Analysis of a group of seismic events using rotational components

Analysis of a group of seismic events which took place in central Italy and have been recorded at the l’Aquila Observatory reveals proportionality between the maximum seismic signal (the displacement velocity) and the maximum amplitudes of rotational components. To compare the seismic events in the aspect of energy emitted as rotational motions, the rotation indices are used; these indices help us also to differentiate between the results obtained for different frequency spectra. In the adopted higher frequency range, 2.6–43 Hz, the relation between maximum displacement velocities and the rotation indices is roughly reciprocal, while for the lower frequencies, 0.3–3 Hz, there is no clear relationship. The share of rotation motions in the whole seismic energy emitted from the source varies during the seismic event. Research on the rotational components hidden in the seismic field gives a new insight into the processes in the source.     

Methods for estimating rotational components of seismic ground motion and their numerical comparisons*

Rotational components play an important role in natural earthquake research, engineering seismic investigation, building monitoring, seismic exploration and other fields. Traditional researches mainly focus on three translational components, but less on rotational ones. As the precision of rotational sensing techniques has increased, many scholars have paid more attention to the seismic rotational motions. Because the rotational observations are not very popular before and now, approximately converting the translational components into rotational components is utilized in rotation analysis. Based on numerical six-component seismic data with the finite difference method, we compare three different conversion methods, the travelling-wave, frequency-domain and the difference method, to analyze their characteristics and feasibilities when they are applied to estimate rotational components with translational observations.     

光纤振动传感之一:旋转测量技术及其地震学应用

地震波场可分解为三分量平动和三分量旋转运动.旋转分量包含重要的波场梯度信息,是地震波场重建的关键要素,但过去由于缺乏稳定的高灵敏度旋转测量仪器,它在不同的地震学应用中常被忽略.光纤旋转地震仪是率先打破测量仪器缺乏困境、最先实现商业化的旋转地震仪,也是目前最有发展前景的地震波旋转直接测量设备.光纤旋转地震仪基于Sagnac效应,并依托成熟的光纤陀螺技术实现振动的旋转分量测量.它具有纯光电传感不受平动影响的测量优势;并且能够在高灵敏度和宽频带旋转测量的基础下实现设备的小型化,有利于旋转测量的应用推广.因此,光纤旋转地震仪和传统的地震仪将形成互补,实现旋转和平动六分量(6C)的观测,更好地提取地震波场特征,提高振动监测能力,有效改善震源过程反演、地下结构成像和地震破坏机理研究等应用.本文主要介绍光纤旋转测量的基本原理、旋转地震学的应用及其潜在应用前景.     

Time-frequency response spectrum of rotational ground motion and its application

The rotational seismic motions are estimated from one station records of the 1999 Jiji (Chi-Chi), Taiwan, earthquake based on the theory of elastic plane wave propagation. The time-frequency response spectrum (TFRS) of the rota-tional motions is calculated and its characteristics are analyzed, then the TFRS is applied to analyze the damage mechanism of one twelve-storey frame concrete structure. The results show that one of the ground motion components can not reflect the characteristics of the seismic moti...     

Approximate formulas for rotational effects in earthquake engineering

The paper addresses the issue of researching into the engineering characteristics of rotational strong ground motion components and rotational effects in structural response. In this regard, at first, the acceleration response spectra of rotational components are estimated in terms of translational ones. Next, new methods in order to consider the effects of rotational components in seismic design codes are presented by determining the effective structural parameters in the rotational loading of structures due only to the earthquake rotational components. Numerical results show that according to the frequency content of rotational components, the contribution of the rocking components to the seismic excitation of short period structures can never be ignored. During strong earthquakes, these rotational motions may lead to the unexpected overturning or local structural damages for the low-rise multi-story buildings located on soft soil. The arrangement of lateral-load resisting system in the plan, period, and aspect ratio of the system can severely change the seismic loading of wide symmetric buildings under the earthquake torsional component.     

Structural response for six correlated earthquake components

The paper examines the effect on the structural response of the inevitable correlation which exists between the six earthquake components acting along a set of structural axes. The rotational components are expressed in terms of the spatial derivatives of the translational components. For the calculation of response, modal analysis is employed so that ground response spectra can also be used as seismic input. A methodology is developed to obtain the maximum mean square response which can occur in a structure, irrespective of its orientation with respect to the impinging seismic waves. The application of this methodology for the calculation of design response is advocated, especially for asymmetric structures. For the assumed model of seismic wave motion, the numerical results show a significant contribution to the response from the rotational components. This contribution is, however, expected to be reduced by structural foundation averaging and interaction effects. Further studies with more complete models of seismic wave motions, and their interaction with structural foundations, are thus warranted for a realistic evaluation and characterization of the rotational inputs for design purposes.     

