Frequency-dependent Quality Factor Research Articles

Noise conversion in Kerr comb RF photonic oscillators

Transfer of amplitude and phase noise from a continuous wave optical pump to the repetition rate of a Kerr frequency comb is studied theoretically, with focus on generation of spectrally pure radio frequency (RF) signals via demodulation of the frequency comb on a fast photodiode. It is shown that both the high order chromatic dispersion of the resonator spectrum and frequency-dependent quality factor of the resonator modes facilitate the optical-to-RF noise conversion that limits spectral purity of the RF signal.

Viscoelastic characteristics of low-frequency seismic wave attenuation in porous media

Mesoscopic fluid flow is the major cause of wave attenuation and velocity dispersion at seismic frequencies in porous rocks. The Johnson model provides solutions for the frequency-dependent quality factor and phase velocity in partially saturated porous media with pore patches of arbitrary shapes. We use the Johnson model to derive approximations for the quality factor Q at the high and low frequency limit, and obtain the approximate equation for Qmin based on geophysical and geometric parameters. A more accurate equation for Qmin is obtained after correcting for the linear errors between the exact and approximate Q values. The complexity of the pore patch shape affects the maximum attenuation of Qmin and the transition frequency ftr; furthermore, the effect on ftr is stronger than that on Qmin. Numerical solutions to Biot’s equation are computationally intensive; thus, we build an equivalent viscoelastic model on the basis of the Zener model, which well approximates the wave attenuation and dispersion in porous rocks in the seismic band.

The potential of imaging subsurface heterogeneities by natural local earthquakes

We have developed a new imaging technique of subsurface heterogeneities that uses Sp-waves from natural earthquakes. This technique can be used as a first screening tool in frontier exploration areas before conventional active exploration. Analyzing Sp-waves from 28 earthquakes ([Formula: see text] 2.0 to 4.2) recorded by two permanent seismic stations, we built an image of the distributions of velocity discontinuities in southeastern offshore Hokkaido, Japan, where intraplate earthquakes in the Pacific plate frequently occur. Our results indicated the presence of three horizontally continuous, distinct discontinuities corresponding to geologic boundaries estimated in a previous study. We also derived the frequency-dependent quality factor [Formula: see text] for P- and S-waves and use it as a method of characterizing physical properties of subsurface structure. The waveform traces with coherent Sp-phases in the southern part of the study area generally show a constant [Formula: see text] ratio, and the waveform traces with randomly distributed phases in the northern part show a large variation of the [Formula: see text] ratio (including several high values).

Eigenfrequencies and quality factors of nanofilm resonators with dissipative surface stress effects

A dissipative surface stress model is adopted to study the size-dependent surface dissipation effect on the quality factor and natural frequencies of vibrating elastic nanofilms (NFs). Kirchhoff plate theory along with the classic Zener model for interior friction in the presence of an initial surface tension is employed to obtain the frequency-dependent quality factor and the differential equation of flexural motion. Resonance frequencies and quality as a function of thickness for square NFs of selected material relaxation times with simply-supported edge conditions are presented and discussed.

CONDITIONS OF PASSAGE AND ENTRAPMENT OF TERRESTRIAL PLANETS IN SPIN-ORBIT RESONANCES

The dynamical evolution of terrestrial planets resembling Mercury in the vicinity of spin-orbit resonances is investigated using comprehensive harmonic expansions of the tidal torque taking into account the frequency-dependent quality factors and Love numbers. The torque equations are integrated numerically with a small step in time, includng the oscillating triaxial torque components but neglecting the layered structure of the planet and assuming a zero obliquity. We find that a Mercury-like planet with its current value of orbital eccentricity (0.2056) is always captured in the 3:2 resonance. The probability of capture in the higher 2:1 resonance is approximately 0.23. These results are confirmed by a semi-analytical estimation of capture probabilities as functions of eccentricity for both prograde and retrograde evolution of spin rate. As follows from analysis of equilibrium torques, entrapment in the 3:2 resonance is inevitable at eccentricities between 0.2 and 0.41. Considering the phase space parameters at the times of periastron, the range of spin rates and phase angles, for which an immediate resonance passage is triggered, is very narrow, and yet, a planet like Mercury rarely fails to align itself into this state of unstable equilibrium before it traverses the 2:1 resonance.

