Moment Tensor Solutions

ISOLA software package has been developed to invert local or regional full-wave seismograms for single- and multiple-point source models. The code was introduced in 2003; since then it has been continually upgraded, and, presently, it can be considered a well-established tool, used worldwide. Originally, the code name came from ‘isolated asperities’, to be resolved at fault planes of large earthquakes. However, with time, the code has been adapted for very diverse applications, ranging from Mw 0.3 to Mw 9. Many research papers based on usage of ISOLA have been published (see References). Almost every new application is challenging—hence the code is continually updated. The objective of this work is to explain the basic principles of the method, review code status, demonstrate a few examples to attract new users, and shortly touch also future development. The code is free, and can be downloaded together with manual and test examples from http://seismo.geology.upatras.gr/isola/ (last accessed March 2018).

Seismic moment tensors of earthquakes in anisotropic media have more complicated properties than in isotropic media. For example. planar shear faulting produces pure double-couple mechanism in isotropy, but generally non-double-couple mechanism in anisotropy. The effects of anisotropy on moment tensors are numerically modelled and exemplified on acoustic emissions measured in the lab, on microearthquakes in the upper crust and on large deep-focus earthquakes in the Tonga subducting slab.

When the wavelength of a seismic signal of interest is much longer than the dimension of the internal seismic source that generates the signal, whether it is an earthquake, an underground explosion or an underground mine collapse, the seismic source may be represented by a symmetric second-order moment tensor.

For the past two decades, the Berkeley Seismological Laboratory has implemented and utilized as part of its routine operations a regional distance.

The main aim of this study is to describe several tools for testing the stability and resolution of waveform inversion focal mechanisms already successfully adopted for crustal earthquakes occurred in the Calabrian Arc region,

Studying regularities of the spatial distribution and temporal variations of tectonic stress is one of the most important issues in a number of disciplines of the Earth sciences. In geodynamics, the problem of understanding of the stress state in the Earth’s crust and in the lithosphere is associated with the need to explain the mechanism of formation of the tectonic structures of various scale levels. In seismology, this is a problem of studying the formation mechanism of the earthquake source at the afterschock stage and the development of the post seismic relaxation at the aftershock stage. In geology, a stress state helps to establish interrelations of the formation conditions of the complex structures, discontinuous structures (slip faults) and other deformation structures with mineral deposits. In mining and oil production, stress data provide a safe and efficient exploration of natural resources.

The seismic moment tensor is a representation of a seismic source, described mathematically by a symmetric tensor of second order.

Moment tensors are a useful tool to characterize different aspects about the mechanics of hydraulic stimulations.

In recent decades, the earthquake mechanism, regardless of scale, has commonly come to be described by the moment tensor (MT).

How continental areas deform has been a subject of intense research, especially in the prism of plate tectonics. The distribution of seismicity in continental areas is not confined to a single fault, but earthquakes are distributed over wide zones, hundreds or even thousands wide, which contain many faults. Within these deforming zones, as for example the Alpine-Himalayan Belt, there are blocks, which are relative aseismic, as the region of central Turkey, and are commonly referred to as microplates.

The empirical Green’s tensor spatial derivative (EGTD) method, proposed by Plicka and Zahradnik (1998), has the potential to deal with differences in focal mechanisms between a targeted event and other small events, and to predict the ground motion for an event with an arbitrary focal mechanism.

Seismic moment tensors help us to increase our understanding about e.g. earthquake processes, tectonics, Earth or planetary structure. Based on ground motion measurements of seismic networks their determination is in general standard for all distance ranges, provided the velocity model of the target region is known well enough. For sparse networks in inaccessible terrain and planetary seismology, the waveform inversion for the moment tensor often fails. Rotational ground motions are on the verge of becoming routinely observable with the potential of providing additional constraints for seismic inverse problems. In this study, we test their benefit for the waveform inversion for seismic moment tensors under the condition of sparse networks. We compare the results of (1) inverting only traditional translational data with (2) inverting translational plus rotational data for the cases of only one, two, and three stations. Even for the single station case the inversion results can be improved when including rotational ground motions. However, from data of a single station only, the probability of determining the correct full seismic moment tensor is still low. When using data of two or three stations, the information gain due to rotational ground motions almost doubles. The probability of deriving the correct full moment tensor here is very high.