A brief theory and computing of seismic ground rotations for structural analyses

The seismic ground rotations are important with respect to spatial structural models, which are sensitive to the wave propagation. The rotational ground motion can lead to significant increasing of structural response, instability and unusual damages of buildings. Currently, the seismic analyses often take into account the rocking and torsion motions separately using artificial accelerograms. We present an exact analytical method, proposed by Nazarov [15] for computing of three rotational accelerograms simultaneously from given translational records. The method is based on spectral representation in the form of Fourier amplitude spectra of seismic waves, corresponding to the given three-component translational accelerogram. The composition, directions and properties of seismic waves are previously determined in the form of a generalized wave model of ground motion. It is supposed that seismic ground motion can be composed by superposition of P, SV, SH- and surface waves. As an example, the dynamic response analysis of 25-story building is presented. Here recorded (low-frequency) and artificial (high-frequency) accelerograms were used; each of them includes three translational and three rotational components. In this structural analysis, we have clarified primarily conditions under which rotational ground motion should be taken into account. Next, we have calculated three rotational components of seismic ground motion. Then they were taken as additional seismic loads components for further seismic analysis of the building. Note, soil–structure interaction (SSI) is not considered in this study. For computing, we use the special software for structural analyses and accelerogram processing (FEA Software STARK ES and Odyssey software, Eurosoft Co., Russia). It was developed and is used in engineering practice in the Central Research Institute of Building Constructions (TsNIISK, Moscow, Russia).     

Transport in fracture processes: Fragmentation and slip

We present a new development in the asymmetric continuum theory with the shear oscillations (twist motions) and independent spin; these motions (displacement velocities and spin) can be shifted in phase to describe the independent rebound processes. Our approach provides an extension of the asymmetric continuum theory by including the microfragmentation processes with a double transport which may appear in an advanced fracture process under very high load. The related nonlinear equations, leading to soliton solutions, are derived.     

AFORS autonomous fibre-optic rotational seismograph: Design and application

We outline the research leading to development of the Autonomous Fibre-Optic Rotational Seismograph (AFORS) and describe the final version of the instrument. The instrument with linear changes of sensitivity keeps accuracy from 5.1 × 10⁻⁹ to 5.5 × 10⁻⁸ rad/s in the detection bandpass 1.66–212.30 Hz; it is designed for a direct measurement of rotational components emitted during seismic events. The presented system is based on the optical part of the fibre optic gyro construction where a special autonomous signal processing unit (ASPU) optimizes its operation for the measurement of rotation motions instead of the angular changes. The application of a newly designed telemetric system based on the Internet allows for a remote system control, as shown in an example of the system’s operation in Książ (Poland) seismological observatory.     

Seismic response of large-span spatial structures under multi-support and multidimensional excitations including rotational components

To achieve rational and precise seismic response predictions of large span spatial structures(LSSSs),the inherent non-uniformity and multidimensionality characteristics of earthquake ground motions should be properly taken into consideration.However,due to the limitations of available earthquake stations to record seismic rotational components,the effects of rocking and torsional earthquake components are commonly neglected in the seismic analyses of LSSSs.In this study,a newly developed method to extract the rocking and torsion components at any point along the area of a deployed dense array from the translational earthquake recordings is applied to obtain the rotational seismic inputs for a LSSS.The numerical model of an actual LSSS,the Dalian International Conference Center(DICC),is developed to study the influences of multi-support and multidimensional excitations on the seismic responses of LSSSs.The numerical results reveal that the non-uniformity and multidimensionality of ground motion input can considerably affect the dynamic response of the DICC.The specific degree of influence on the overall and local structural displacements,deformations and forces are comprehensively investigated and discussed.     

Investigation of ground rotational motions caused by direct and scattered P-waves from the 4 March 2008 TAIGER explosion experiment

High-frequency rotational motions of P-waves and coda waves were analysed using rotation rate sensors and strong motion array data from the 4 March 2008 TAiwan Integrated GEodynamics Research (TAIGER) explosion experiment in northeastern Taiwan. Theoretical and observational investigations focussed on the effects of this experiment on the free surface. The main goal of this study was to explore possible applications of combined measurements of artificial explosion-derived translational and rotational motions. Also investigated was the consistent ground rotation observed directly by rotation rate sensors and derived using translational seismic arrays. Common near-source high-frequency rotational motion observations and array-recorded translational motions from one shallow borehole explosion are analysed in this study. Using a half-space assumption of plane P-wave propagation across the recording site, we conclude that: (1) rotational motions induced by direct P-waves interacting with a free surface in theory can be used to estimate wave radial direction, velocity and anisotropic properties; (2) rotational motions derived from scattering are predominant among the observed rotations during the TAIGER explosion experiments and allow us to image the heterogeneous structure of the medium at the investigated site; and (3) rotation sensor measurements undertaken during TAIGER explosion experiments may be affected by cross-axis sensitivities, which need to be considered when using the data obtained during these experiments.     