BENCHMARK TESTS FOR STRONG GROUND MOTION PREDICTION METHODS: CASE FOR THEORETICAL METHODS (PART 2)

Following the 2009 benchmark test, we conducted a subsequent test for the strong motion simulation methods in more complex media, using various theoretical methods (the wavenumber integration method, the discrete wavenumber method, and the thin layer method). All the results show generally good agreements, but the results for damping media show discrepancies, especially in the fling step at very close stations to a surface fault. This is because the frequency-dependent quality factors violate severely the causality condition in the waveforms, especially at lower frequencies.

Impact of fluid saturation on the reflection coefficient of a poroelastic layer

The impact of changes in saturation on the frequency-dependent reflection coefficient of a partially saturated layer was studied. Seismic attenuation and velocity dispersion in partially saturated (i.e., patchy saturated) poroelastic media were accounted for by using the analytical solution of the 1D White’s model for wave-induced fluid flow. White’s solution was applied in combination with an analytical solution for the normal-incidence reflection coefficient of an attenuating layer embedded in an elastic or attenuating background medium to investigate the effects of attenuation, velocity dispersion, and tuning on the reflection coefficient. Approximations for the frequency-dependent quality factor, its minimum value, and the frequency at which the minimum value of the quality factor occurs were derived. The approximations are valid for any two alternating sets of petrophysical parameters. An approximation for the normal-incidence reflection coefficient of an attenuating thin (compared to the wavelength) layer was also derived. This approximation gives insight into the influence of contrasts in acoustic impedance and/or attenuation on the reflectivity of a thin layer. Laboratory data for reflections from a water-saturated sand layer and from a dry sand layer were further fit with petrophysical parameters for unconsolidated sand partially saturated with water and air. The results showed that wave-induced fluid flow can explain low-frequency reflection anomalies, which are related to fluid saturation and can be observed in seismic field data. The results further indicate that reflection coefficients of partially saturated layers (e.g., hydrocarbon reservoirs) can vary significantly with frequency, especially at low seismic frequencies where partial saturation may often cause high attenuation.

Investigation of Geometrical Spreading and Quality Factor Functions in the New Madrid Seismic Zone

The accuracy and applicability of geometrical spreading and quality factor functions are investigated for the New Madrid seismic zone (NMSZ) using recorded small and moderate earthquakes. These functions represent the path effect in frequency domain. The database used in this study consists of 500 broadband seismograms from 63 eventsofmagnitudeMw 2.5to5.2,recordedbytheCenterforEarthquakeResearchand Information (CERI) at the University of Memphis. The hypocentral distances range from 10 to 400 km. All the broadband stations are located within the Mississippi embayment with different site conditions. The vertical components of the records areprocessedandusedtodefinethepatheffectterminfrequencyrangeof0.2to30Hz. A hinged-trilinear geometrical spreading and frequency-dependent quality factor functions are used to describe the path term. The regression analysis using a genetic algorithm(GA)indicatesthatatdistanceslessthan70kmthespectralamplitudesdecay as R � 1 ; between 70 and 140 km spectral amplitudes increase with distance and the geometric spreading is defined as R � 0:25 ; beyond 140 km, the attenuation is described by R � 0:5 . The quality factor function is expressed as Q � 614f 0:32 for frequencies greater than 1 Hz after the regression analysis. For the broader range offrequency used in this study (0.2 to 30 Hz), the Q function is described by a third-degree polynomial described as logQf �� 2:898 � 0:464logf � 1:238� logf� 2 � 0:540� logf� 3 . The results of this study are compared with those of Atkinson (2004) and Samiezade-Yazd etal.(1997).Thepathtermobtainedinthisstudycanbeusedinthestochasticmethodto predict ground motions in the NMSZ and eastern North America (ENA).