The determination of earthquake source parameters is of fundamental importance in seismological research. Moment tensor analysis involves fitting theoretical waveforms to observed broadband waveforms and inverting for the moment tensor elements, and allows for the calculation of focal mechanism (strike, dip, and rake), seismic moment (M₀), moment magnitude (M_w) which is calculated directly from M₀, and centroid depth of an earthquake. A comprehensive catalogue of moment tensor solutions is of great importance in seismic hazard analysis and tectonic studies. For example, seismic hazard estimates typically use M_w in earthquake forecasts and risk analysis, and moment release rates along plate boundaries are important in calculating predicted plate motions in tectonic studies.

Centroid Moment Tensor solutions (CMT’s) provide valuable information on the physics of an earthquake source, focal depth, and seismic moment. The earthquake rupture is described in terms of nine generalised force couples (a 3 × 3 matrix) that represent shear dislocation and volume change (see Jost and Herrmann 1989).

Plate tectonics provides a highly successful framework to describe a wide range of geological observations invoking the motion of lithospheric plates. In its simplest form the plates are rigid and earthquakes are confined to boundaries where plates move relative to each other.

The Aegean Sea, is one of the most seismically active areas of the Eastern Mediterranean region (Fig. 1). Generally, North Aegean Sea region has been tectonically developed after the collision of Arabian plate with the Eurasian in the Late Miocene time and the subsequent westward escape of the Anatolian Plate relative to the Eurasian Plate, during the Early Pliocene.

The $$M_w=7.6$$ earthquake, known as Centenary Earthquake, occurred in the Scotia Sea region near the South Orkney Islands, Laurie Island, where is located the permanent Argentinean Antarctic Base Orcadas, here from 1997 operates a seismographic station ORCD, which has recorded several thousands of aftershocks, the most energetic ones recorded by all the instruments of the Antarctic Seismographic Argentinean-Italian Network (ASAIN). The aftershocks data available at ORCD station, till 60 days following the main shock were compiled. The plot of aftershocks rate with time was found to be oscillatory decay. Then, we inverted regional waveforms from ASAIN and International Federation of Digital Seismograph Networks (FSDN) stations to determine source parameters and source time functions for a set of aftershocks with magnitudes in the range 4.3–5.6 $$m_b$$. For the regional inversion we applied a methodology for the determination of the seismic moment tensor by means of full waveform inversion. The results obtained reflect the normal character of the main system fault, characterizing the study area.

A strong earthquake of Mw 6.1 struck Bhutan on September 21, 2009 with casualties of several people. The epicentre of the event was given at latitude 27.34° N and longitude 91.41° E, and depth ~ 10 km (USGS report; http://earthquake.usgs.gov). Shaking from the earthquake was felt in the Bhutan, Tibet and in the adjoining North East region of India including Bangladesh.

This work describes the derivation of the tectonic stress from the inversion of focal mechanisms of double-couple earthquakes. The presented material is based, in large part, on several review papers, lecture notes and practices on the matter, developed by the authors during the last years.

We relocate 27 small earthquakes and invert the state of stress in the East of the Central Marmara basin through re-identification of P and S phases using a joint data set. Also, we derive relative locations of 425 clustered earthquakes with ML ≥ 1.5 in the Marmara Region using the Hypodd software. The main objective is to achieve the definition of geometrical orientations and seismic behaviours of the fault segments. Locating between the 1912 Mürefte and 1999 Izmit earthquakes and being a seismic gap, seismic and geodetic analyzes in the Central Marmara Sea are significant. We use well-defined P and S phases for locations, and completely observable P-wave first motion polarities (FMPs) for simultaneously determined individual fault plane solutions (FPSs) and stress orientations. We get data from 105 seismic stations, including 5 continuous OBSs; hence, each FPS has at least 10 FMPs and maximum 1 inconsistent station. We observe normal and oblique focal mechanism solutions, and a NE-SW trended extensional state of stress in the Eastern Central Marmara by this comprehensive research, although the main Marmara Fault, the western branch of the North Anatolian Fault Zone (NAFZ), is dominated by a right lateral strike-slip regime. Due to the use of a dense network, we observe neither horizontal nor vertical large shifts in the locations of earthquakes: a total of 398 out of 425 are from Korkusuz Öztürk et al. (Tectonophysics 665:37–57, 2015), after the relative relocation process. As a result, we could not observe fault dip angles clearly, but define seismic zones for each segment which has not been done before for many segments in the Sea of Marmara, and interpret current stress loads. Consequently, our sensitive relocations and stress tensor inversion analyses will make an important contribution to a better understanding of the fault movements in the Sea of Marmara, and shed light on especially earthquake rupture and tsunami analyses.