旋转运动在地震学中的应用概述

旋转地震学是研究由天然地震、爆破和周围环境振动引起的地面旋转运动的新兴学科。对于它的研究不仅有助于对质点运动(平移运动、旋转运动和形变)进行完整的描述,而且对广义地球物理学,如强地面运动地震学、地震工程学、地震物理学、地震仪器等的研究也有重要指导意义。本文系统介绍了旋转运动在地震学中4个方面的应用。首先,介绍基于平移运动和旋转运动的共同测量,得出了计算远震瑞利波和勒夫波相速度的理论公式,并以西伯利亚地震为例,得出台站附近的相速度结构;其次,利用环形激光仪仅对地震SH波敏感的特性,分离P波和S波,分辨海洋噪声和面波,确定海洋噪声的反方位角;然后,介绍利用旋转传感器对自由振荡的长周期环形模式的观测;最后,对包含旋转观测量的多参数反演问题的重要性和实用性进行了阐述,并分析了旋转地震学研究现存的问题。     

Spatial coherency analysis of seismic ground motions from a rock site dense array implemented during the Kefalonia 2014 aftershock sequence

The objective of studies presented in this paper is to analyse the spatial incoherency of seismic ground motions using signals from a velocimeter dense array located on a rock site, recording the aftershock sequence of the two M6 Kefalonia earthquakes that occurred in January/February 2014 (Kefalonia island, Greece). The analyses are carried out with both horizontal and vertical components of velocigrams for small separation distances of stations (<100 m). The coherencies of seismic ground motions identified from strong motion windows are compared with those identified from coda parts of signals. It is realized that there is no significant difference between the coherencies estimated from those two parts of signals. The influence of earthquake event number on the result of coherencies and the dispersions of coherencies estimated from different earthquake events are presented. Finally, coherencies estimated from the dense array are compared with several coherency models proposed and widely used in the literature. The possibility of modifying some parameters of those existing coherency models to fit with in situ coherencies are discussed and presented. Copyright © 2017 John Wiley & Sons, Ltd.     

RESEARCH ON PASSIVE SERVO SEISMIC ROTATIONAL ACCELERATION SENSOR WITH LARGE DAMPING

Many strong motion records show that under the strong seismic vibration of, the torsional disfigurement of building structures is a common and serious damage. At present, there are no special sensors for measuring seismic rotation in the world. Most of the experts obtain rotational components through observing deformation, theoretical analysis and calculation. The theory of elastic wave and source dynamics also prove the conclusion that the surface of the earth will rotate when an earthquake occurs. Based on a large number of investigations and experiments, a rotational acceleration sensor was developed for the observation of the rotational component of strong ground motions. This acceleration sensor is a double-pendulum passive servo large-damped seismic rotational acceleration sensor with the moving coil transducer. When an earthquake occurs, the seismic rotational acceleration acts on the bottom plate at the same time. The magnetic circuit system and the middle shaft fixedly connected to the bottom plate follow the bottom plate synchronous vibration, and the moving part composed of the mass ring, the swing frame and the moving ring produces relative corners to the central axis. The two working coils mounted on the two pendulums produce the same relative motion with respect to the magnetic gaps of the two magnetic circuits. Both working coils at this time generate an induced electromotive force by cutting magnetic lines of force in the respective magnetic gaps. The generated electromotive forces are respectively input to respective passive servo large damper dynamic ring transducer circuits and angular acceleration adjusting circuits, and the signals are simultaneously input to the synthesizing circuit after conditioning. Finally, the composite circuit outputs a voltage signal proportional to the seismic rotational acceleration to form a seismic rotational acceleration sensor. The paper presents the basic principles of the rotational acceleration sensor, including its mechanical structure diagram, circuit schematic diagram and mathematical models. The differential equation of motion and its circuit equation are derived to obtain the expressions of the main technical specifications, such as the damping ratio and sensitivity. The calculation shows that when the damping ratio is much larger than 1, the output voltage of the passive servo large damping dynamic coil transducer circuit is proportional to the ground rotation acceleration, and the frequency characteristic of bandpass is wider when the damping ratio is larger. Based on the calibration test, the dynamic range is greater than or equal to 100dB and the linearity error is less than 0.05%. The amplitude-frequency characteristics, the phase-frequency characteristics and their corresponding curves of the passive servo rotational acceleration sensor are acquired through the calculations. Based on the accurate measurement of the micro-vibration of the precision rotating vibration equipment, the desired result is obtained. The measured data are presented in the paper, which verify the correctness of the calculation result. The passive servo large damping rotational acceleration sensor has simple circuit design, convenient operation and high resolution, and can be widely applied to seismic acceleration measurement of earthquake or structure.     

