Determination of Resonance Frequency of Two-Dimensional Alluvial Valley by Background Phase Subtraction Method

1998 ◽  
Vol 14 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Tsung-Jen Teng ◽  
Juin-Fu Chai ◽  
Chau-Shioung Yeh

ABSTRACTThis paper is to develop the background phase subtraction method to determine the resonance frequency of a two-dimensional alluvial valley subjected to an incident plane SH-wave. The scattered wave due to the alluvium can be expressed in a series of basis functions, and the associated coefficients are related to the coefficients of free field by the so-called T-matrix method. By applying the resonance scattering theory, the effects among all normal modes can be decoupled and hence one can obtain the phase shift of each eigen partial wave. Similarly, the phase shift of each eigen partial wave due to a canyon with the same geometrical shape of the alluvium can be determined, and is recognized as the background effect. Furthermore, based on the phase represented scattering matrix, the resonance frequencies of each normal mode and its overtones can be determined by the subtraction of the associated phase dependent function due to the canyon from that due to the alluvium.

2017 ◽  
Vol 17 (6) ◽  
pp. 925-937 ◽  
Author(s):  
Andrej Gosar

Abstract. The town of Idrija is located in an area with an increased seismic hazard in W Slovenia and is partly built on alluvial sediments or artificial mining and smelting deposits which can amplify seismic ground motion. There is a need to prepare a comprehensive seismic microzonation in the near future to support seismic hazard and risk assessment. To study the applicability of the microtremor horizontal-to-vertical spectral ratio (HVSR) method for this purpose, 70 free-field microtremor measurements were performed in a town area of 0.8 km2 with 50–200 m spacing between the points. The HVSR analysis has shown that it is possible to derive the sediments' resonance frequency at 48 points. With the remaining one third of the measurements, nearly flat HVSR curves were obtained, indicating a small or negligible impedance contrast with the seismological bedrock. The isofrequency (a range of 2.5–19.5 Hz) and the HVSR peak amplitude (a range of 3–6, with a few larger values) maps were prepared using the natural neighbor interpolation algorithm and compared with the geological map and the map of artificial deposits. Surprisingly no clear correlation was found between the distribution of resonance frequencies or peak amplitudes and the known extent of the supposed soft sediments or deposits. This can be explained by relatively well-compacted and rather stiff deposits and the complex geometry of sedimentary bodies. However, at several individual locations it was possible to correlate the shape and amplitude of the HVSR curve with the known geological structure and prominent site effects were established in different places. In given conditions (very limited free space and a high level of noise) it would be difficult to perform an active seismic refraction or MASW measurements to investigate the S-wave velocity profiles and the thickness of sediments in detail, which would be representative enough for microzonation purposes. The importance of the microtremor method is therefore even greater, because it enables a direct estimation of the resonance frequency without knowing the internal structure and physical properties of the shallow subsurface. The results of this study can be directly used in analyses of the possible occurrence of soil–structure resonance of individual buildings, including important cultural heritage mining and other structures protected by UNESCO. Another application of the derived free-field isofrequency map is to support soil classification according to the recent trends in building codes and to calibrate Vs profiles obtained from the microtremor array or geophysical measurements.


2017 ◽  
Author(s):  
Andrej Gosar

Abstract. The Idrija town is located in area with increased seismic hazard in W Slovenia and is partly built on alluvial sediments or artificial mining and smelting deposits which can amplify seismic ground motion. There is a need to prepare a comprehensive seismic microzonation in the near future to support seismic hazard and risk assessment. To study the applicability of microtremor Horizontal-to-Vertical Spectral Ratio (HVSR) method for this purpose, 70 free-field microtremor measurements were performed in 0.8 km2 large town area with 50–200 m spacing between points. HVSR analysis has shown that it is possible to derive sediments resonance frequency at 48 point, whereas at remaining one third of measurements nearly flat HVSR curves were obtained indicating small or no impedance contrast with the seismological bedrock. Iso-frequency (range 2.5–19.5 Hz) and HVSR peak amplitude (range 3–6, with few larger values) maps were prepared by using natural neighbour interpolation algorithm and compared with the geological map and map of artificial deposits. Surprisingly no clear correlation was found between distribution of resonance frequencies or peak amplitudes and the known extent of supposed soft sediments or deposits. This can be explained by relatively well compacted and rather stiff deposits and complex geometry of sedimentary bodies. However, at several individual locations it was possible to correlate the shape and amplitude of the HVSR curve with the known geological structure and prominent site effects were established in different places. On the other hand, in given conditions (very limited free space and high level of noise) it would be difficult to perform active seismic refraction or MASW measurements to investigate the S-waves velocity profiles and thickness of sediments in details, which would be representative enough for microzonation purposes. The importance of microtremor method is therefore even greater, because it enables direct estimation of the resonance frequency without knowing the internal structure and physical properties of the shallow subsurface. The results of this study can be used directly in analyses of possible occurrence of soil-structure resonance of individual buildings, including important cultural heritage mining and other structures protected by UNESCO. Second application of the derived free-field iso-frequency map is to support soil classification according to the recent trends in building codes.