The mechanism of the earthquake focus is one of the most important parameters characterizing the seismic event. In modern seismology, it is associated with the sudden movement of rocks accompanied by the emission of seismic waves along the surface of weakened strength, and reflects simultaneously the spatial orientation of the axes of the principal stresses, possible planes of discontinuities and motions in the earthquake source, and represent almost the bulk of information on the stress state of the earth’s interior (Kangarli et al. 2017). It is data on the stress and strain fields, together with the geological, structural-tectonic structure, that make it possible to solve the problem of creating models of deformation processes in the tectonic structures of the earth’s crust (Sychev 2005).

Focal parameters of the earthquakes occurred within the Mongol-Baikal seismic belt have been considered from seismological and geological literature data for 9 strongest instrumentally recorded seismic events (1905–1967) and calculated for 89 medium regional earthquakes (2000–2016) on the basis of the data on surface wave amplitude spectra. The obtained seismic moment tensor solutions significantly complete the existing dataset on reliable focal parameters of medium earthquakes and allow us to carry out the seismotectonic reconstruction more precisely. It has been shown that the regions of recent mountain building in southern Siberia and western Mongolia are characterized by transpression and strike-slip regimes. Normal-fault deformation is observed in the central segment of the Baikal rift and in the major part of its northeastern flank. Transpression and strike-slip regimes dominate at the southeastern rift flank and in the junction of the rift and the Olekma-Stanovoi zone.

This chapter will present the results of inversion of modern state of stress, obtained by the method of cataclastic analysis of discontinuous displacements (MCA), for three seismically active regions of Asia: the Northern Tien Shan, the Altai-Sayan region and the Kuril-Kamchatka region. The stress data on the earthquake focal mechanisms are taken from global and regional seismic catalogues. The Northern Tien Shan and the Altai-Sayan region are the intracontinental orogens. The Kuril Islands and Kamchatka are active continental margins. The similarities and differences in the state of stress between these two geodynamic types of deformation of the lithosphere are shown in this chapter.

The North Anatolian Fault Zone is (NAFZ), which is one of the world’s most active seismic structures, runs along the northern part of Turkey. Seismic velocity structure of the crust in the seismically active regions such as NAFZ plays an important role not only in the accurate hypocenter location and characterization of earthquakes but also in the determination of source mechanism and fault properties. We investigated the Moment Tensor (MT) solutions of earthquakes with respect to different crustal velocity models. MT solutions of earthquakes (M > 4.0) occurred in Yedisu segment, which is located near the intersection of North Anatolian Fault Zone and East Anatolian Fault Zone were examined in the study. MT solutions were calculated by full waveform inversion using the software package ISOLA. Different crustal velocity models and hypocenter location parameters were tested during the computation of MT solutions. All observations are very well justified in terms of moment tensor resolvability (a well-posed problem with a low condition number), satisfactory fit between observed and synthetic waveforms, and large doublecouple percentages. Obtained results provide valuable information in understanding the seismotectonic behaviour of one of the most seismically active regions along the NAFZ.

In the past few decades, the Black Sea has been the subject of intense geological and geophysical studies, including deep seismic sounding, reflection profiling, gravity and magnetic surveys for scientific and petroleum exploration purposes (Nikishin et al. 2010; Soson et al. 2010; Stephenson and Schellart 2010).

The Italian Apennines are seat of extensional deformation, concentrated along the inner part of the mountain belt due to the opening of the Tyrrhenian back-arc basin during the late Miocene and the following rolling back subduction of Adriatic plate with an extension velocity of about 3 mm year−1 (D’Agostino et al. 2008; Faccenna et al. 2004). Apennines chain is a zone of high seismic hazard (http://zonesismiche.mi.ingv.it; “Mappa di pericolositàsismica del territorionazionale”; D’Amico et al. 2013a) and it has been affected by a number of earthquakes in the past century suffering intensity X or higher several times in the past centuries (Boschi et al. 2000; CPTI Working Group 2004). The most recent examples are the 1980, M = 6.9, Irpinia events (Pino et al. 2008; Secomandi et al. 2013); the 1997–1998 Umbria-Marche (Caccamo et al. 2007) and the 2009 L’Aquila (D’Amico et al. 2010a, 2013b) sequences.