Inversion Analysis of Site Responses in the Kanto Basin Using Data from a Dense Strong Motion Seismograph Array

Abstract We applied nonlinear inversion analysis to estimate site response in the Kanto area using data from 19 moderate-sized earthquakes observed at the 843 stations constituting strong motion accelerograph networks of the Seismic Kanto strong motion network (SK-net), K-NET, and KiK-net. We determined the source parameters (seismic moment, M 0 ; corner frequency, f c ) for each event and the quality factor ( Q ( f )) for the propagation path based on borehole records. We also determined the frequency-independent and reference-independent site responses. The resulting seismic moments are in good agreement with those determined by the National Research Institute for Earth Science and Disaster Prevention (NIED) and are proportional to . We found a frequency-dependent quality factor for the propagation path: Q ( f )=107 f 0.52 . The site responses, averaged over 0.5–1.0 Hz, correlate well with shear-wave velocities for the upper 30 m (AVS30; correlation coefficient of -0.63) and with depth to the seismic basement, the shear-wave velocity of which is around 3.0 km/sec. Large site responses are found in areas of unconsolidated sediments, such as swampy land. The predominant frequencies of our site responses roughly agree with those of the horizontal to vertical (H/V) spectral ratio. This indicates that the H/V ratio is valid for estimating predominant frequencies of S -wave amplification.

Size effect of dissipative surface stress on quality factor of microbeams

A dissipative surface stress model is suggested to study the surface dissipation of vibrating elastic microbeams. The model is an extension of the well-known Zener model from bulk materials to the surface in the presence of an initial surface tension. Explicit formulas are derived for the frequency-dependent quality factor and the maximum surface dissipation. This model predicts a size-dependent surface dissipation when the size of the cross section downs to nanometers. In particular, the model offers plausible explanation for a few experimental phenomena reported in the most recent literature.

Frequency Dependence of Coda Q, Part I: Numerical Modeling and Examples from Peaceful Nuclear Explosions

Frequency-dependent coda attenuation values are often reported; however, such measurements usually depend on the types of the Q ( f ) models employed. We use numerical modeling of peaceful nuclear explosion (PNE) coda at far-regional to teleseismic distances to compare two such models, namely, the conventional frequency-dependent quality factor ( Q coda( f )= Q f η ) and frequency-independent coda attenuation ( Q c ) with geometrical attenuation ( γ ). The results favor strongly the ( γ , Q c ) model and illustrate the mechanisms leading to apparent Q coda( f ) dependencies. Tests for variations of the crustal velocity structures show that the values of γ are stable and related to lithospheric structural types, and the inverted Q c -values can be systematically mapped into the true S -wave attenuation factors within the crust. Modeling also shows that γ could increase in areas where relatively thin attenuating layers are present within the crust; such areas could likely be related to younger and active tectonics. By contrast, when interpreted by using the traditional ( Q , η ) approach, the synthetic coda shows a strong and spurious frequency dependence with η ≈0.5, which is also similar to the observations. Observed Lg coda from two PNEs located in different areas in Russia show similar values of γ ≈0.75×10-2 sec-1, which are also remarkably close to the independent numerical predictions. At the same time, coda Q c -values vary strongly, from 850 in the East-European platform to 2500 within the Siberian Craton. This suggests that parameters γ and Q c could provide stable and transportable discriminants for differentiating between the lithospheric tectonic types and ages and also for seismic coda regionalization in nuclear test monitoring research.