1992 ◽  
Vol 47 (1-2) ◽  
pp. 382-388 ◽  
Author(s):  
E. Rommel ◽  
P. Nickel ◽  
F. Rohmer ◽  
R. Kimmich

AbstractExchange between positions with different resonance frequencies can be studied by two-dimensional spectroscopy originally developed for the NMR case. Cross intensity reflects changes of the resonance frequency due to different line shifts or anisotropic interactions. We now present analogous experiments carried out with pure NQR of polycrystalline samples. The specific requirements are discussed in comparison to 2D exchange NMR spectroscopy. The method has been demonstrated with chloroform and p-chlorobenzotrichloride, where the resonances of the 35Cl nuclei were investigated. Isomeric changes taking place in these compounds reveal themselves as cross-peaks provided the right ranges of the temperature and the mixing time are chosen. The corresponding dependences were recorded and are discussed.


2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Mert Besken ◽  
Jan de Boer ◽  
Grégoire Mathys

Abstract We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and the Virasoro algebra of two-dimensional CFT. We then consider commutators of light-ray operators built from the stress-tensor. Using simplifying features of the light sheet limit in four-dimensional CFT we provide a direct computation of the BMS algebra formed by a specific set of light-ray operators in theories with no light scalar conformal primaries. In four-dimensional CFT we define a new infinite set of light-ray operators constructed from the stress-tensor, which all have well-defined matrix elements. These are a direct generalization of the two-dimensional Virasoro light-ray operators that are obtained from a conformal embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity conditions similar to their two-dimensional analogues, and also share the property that a semi-infinite subset annihilates the vacuum.


1973 ◽  
Vol 43 (1) ◽  
pp. 39-41 ◽  
Author(s):  
Le Dang Khoi ◽  
P. Veillet ◽  
J-P. Renard ◽  
C. Jacoboni

2022 ◽  
Author(s):  
Linhui Ding ◽  
Ningning Wang ◽  
Leiming Chen ◽  
Kui Han ◽  
Xiaopeng Shen ◽  
...  

Abstract Plasmonics in two-dimensional materials, an emerging direction of nano-optics, has attracted great attention recently, which exhibits unique properties than that in noble metals. Extending its advanced features by different manipulations is very beneficial for its promotion. In this paper, we study plasmonic excitations in graphene and black phosphorus (BP) nanostructures, where the effects of structural symmetry and material anisotropy are discussed. We show that the two factors are crucial to mode excitations, e.g. the extinction can be dominated by higher order modes rather than dipole resonance. The behavior occurs only in the direction hosting larger resonance frequencies, e.g. armchair (AC) direction of BP and shorter side of graphene rectangles. In BP rectangles along AC direction, the two factors are competing, and thus can be applied cooperatively to tune plasmonic resonance, from dipole to higher order excitations. Besides, the manipulation can also be achieved by designing BP square rings, in which the interaction between outer and inner edges show great impact on mode excitations. Our studies further promote the understanding of plasmonics in two-dimensional materials, and will pave the way for particular plasmonic applications.