On the characteristics of ground motion rotational components using Chiba dense array data

An effort is made to examine the properties of rotational (torsional and rocking) ground motions using Chiba dense array data. The Chiba array system, located 30 km east of Tokyo, Japan, is composed of 15 boreholes with separation distances varying from 5 to 320 m. This provides a unique opportunity to examine the characteristics of rotational components. For this purpose, 17 events are considered and rotational ground motions are evaluated using spatial derivatives of translational ones. The effects of seismological parameters and separation distances between stations on properties of rotational motions are examined, showing a sudden increase in rotational motions for the earthquakes with large magnitude or PGA and decrease of these motions with increasing separation distance. While the duration of torsional motion is found to be larger than translational ones, there is no significant difference between durations of rocking and vertical motions. The effects of separation distance and earthquake magnitude on rotational response spectra are also investigated. The normalized rotational response spectra are found to be strongly affected by separation distance. The spectral ratios of rotational and translational motions are not linearly proportional to period as suggested by the previous studies. Finally, the torsional motion is predicted from translation ones for different separation distances at the site. The comparison of the predicted and the calculated torsional motions reveals a weak estimation in close separation distances (<30m) and satisfactory predictions in other cases. Copyright © 2007 John Wiley & Sons, Ltd.     

Enhancement of long period components of recorded and synthetic ground motions using InSAR

Tall buildings and flexible structures require a better characterization of long period ground motion spectra than the one provided by current seismic building codes. Motivated by that, a methodology is proposed and tested to improve recorded and synthetic ground motions which are consistent with the observed co-seismic displacement field obtained from interferometric synthetic aperture radar (InSAR) analysis of image data for the Tocopilla 2007 earthquake (M_w=7.7) in Northern Chile. A methodology is proposed to correct the observed motions such that, after double integration, they are coherent with the local value of the residual displacement. Synthetic records are generated by using a stochastic finite-fault model coupled with a long period pulse to capture the long period fling effect.It is observed that the proposed co-seismic correction yields records with more accurate long-period spectral components as compared with regular correction schemes such as acausal filtering. These signals provide an estimate for the velocity and displacement spectra, which are essential for tall-building design. Furthermore, hints are provided as to the shape of long-period spectra for seismic zones prone to large co-seismic displacements such as the Nazca-South American zone.     

Seismic response of reduced micropolar elastic half-space

This paper explores reduced micropolar theory to simulate ground motion during an earthquake. In this theory, rotational motions are kinematically independent of translational motions. Analytical expressions for ground displacement and rotational motions due to a buried seismic source are presented in this paper. This theory requires two additional material constants which characterise the microstructure of the medium compared with linear elastic theory. Ground motions are simulated for an earthquake of magnitude (M _w) 5.0. The sensitivity of ground motion to these new material constants is reported. It is observed that rotations are sensitive to microstructure of the medium. A comparison with recorded rotations of the M _w 5.2 Izu peninsula, Japan event is also presented in this article.     

On planar seismic wavefront modeling for estimating rotational ground motions: Case of 2-D SH line-source

At large hypocentral distances, it is convenient to approximate the curved transient seismic wavefronts as planar to estimate rotational ground motions from the single-station recordings of translational ground motions. In this paper, we investigate whether and when this approximation, referred to as the ‘plane-wave’ approximation, can be considered adequate close to the source. For this, we consider a simplistic source model comprising a two-dimensional, kinematic shear dislocation SH line-source buried in a homogenous, elastic half-space and assume this to be an equivalent representation of a finite-sized fault. The ‘plane-wave’ rotational motion is then synthesized from the exact translational motion solution to the assumed model and compared with the exact rotational motion solution for this model. The comparison between the two sets of rotational amplitudes in frequency domain suggests that the plane-wave approximation may be adequate, when the wavelengths of the seismic waves are much smaller than the source depth. When this is not true, the plane-wave approximation is seen to underestimate the Fourier amplitudes close to the source by several orders, particularly when the fault planes are vertically oriented. A similar comparison in the time domain indicates that a severe underestimation may also occur when the source rise time is longer than the shear-wave arrival time at the epicenter. Significant discrepancies are also observed between the waveforms of the exact and plane-wave rotational motions.