Simultaneous Inversion of Source Spectra, Attenuation Parameters, and Site Responses: Application to the Data of the French Accelerometric Network

Displacement spectra of earthquakes recorded by the French accelero- metric network at regional scale are modeled as the product of source, propagation (including geometric and anelastic attenuation), and site effects. We use an iterative Gauss-Newton inversion to solve the nonlinear problem and retrieve these different terms. This method is easy to implement because the partial derivatives of the am- plitude spectrum with respect to the different parameters have simple analytic forms. After convergence, we linearize the problem around the solution to compute the cor- relation matrix, which allows us to identify the parameters which are poorly resolved. We analyze data from two tectonically active regions: the Alps and the Pyrenees. Eighty-three earthquakes with local magnitudes between 3.0 and 5.3 are analyzed, with epicentral distances in the range 15-200 km. S-wave displacement spectra are computed using a fast Fourier transform and integration in the 0.5-15-Hz fre- quency domain. We assume a Brune-type source, with a geometric attenuation of the form R � γ , γ being constant, and a frequency-dependent quality factor of the form QQ0 × f α . The results reveal that the attenuation parameters are correlated to each other and to the seismic moments. The two regions have different attenuation patterns. The geometrical spreading factor is equal to 1 for the Alps and 1.2 for the Pyrenees. The anelastic attenuation exhibits low Q0 values (322 and 376 for the Alps and the Pyrenees, respectively) with regional variations for α (0.21 in the Alps and 0.46 in the Pyrenees). Computed moment magnitudes are generally 0.5 unit smaller than local magnitudes, and the logarithms of the corner frequencies decrease linearly with mag- nitude according to log10� fc �� 1:72 � 0:32 × Mw. Stress drops range from 10 5 to 10 7 Pa (i.e., 1-100 bars), with a slight dependence to magnitude (large stress drops for large magnitudes). Finally, robust site responses relative to an average rock-site response are derived, allowing us to identify good reference rock sites.

Frequency-Dependent Lg Q within the Continental United States

Frequency-dependent crustal attenuation (1/ Q ) is determined for seven distinct physiographic/tectonic regions of the continental United States using high-quality Lg waveforms recorded on broadband stations in the frequency band 0.5 to 16 Hz. Lg attenuation is determined from time-domain amplitude measurements in one-octave frequency bands centered on the frequencies 0.75, 1.0, 3.0, 6.0, and 12.0 Hz. Modeling errors are determined using a delete-j jackknife resampling technique. The frequency-dependent quality factor is modeled in the form of Q = Q 0 f η. Regions were initially selected based on tectonic provinces but were eventually limited and adjusted to maximize ray path coverage in each area. Earthquake data was recorded on several different networks and constrained to events occurring within the crust ( m b 3.5 in size. A singular value decomposition inversion technique was applied to the data to simultaneously solve for source and receiver terms along with Q for each region at specific frequencies. The lowest crustal Q was observed in northern and southern California where Q is described by the functions Q = 152(±37) f 0.72(±0.16) and Q = 105(±26) f 0.67(±0.16) , respectively. The Basin and Range Province, Pacific Northwest, and Rocky Mountain states also display lower Q and a strong frequency dependence characterized by the functions Q = 200(±40) f 0.68(±0.12) , Q = 152(±49) f 0.76(±0.18) , and Q = 166(±37) f 0.61(±0.14) , respectively. In contrast, in the central and northeast United States Q functions are Q = 640(±225) f 0.344(±0.22) and Q = 650(±143) f 0.36(±0.14) , respectively, show a high crustal Q and a weaker frequency dependence. These results improve upon previous Lg modeling by subdividing the United States into smaller, distinct tectonic regions and using significantly more data that provide improved constraints on frequency-dependent attenuation and errors. A detailed attenuation map of the continental United States can provide significant input into hazard map mitigation. Both scattering and intrinsic attenuation mechanisms are likely to play a comparable role in the frequency range considered in the study.

Frequency dependent Lg attenuation in south‐central Alaska

The characteristics of seismic energy attenuation are determined using high frequency Lg waves from 27 crustal earthquakes, in south‐central Alaska. Lg time‐domain amplitudes are measured in five pass‐bands and inverted to determine a frequency‐dependent quality factor, Q(f), model for south‐central Alaska. The inversion in this study yields the frequency‐dependent quality factor, in the form of a power law: Q(f)=Q0 fη = 220(±30) f0.66(±0.09) (0.75≤f≤12Hz). The results from this study are remarkably consistent with frequency dependent quality factor estimates, using local S‐wave coda, in south‐central Alaska. The consistency between S‐coda Q(f) and Lg Q(f) enables constraints to be placed on the mechanism of crustal attenuation in south‐central Alaska. For the range of frequencies considered in this study both scattering and intrinsic attenuation mechanisms likely play an equal role.

