Moment tensor inversion

Fault-plane size - Moment tensor inversion... 

Inversion methods are used to determine the fracture type and orientation of a rupture (fault), as well as the seismic moment, which describes the rupture area that is related to the released energy from the waveforms of the recorded AE events. As illustrated in Fig. 5.16, the failure of a brittle specimen is accompanied by a sudden release of energy in the form of acoustic waves. Using an inversion algorithm, in combination with three-dimensional localization, a fault plane solution can be determined that enables the analysis of the fracture process in the material. Another more comprehensive method of fracture analysis is the application of moment tensor inversion methods. In this section, some examples of simple inversion techniques are given along with the basics of moment tensor inversion. 

Typical input data for a moment tensor inversion consist of the network geometry (coordinates of the sensors) knowledge of sensor polarity (i.e. whether an upwards deflection at the sensor indicates a compression or dilatation) sensor orientation source coordinates P and/or S-wave displacement amplitudes recorded at each sensor (time-domain inversion) or P and/or S-wave spectral amplitudes (frequency-domain inversion) and the polarities of the wave phases. 

Moment tensor inversion (MTI) can provide quantitative information regarding the failure modes causing the AE. A moment tensor analysis using all the AE waveform data during the loading of a specimen can give insight into the complete failure history. 

Numbers of moment tensor inversion (MTI) techniques have been proposed in the literature. The methods applied differ greatly according to the available data and the purpose of the study. For the purposes of this textbook, it is useful to distinguish between the absolute and relative methods. These broad classes of inversion procedure are based on methods used to estimate the Green s functions, which describe the wave propagation between the source and receiver. 

Andersen LM (2001) A relative moment tensor inversion technique applied to seismicity induced by mining. PhD thesis, University of the Witwatersrand, Johannesburg, p 230... 

Barker JS, Langston CA (1982) Moment tensor inversion of complex earthquakes. Geophys. J. R. Astr. Soc. 46 341-371... 

Dahm T (1996) Relative moment tensor inversion based on ray theory theory and synthetic tests. Geophys. J. Int. 124 245-257... 

Feignier B, Young RP (1992) Moment tensor inversion of induced microseismic events Evidence of nonshear failures in the < M < -2 moment magnitude range, Geophys. Res. Lett. 19 1503-1506... 

The double-difference method has been further developed by Spottis-woode and Linzer [2005]. This method is referred to as the hybrid method because it is a combination of the double difference method and absolute (single event) methods, and is similar to the approach taken by Andersen (now Linzer) [2001] for moment tensor inversions. The hybrid method has evolved from the approach used by Spottiswoode and Milev [1998], who only considered groups of similar events. 

In seismology, linear inversion techniques were proposed to determine the moment tensor component in both time and frequency domains (Stump Johnson 1977) and (Kanamori Given 1981). Although all components of the moment tensor must be determined, the moment tensor inversion with constraints has been normally applied to obtaining stable solutions in seismology (Dziewonski Woodhouse 1981). This is partly because a fault motion of an earthquake is primarily associated with shear motion, corresponding to off-diagonal components in the moment tensor. One application of the moment tensor inversion with constraints is found in rock mechanics (Dai, Labuz et al. 2000). 

In contrast, both tensile motion of diagonal components and shear motion of off-diagonal are definitely present in crack motions as an AE source. Consequently, general treatment on the moment tensor components of diagonal and off-diagonal components is discussed. Elsewhere, another procedure named the relative moment tensor inversion is proposed (Dahm 1996). 

Aki K, Richards PG (1980) Quantitative seismology Theory and methods. Vol. I, WH Freeman and Compaity, San Francisco Dahm T (1996) Relative moment tensor inversion based on ray theory Theory and Synthetic Tests. Geophys. J Int., 124 245-257 Dai ST, Labuz JF, Carvalho F (2000) Softening response of rock observed in plane-strain compression. Trends in Rock Mechanics, Geo SP-102, ASCE, pp 152-163... 

Obviously the practical reach depends also on the intended procedure of the signals. Pure counting of events will work for larger distances than localizing of the source or even more refined methods like the moment tensor inversion. 

Magnitude squared coherence Moment tensor inversion Non-destmctive evaluation Non-destmctive testing Propability density function Polymethylmethacrylat Polyvinylidene fluoride Compressional wave Lead zirconate titanate Radio Detection and Ranging Reinforced concrete Root mean sqtrare Relative moment tensor inversion Shear wave Sottrce function... 

Ghose, S. Hamburger, M.W., Ammon, Ch. J. 1998. Source parameters of moderate-sized earthquakes in the Tien-Shan, Central Asia from regional moment tensor inversion. Geophysical research letters, 16 (25) 3181-3184. 

Example of a Seismic Moment Tensor Inversion for Double-Couple and Non-Double-Couple Cases... 

Long-Period Moment-Tensor Inversion The Global CMT Project... 

Existence of tensile swarm earthquakes is still a question at issue. The percentage of the non-DC part in the moment tensor of tensile events is fairly sensitive to the deviation of the slip vector, for example, a deviation of ot = 5° out of the fault plane generates up to 20 % of the non-DC components (Fig. 2 of Vavrycuk 2001). However, even large non-DC components can be an artifact of the inconsistency of data, which are inverted for moment tensor. Typically, insufficient distribution of sensors around the focus gives rise to apparently large fictitious non-DC components, particularly of CLVD. Further causes can be inaccurate or noisy data used for the moment-tensor inversion, inaccurate localization of the hypocenter, or a poor seismic-velocity model of the area under study. 

Global centroid-moment-tensor inversion Long-period earthquake analysis... 

Long-Period Moment-Tensor Inversion The Global CMT Project, Fig.l Kernel east-west seismograms for a hypothetical deep earthquake (/i = 500 km) in Bolivia recorded at a station in Los Angeles, California. Each trace corresponds to the motion associated with a single moment-tensor element/. The ground motion has been filtered between 30 and 300 s... 

Long-Period Moment-Tensor Inversion The Global analyses in 2012. Stations that contributed data for more CMT Project, Fig. 2 Map showing the locations of than 200 earthquakes ate shown with hexagons, other 206 stations that contributed seismograms to the GCMT stations are shown with squares... 

Long-Period Moment-Tensor Inversion The Global CMT Project, Fig. 3 A selection of observed black) and modeled red) waveforms for the May 20,2012, Mn = 6.1 Emilia-Romagna, Italy, earthquake (875 waveforms were used in the CMT inversirai). The station, network, and channel of motion are given to the right of each pair of... 

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