Earthquake dynamics on circular faults: a review 1970–2015

We review the development of earthquake dynamics taken from the point of view of the origin of seismic radiation instead of the detailed study of rupture propagation on complex surfaces. Many features of seismic radiation can be explained by simple models that serve as elementary canonical problems. Some of these properties are very well known like the fact that at low frequencies, the seismic spectrum is proportional to the seismic moment. At high frequencies, on the other hand, radiation is generated by the motion of the rupture front, in particular stopping phases and geometrical obstacles (barriers). A rupture front moving at constant speed does not produce far-field radiation. For many practical applications, for determining source size and stress drop, for example, it is not necessary to determine geometrical details of the rupture. For such cases, a simple circular crack model is quite sufficient. An improvement on this method is to do dynamic inversion on simple, elliptical-shaped sources and letting the rupture start arbitrarily from a point on the fault. This problem can be solved nowadays with finite differences and a variety of inversion techniques.     

Singularity-free expression of magnetic field of cuboid under undulating terrain

Most of the current computing methods used to determine the magnetic field of a uniformly magnetized cuboid assume that the observation point is located in the upper half space without a source. However, such methods may generate analytical singularities for conditions of undulating terrain. Based on basic geomagnetic field theories, in this study an improved magnetic field expression is derived using an integration method of variable substitution, and all singularity problems for the entire space without a source are discussed and solved. This integration process is simpler than that of previous methods, and final integral results with a more uniform form. ΔT at all points in the source-free space can be calculated without requiring coordinate transformation; thus forward modeling is also simplified. Corresponding model tests indicate that the new magnetic field expression is more correct because there is no analytical singularity and can be used with undulating terrain.     

Seismic evaluation of rocking structures through performance assessment and fragility analysis

Numerical studies have been conducted for low- and medium-rise rocking structures to investigate their efficiency as earthquake-resisting systems in comparison with conventional structures. Several non-linear time-history analyses have been performed to evaluate seismic performance of selected cases at desired ground shaking levels, based on key parameters such as total and flexural story drifts and residual deformations. The Far-field record set is selected as input ground motions and median peak values of key parameters are taken as best estimates of system response. In addition, in order to evaluate the probability of exceeding relevant damage states, analytical fragility curves have been developed based on the results of the incremental dynamic analysis procedure. Small exceedance probabilities and acceptable margins against collapse, together with minor associated damages in main structural members, can be considered as superior seismic performance for medium-rise rocking systems. Low-rise rocking systems could provide significant performance improvement over their conventional counterparts notwithstanding certain weaknesses in their seismic response.     

Spatial distribution analysis of landslides triggered by the 2013-04-20 Lushan earthquake,China

The 2013-04-20 Lushan earthquake(seismic magnitude Ms 7.0 according to the State Seismological Bureau)induced a large number of landslides.In this study,spatial characteristics of landslides are developed by interpreting digital aerial photography data.Seven towns near the epicenter,with an area of about 11.11 km2,were severely affected by the earthquake,and 703 landslides were identified from April 24,2013 aerial photography data over an area of 1.185 km2.About 55.56% of the landslide area was less than 1000 m2,whereas about 3.23 % was more than 10,000 m2.Rock falls and shallow landslides were the most commonly observed types in the study area,and were primarily located in the center of Lushan County.Most landslide areas were widely distributed near river channels and along roads.Five main factors were chosen to study the distribution characteristics of landslides:elevation,slope gradients,fault,geologic unit and river system.The spatial distribution of coseismal landslides is studied statistically using both landslide point density(LPD),defined as the number of landslides(LS Number)per square kilometer,and landslide area density(LAD),interpreted as the percentage of landslides area affected by earthquake.The results show that both LPD and LAD have strong positive correlations with five main factors.Most landslides occurred in the gradient range of 40°-50° and an elevation range of 1.0-1.5 km above sea level.Statistical results also indicate that landslides were mainly formed in soft rocks such as mudstone and sandstone,and concentrated in IX intensity areas.     

Newmark design spectra considering earthquake magnitudes and site categories

Newmark design spectra have been implemented in many building codes, especially in building codes for critical structures. Previous studies show that Newmark design spectra exhibit lower amplitudes at high frequencies and larger amplitudes at low frequencies in comparison with spectra developed by statistical methods. To resolve this problem, this study considers three suites of ground motions recorded at three types of sites. Using these ground motions, influences of the shear-wave velocity, earthquake magnitudes, source-to-site distances on the ratios of ground motion parameters are studied, and spectrum amplification factors are statistically calculated. Spectral bounds for combinations of three site categories and two cases of earthquake magnitudes are estimated. Site design spectrum coefficients for the three site categories considering earthquake magnitudes are established. The problems of Newmark design spectra could be resolved by using the site design spectrum coefficients to modify the spectral values of Newmark design spectra in the acceleration sensitive, velocity sensitive, and displacement sensitive regions.     

Hydrodynamic Equilibrium for Sediment Transport and Bed Response to Wave Motion

An experimental and theoretical identification of hydrodynamic equilibrium for sediment transport and bed response to wave motion are considered. The comparison between calculations and the results of laboratory experiments indicates the linear relation between sediment transport rate and the thickness zm of bed layer in which sediments are in apparent rectilinear motion. This linear relationship allows to use the first order “upwind” numerical scheme of FDM ensuring an accurate solution of equation for changes in bed morphology. However, it is necessary to carry out a decomposition of the sediment transport into transport in onshore direction during wave crest and offshore direction during wave trough. Further, the shape of bed erosion in response to sediment transport coincides with the trapezoid envelope or with part of it, when some sediments still remain within it. Bed erosion area is equal to the one of a rectangle with thickness znm.     

Experimental Study on Velocity Profiles with Different Roughness Elements in a Flume

The classical log law for velocity profile is applied to engineering practice. Field observations indicate that the composition of the bed materials obviously influences the shape of vertical velocity distribution. To clearly understand the roughness effect, six types of materials were laid separately at various depths for the investigation of the effects of roughness elements on the vertical velocity distribution. A down-looking 3D acoustic Doppler velocimeter was used to measure the velocity profiles. The experimental results showed that the curve characteristics of velocity profiles are strongly dependent on the roughness scale and related flow parameters. If d/R, Fr, and Re are larger than 0.15, 0.47, and 60 000, respectively, the velocity distribution may resemble an S-shape profile. The inflexion position Z*/H for a given S-shape profile was empirically deduced as Z*/H = ?0.4481d/R + 0.3225. Otherwise, the velocity profile agrees well with the logarithmic law. The findings of this study are useful in engineering practice (i.e., depth-averaged velocity and flow rate estimate). Key words: velocity profiles, acoustic Doppler velocimeter, roughness elements, logarithmic law, S-shape curve.     

Detection of the Long Period Long Duration (LPLD) Events in Time-and Frequency-Domain

Long Period Long Duration (LPLD) signals are unusual seismic events that can be observed during hydraulic fracturing. These events are very similar in appearance to tectonic tremors sequences, which were first observed in subduction zones. Their nature is not well known. LPLD might be related to the productivity of the reservoir. Different methods of the LPLD events’ detection recorded during hydraulic fracturing are presented. The author applied two methods for LPLD detection–Butterworth filtering and Continuous Wavelet Transform (CWT). Additionally, a new approach to LPLD events detection–instantaneous seismic attributes–was used, common in a classical seismic interpretation but not in microseismic monitoring.