Attenuation and excitation of three-component ground motion in southern California

AbstractGround motion attenuation with distance and the variation of excitation with magnitude are parameterized using three-component, 0.25 to 5.0-Hz earthquake ground motions recorded in the distance range of 15-500 km for southern California to define a consistent model that describes both peak ground motion and Fourier spectra observations. The data set consists of 820 three-component TERRAscope recordings from 140 earthquakes, recorded at 17 stations, with moment magnitudes between 3.1 and 6.7. Regression analysis uses a simple model to relate the logarithm of measured ground motion to excitation, site, and propagation effects. The peak motions are Fourier velocity spectra and peak velocities in selected narrow bandpass-filtered frequency ranges. Regression results for Fourier amplitude spectra and peak velocities are used to define a piecewise continuous geometrical spreading function, frequency dependent Q(f), and a distance dependent duration that can be used with random vibration theory (RVT) or stochastic simulations to predict other characteristics of the ground motion.The duration results indicate that both the variation of the duration data with distance and its scattering decrease with increasing frequency. The ratio of horizontal to vertical component site terms is about √2 for all frequencies. However, this ratio is near unity for rock sites and is larger for soil sites.Simple modeling indicates that the Fourier velocity spectra are best fit by bilinear geometrical spreading of r−1 for r < 40 km and r−1/2 for r > 40 km. The frequency-dependent quality factor is Q(f) = 180f0.45 for each of the three components and also for the combined three-component data sets. The T5%-75% duration window provides good agreement between observed and RVT predicted peak values.

Evaluation of local site effects and their removal from borehole records observed in the Sendai region, Japan

AbstractWe present results from a borehole observation network composed of 12 borehole sites deployed in a 20 × 20 km area in the Sendai region, Japan. The subsurface Quaternary layers vary with each site, but a Pliocene layer is commonly underlying at a depth of 0 to 80 m throughout the Sendai region. We define this Pliocene layer, whose S-wave velocity is larger than 500 m/sec and whose N value of the standard penetration test is greater than 50, as an engineering bedrock in the region. Once we characterize ground motions at the engineering bedrock, we can either use these motions directly in the response analysis of whole soil-building systems or use them in the nonlinear analysis of soft soil layers as an input. The purpose of this study is to evaluate the local site effects due to surface layers overlying the engineering bedrock and to remove them by using one-dimensional (1D) soil models whose properties are determined by weak-motion records of 18 events. First we identify S-wave velocities and frequency-dependent quality factors Q from amplification factors between surface records and borehole records observed at 10 sites at depths of several tens of meters. The identified S-wave velocities are very close to S-wave logging values. The identified Q values show strong frequency dependence, proportional to f(0.46 to 1.16), where f is frequency. We confirm that the observed amplification factors in the frequency range from about 0.1 to 20 Hz can be explained well by the theoretical ones based on the 1D wave propagation theory with the identified S-wave velocities and Q. Then we estimate the so-called engineering bedrock waves, which are supposed to be observed on the outcrop of the engineering bedrock, from borehole records by using the 1D models with these identified soil constants. We confirm that local site effects due to surface layers overlying the engineering bedrock are properly removed so that we have similar characteristics in the resultant engineering bedrock waves from records at different sites.

