some other source, such as an explosion. Seismograms can record lots of things, and record many little waves, called microseisms. These tiny microseisms can be caused by heavy traffic near the seismograph, waves hitting a beach, the wind, and any number of other ordinary things that cause some shaking of the seismograph.

In electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. A frequency-domain representation can also include information on the phase shift that must be applied to each sinusoid in order to be able to recombine the frequency components to recover the original time signal.

Seismic tomography is a technique for imaging the subsurface of the Earth with seismic waves produced by earthquakes or explosions. P-, S-, and surface waves can be used for tomographic models of different resolutions based on seismic wavelength, wave source distance, and the seismograph array coverage. The data received at seismometers are used to solve an inverse problem, wherein the locations of reflection and refraction of the wave paths are determined. This solution can be used to create 3D images of velocity anomalies which may be interpreted as structural, thermal, or compositional variations. Geoscientists use these images to better understand core, mantle, and plate tectonic processes.

In mathematics and signal processing, an analytic signal is a complex-valued function that has no negative frequency components. The real and imaginary parts of an analytic signal are real-valued functions related to each other by the Hilbert transform.

A response spectrum is a plot of the peak or steady-state response of a series of oscillators of varying natural frequency, that are forced into motion by the same base vibration or shock. The resulting plot can then be used to pick off the response of any linear system, given its natural frequency of oscillation. One such use is in assessing the peak response of buildings to earthquakes. The science of strong ground motion may use some values from the ground response spectrum for correlation with seismic damage.

Instantaneous phase and instantaneous frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase of a complex-valued function s(t), is the real-valued function:

Seismic Unix is an open source seismic utilities package supported by the Center for Wave Phenomena (CWP) at the Colorado School of Mines (CSM).

The so-called Richter magnitude scale – more accurately, Richter's magnitude scale, or just Richter magnitude – for measuring the strength ("size") of earthquakes refers to the original "magnitude scale" developed by Charles F. Richter and presented in his landmark 1935 paper, and later revised and renamed the Local magnitude scale, denoted as "ML" or "M_L". Because of various shortcomings of the ML scale most seismological authorities now use other scales, such as the moment magnitude scale (M_w ), to report earthquake magnitudes, but much of the news media still refers to these as "Richter" magnitudes. All magnitude scales retain the logarithmic character of the original, and are scaled to have roughly comparable numeric values.

The 2007–2008 Nazko earthquakes were a series of small volcanic earthquakes measuring less than 4.0 on the Richter magnitude scale. They took place in the sparsely populated Nazko area of the Central Interior of British Columbia, Canada starting on October 9, 2007 and ending on June 12, 2008. They occurred just west of Nazko Cone, a small tree-covered cinder cone that last erupted about 7,200 years ago.

In reflection seismology, a seismic attribute is a quantity extracted or derived from seismic data that can be analysed in order to enhance information that might be more subtle in a traditional seismic image, leading to a better geological or geophysical interpretation of the data. Examples of seismic attributes can include measured time, amplitude, frequency and attenuation, in addition to combinations of these. Most seismic attributes are post-stack, but those that use CMP gathers, such as amplitude versus offset (AVO), must be analysed pre-stack. They can be measured along a single seismic trace or across multiple traces within a defined window.

Interferometry examines the general interference phenomena between pairs of signals in order to gain useful information about the subsurface. Seismic interferometry (SI) utilizes the crosscorrelation of signal pairs to reconstruct the impulse response of a given media. Papers by Keiiti Aki (1957), Géza Kunetz, and Jon Claerbout (1968) helped develop the technique for seismic applications and provided the framework upon which modern theory is based.

The Ferndale Museum, located in Ferndale, California, houses and exhibits artifacts, documents and papers from settlement during the California Gold Rush to the present including an active Bosch-Omori seismograph. The area of collection covers the lower Eel River Valley as far south as the Mattole River Valley and west to the Pacific Ocean. Collections include over 6,000 photographs, back issues of the Ferndale Enterprise newspaper, and family papers spanning 140 years.

Dispersive body waves is an important aspect of seismic theory. When a wave propagates subsurface materials both energy dissipation and velocity dispersion takes place. Energy dissipation is frequency dependent and causes decreased resolution of the seismic images when recorded in seismic prospecting. The attendant dispersion is a necessary consequence of the energy dissipation and causes the high frequency waves to travel faster than the low-frequency waves. The consequence for the seismic image is a frequenme-shift of the data, and so correct timings for lithological identification cannot be obtained.

Stabilized inverse Q filtering is a data processing technology for enhancing the resolution of reflection seismology images where the stability of the method used is considered. Q is the anelastic attenuation factor or the seismic quality factor, a measure of the energy loss as the seismic wave moves. To obtain a solution when we make computations with a seismic model we always have to consider the problem of instability and try to obtain a stabilized solution for seismic inverse Q filtering.

Mathematical Q models provide a model of the earth's response to seismic waves. In reflection seismology, the anelastic attenuation factor, often expressed as seismic quality factor or Q, which is inversely proportional to attenuation factor, quantifies the effects of anelastic attenuation on the seismic wavelet caused by fluid movement and grain boundary friction. When a plane wave propagates through a homogeneous viscoelastic medium, the effects of amplitude attenuation and velocity dispersion may be combined conveniently into the single dimensionless parameter, Q. As a seismic wave propagates through a medium, the elastic energy associated with the wave is gradually absorbed by the medium, eventually ending up as heat energy. This is known as absorption and will eventually cause the total disappearance of the seismic wave.

The World-Wide Standardized Seismograph Network (WWSSN) – originally the World-Wide Network of Seismograph Stations (WWNSS) – was a global network of about 120 seismograph stations built in the 1960s that generated an unprecedented collection of high quality seismic data. This data enabled seismology to become a quantitative science, elucidated the focal mechanisms of earthquakes and the structure of the earth's crust, and contributed to the development of plate tectonic theory. The WWSSN is credited with spurring a renaissance in seismological research.

References

↑ Barnes, A.E. (2007). "A tutorial on complex seismic trace analysis". Geophysics. 72: W33–W43. Bibcode:2007Geop...72...33B. doi:10.1190/1.2785048.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[Barnes-1] Barnes, A.E. (2007). "A tutorial on complex seismic trace analysis". Geophysics. 72: W33–W43. Bibcode:2007Geop...72...33B. doi:10.1190/1.2785048.