2011 ◽  
Vol 2-3 ◽  
pp. 140-143
Author(s):  
Qing Feng Yang ◽  
Peng Wang ◽  
Yu Hong Wang ◽  
Kai Zhang

The resonance frequency of the cymbal transducer ranges from 2kHz to 40kHz and its effective electromechanical coupling factor is around 20%. Finite element analysis has been performed to ascertain how the transducer’s makeup affect the transducer’s performance parameters. Two-dimensional axisymmetric model of the cymbal transducer was founded by finite element software-ANSYS, the application of the element type was discussed and the FEM models were built up under the far field condition. Eight groups of cymbal transducers of resonance frequency around 3kHz with different structural dimensions were designed. It was better for choosing the cymbal transducer of the 8mm cavity coping diameter, 20.8mm cavity bottom diameter and 26.8mm piezoelectric ceramic wafer diameter than others for reducing distortion degree of the signal and improving communication turnover in the researched cymbal transducers. It was appropriate for choosing the cymbal transducer of the 8mm cavity coping diameter, 22.4mm cavity bottom diameter and 26.4mm piezoelectric ceramic wafer diameter in order to improve the free-field voltage sensitivity and transmission efficient.


2019 ◽  
Author(s):  
Hedyeh Rezaei ◽  
Ad Aertsen ◽  
Arvind Kumar ◽  
Alireza Valizadeh

AbstractTransient oscillations in the network activity upon sensory stimulation have been reported in different sensory areas. These evoked oscillations are the generic response of networks of excitatory and inhibitory neurons (EI-networks) to a transient external input. Recently, it has been shown that this resonance property of EI-networks can be exploited for communication in modular neuronal networks by enabling the transmission of sequences of synchronous spike volleys (‘pulse packets’), despite the sparse and weak connectivity between the modules. The condition for successful transmission is that the pulse packet (PP) intervals match the period of the modules’ resonance frequency. Hence, the mechanism was termed communication through resonance (CTR). This mechanism has three sever constraints, though. First, it needs periodic trains of PPs, whereas single PPs fail to propagate. Second, the inter-PP interval needs to match the network resonance. Third, transmission is very slow, because in each module, the network resonance needs to build-up over multiple oscillation cycles. Here, we show that, by adding appropriate feedback connections to the network, the CTR mechanism can be improved and the aforementioned constraints relaxed. Specifically, we show that adding feedback connections between two upstream modules, called the resonance pair, in an otherwise feedforward modular network can support successful propagation of a single PP throughout the entire network. The key condition for successful transmission is that the sum of the forward and backward delays in the resonance pair matches the resonance frequency of the network modules. The transmission is much faster, by more than a factor of two, than in the original CTR mechanism. Moreover, it distinctly lowers the threshold for successful communication by synchronous spiking in modular networks of weakly coupled networks. Thus, our results suggest a new functional role of bidirectional connectivity for the communication in cortical area networks.Author summaryThe cortex is organized as a modular system, with the modules (cortical areas) communicating via weak long-range connections. It has been suggested that the intrinsic resonance properties of population activities in these areas might contribute to enabling successful communication. A module’s intrinsic resonance appears in the damped oscillatory response to an incoming spike volley, enabling successful communication during the peaks of the oscillation. Such communication can be exploited in feedforward networks, provided the participating networks have similar resonance frequencies. This, however, is not necessarily true for cortical networks. Moreover, the communication is slow, as it takes several oscillation cycles to build up the response in the downstream network. Also, only periodic trains of spikes volleys (and not single volleys) with matching intervals can propagate. Here, we present a novel mechanism that alleviates these shortcomings and enables propagation of synchronous spiking across weakly connected networks with not necessarily identical resonance frequencies. In this framework, an individual spike volley can propagate by local amplification through reverberation in a loop between two successive networks, connected by feedforward and feedback connections: the resonance pair. This overcomes the need for activity build-up in downstream networks, causing the volley to propagate distinctly faster and more reliably.


2001 ◽  
Vol 45 (03) ◽  
pp. 216-227
Author(s):  
R. Centeno ◽  
K. S. Varyani ◽  
C. Guedes Soares

An experimental program was performed with hard-chine catamaran models in regular waves. The distance between the demi-hulls of the models was changed to assess its effects on the wave-induced motions. The results allowed the study of some aspects related to catamaran motions, like the interference between the hulls and resonance frequencies. The experimental results are compared with calculations performed with a recently developed code based on a two-dimensional potential flow theory in which viscous forces are included through a cross-flow drag approach. The effect of the hull distance in the heave and pitch motion responses and the importance of the viscous forces in such hull configurations are shown.


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