Attenuation dispersion of Love waves in a two-layered half space

The attenuation of dispersive Love waves in an anelastic two-layered half space and in a simple symmetric homogeneous three-layered model has been investigated by introducing the complex propagation functions into the known explicit dispersion relation. A frequency-dependent attenuation relation is explicitly given assuming that the media quality factors are constant. The resultant quality factor of Love waves depends not only on the frequency, but also on the layer depth, via media quality factors. The attenuation coefficient of the Love waves becomes therefore a non-linear function of the frequency. The result is consistent with the results given in the literature on seismology and in-seam seismics. It is known that the spectral ratio method can only be used to estimate the frequency-independent quality factor. Therefore, a modification of the spectral ratio method is presented to invert the frequency-dependent quality factor of Love-waves. The modification facilitates investigations of frequency-dependent quality of the medium over previous methods.

Source parameters for the Roermond aftershocks of 1992 April 13-May 2 and site spectra for P and S waves at the Belgian seismic network

SUMMARY One- and three-component digital recordings from six stations of the Belgian seismic network were used to invert simultaneously for source velocity spectra of 18 aftershocks of the ML5.8 Roermond earthquake and for site amplification spectra at these stations. The events were selected to have well-constrained fault-plane solutions and the stations to be within 140 km epicentral distance. Frequency-dependent quality factors were computed from the coda waves of the same events. The Joint Source-Site Determination method we used, first corrects the body-wave spectra for radiation pattern, geometrical spreading, attenuation and free surface effect and then is formulated as a linear inverse problem repeated over frequencies (in this application between 1 and 30 Hz), with one reference station for which the site amplification spectrum is given as constant (in this application: La Chartreuse). The unbiased source velocity spectra were fitted with a Brune-type spectral function to obtain a scale factor and a corner frequency, from which, among others, the seismic moment, source radius, stress drop, final disolcation and fracture energy were calculated. In the 1.9-3.4 ML magnitude range, the stress drop, seismic energy and fault radius tend to increase with seismic moment, and seismic efficiency with fault dimension. Brune's stress drop varies between 0.4 and 4.6 MPa. Frictional overshoot prevails over partial stress drop. The average ratio of P- and S-wave corner frequencies is 1.6. The site amplification spectra vary between 1 and 10. Strong site effects were observed at stations Membach and Vianden.

Local Characteristics of the fmax of Bedrock Motion in the Tokyo Metropolitan Area, Japan.

On the basis of S-wave acceleration data observed at the bottom of a 2.3 km borehole drilled at the Shimohsa Crustal Activity Observatory (SHM), we studied the source region dependence of the fmax of bedrock motion in the Tokyo metropolitan area. In order to study a variety of fmax in this area, we divided the earthquakes that occurred beneath the Kanto district into six source groups. This division of earthquake sources leads us to the conclusion that the fmax of events that occurred in the boundary zone where the Philippine Sea plate is colliding with the Pacific and Eurasian plates is lower than 10 Hz and that of interplate events is higher than 20 Hz. This conclusion is certified using data recorded at another deep borehole site at Iwatsuki. We cannot deny the existence of source-controlled fmax, on the assumption that the path attenuation effect is independent of source region. Using estimates of frequency-dependent quality factor for S-waves obtained by Aki (1980), we find that the fmax of the source spectrum from events that occurred in the boundary zone where the Philippine Sea plate is colliding with the Pacific plate is about 10 Hz and that from events that occurred in other source regions which do not include the active seismic region in eastern Yamanashi Prefecture, is higher than 25 Hz.

Estimation of the coda quality factor for the Romanian territory

Abstract The coda Q is estimated for crustal and intermediate-depth earthquakes that occurred in different seismic regions in Romania during 1981–1988. The ‘ ƒ p vs. t ’ method is used for the computation of the frequency-dependent quality factor. The data used are short-period S-13 and DD-1 recordings of local earthquakes, obtained at the seismic stations of the national network. A crustal coda Q map is presented and compared with the heat-flow distribution for Romania. For crustal events, Q ranges between 40 and 450 at 1 Hz, and shows two distinct types of power of frequency dependence: 0.1–0.2 and 0.7–0.9. For intermediate-depth earthquakes, Q = 700–800 at 1 Hz and the power of frequency dependence is 0.1–0.2.