The destruction of the lithosphere with the formation of fault zones is one of the leading geological processes determining the structure of the continents, both in the past and at the present stage. Seismicity providing information on the structure and dynamics of formation of large fault zones in real time reflects the modern fault formation in the crust. For its study, both the epicentral field of earthquakes (see, for example, Sherman 2009) and the data on the position of their hypocenters are actively used (see, for example, Kaven and Polland 2013). To determine the orientation of modern faults of various orders, one can also use data on the earthquake focal mechanism solutions preliminarily distinguishing the true fault planes in the source. In the case of strong earthquakes, the geological data (the outcrop of the fault on the surface, the existing of faults with similar geometry, etc.), the data on the orientation of the aftershock field, the shape of the first isoseits, and other data are indirect features that help to choose one plane or another as the true fault plane. These approaches are inapplicable in study of weak earthquakes (magnitude M ≤ 4.0) and the only information available on them is concerned with their waveforms.

The Calabria Arc presents the highest probability of occurrence of major earthquakes in the Italian peninsula. Several destructive historical earthquakes (i.e. 1638, 1659, 1783, 1905 and 1908) affected, in particular, the Catanzaro Trough and its neighbouring areas. These events have been tentatively related to the activity of NE-SW trending normal faults. Some of these earthquakes have been followed by tsunamis, which caused further damages along the Tyrrhenian coast. In this paper, we reconstruct the Quaternary evolution of the Catanzaro Trough by combining field geo-structural and marine geophysical data. The results have been compared with existing database of earthquake focal mechanisms, updated with 8 new focal solutions performed in the present work. Analysis of faults offsetting the Lower-Middle Pleistocene deposits shows that the Catanzaro Trough experienced transcurrent and extensional phases of deformation. In particular, conjugate systems with NW-SE right-lateral and NE-SW left lateral faults were observed to displace the Lower Pleistocene deposits. Whereas NE–SW and N-S oriented normal faults have been identified as the main fault systems acting during late Pleistocene-Holocene phase. The interpretation of on-land structural datasets has been supported by geophysical data (multichannel and Chirp profiles) acquired in the offshore and onshore of the study area. Multidisciplinary approach has allowed to define NE-SW elongated sedimentary basins, as the Lamezia Basin, bordered on the one hand by Sant’Eufemia Fault that may extend up to 30 km-length, on the other hand by two overstepping faults, Vibo Valentia and San Pietro Lametino Faults. These findings carry some relevant implications in terms of seismic hazard, as they suggest that the longer fault segment, the greater its energetic seismic event. Finally, these data fit perfectly with the observed late Pleistocene-Holocene WNW-ESE extensional stress regime derived from existing and new database of earthquake focal mechanisms. This is in agreement with the orientation of the most seismically active grabens of the Calabrian Arc (the Crati, the Mesima and the Gioia Tauro Basins). Amongst these structural lineaments, the NE-SW and N-S trending normal faults play surely a relevant role as part of recent seismotectonics processes controlling the Late Quaternary geodynamics of the central Calabrian Arc, representing the source of the main destructive earthquakes occurred in the region.

Known seismic activity in the northern Algeria-Morocco region (Fig. 1), especially during the last 50 years, includes several damaging earthquakes. In particular, in the El Asnam region (nowadays Cheliff) have been located the most destructive and damaging earthquakes recorded in northern Algeria.

Earthquake recurrence cycle has been thought as repetition of stress accumulation for long term as interseismic stage and stress release for short period as coseismic stage.

The Generic Mapping Tools is a free computer software package developed to help scientists, in particular, geoscientists, visualise their data. In this chapter, you will find basic examples to help you get started with making high-quality GMT figures and maps.

Generally, a rotational ground motion can be induced by earthquakes, explosions, and ambient vibrations. From the above point of view, it is interesting for a study concerning the area of rotational seismology (Lee et al. 2009a).