Power-law Frequency Dependence Research Articles

Direct Observations of Wave‐Sea Ice Interactions in the Antarctic Marginal Ice Zone

AbstractWave energy propagating into the Antarctic marginal ice zone effects the quality and extent of the sea ice, and wave propagation is therefore an important factor for understanding and predicting changes in sea ice cover. Wave‐sea ice interactions are notoriously hard to model and in situ observations of wave activity in the Antarctic marginal ice zone are scarce, due to the extreme conditions of the region. Here, we provide new in situ data from two drifting Surface Wave Instrument Float with Tracking (SWIFT) buoys deployed in the Weddell Sea in the austral winter and spring of 2019. The buoy location ranges from open water to more than 200 km into the sea ice. We estimate the attenuation of swell with wave periods 8–18 s, and find an attenuation coefficient α = 4 · 10−6 to 7 · 10−5 m−1 in spring, and approximately five‐fold larger in winter. The attenuation coefficients show a power law frequency dependence, with power coefficient close to literature. The in situ data also shows a change in wave direction, where wave direction tends to be more perpendicular to the ice edge in sea ice compared to open water. A possible explanation for this might be a change in the dispersion relation caused by sea ice. These observations can help shed further light on the influence of sea ice on waves propagating into marginal ice zones, aiding development of coupled wave‐sea ice models.

Site-Specific Amplitude-Distance Laws, Wave Velocities, Damping, and Transfer Functions of the Soil from Hammer Impacts and Application to Railway-Induced Ground Vibration: Similarities and Mid-Frequency Differences

PurposeThe purpose of this article is to check if and how hammer experiments can be applied to the prediction of railway vibration.MethodsThe propagation of ground vibrations is theoretically analysed with frequency-wavenumber and simplified methods. Experimental methods are presented which can characterise the site-specific ground vibrations by wave velocities, stiffness and damping. Measurements with hammer and train excitation have been performed at several sites.Results The one-third octave spectra show the stiffness-dependent amplitudes and the low- and high-frequency filter effects due to the layering and the damping of the soil. Specific train effects, an additional high-frequency filter, the sleeper passage frequency, and an amplified mid-frequency component can be clearly found. The attenuation with distance is analysed in detail where the theoretical exponential and the empirical frequency-dependent power law are considered. Hammer and train excitation show the same site-specific effects which are mainly due to the stronger or weaker damping of the soil. The train attenuation is generally weaker than the hammer attenuation. The attenuation exponent of the power law, which is strongly dependent on the site and the frequency, is reduced for the train vibration by 0.3–0.5 in agreement with the theory. Reasons are discussed for the overall power law and for the dominating mid-frequency component.ConclusionTherefore, it can be concluded that hammer experiments can well be used for the prediction of train vibrations.

The Impact of Internal Gravity Waves on the Spectra of Turbulent Fluctuations of Vertical Wind Velocity in the Stable Atmospheric Boundary Layer

The wave turbulence interactions in the stable boundary layer (SBL) of the atmosphere are studied based on data from lidar measurements of the vertical component of wind velocity during the propagation of internal gravity waves (IGWs). It is shown that as an IGW appears, the amplitude of the spectra of turbulent fluctuations of vertical wind velocity nearby the frequency of quasi-harmonic oscillations induced by an IGW increases significantly, sometimes by several orders of magnitude, compared to the spectra in the absence of an IGW. Since IGW energy is transferred to small-scale turbulence, the amplitude of spectra with the Kolmogorov–Obukhov −5/3 power-law frequency dependence in the inertial frequency range increases. The slope of the spectra in the low-frequency range between the frequency of IGW-induced oscillations and the frequency of the lower boundary of the inertial range exceeds the slope, corresponding to the −5/3 power-law dependence. In this frequency range, the spectra obey the power-law dependence on the frequency with the exponent ranging from −4.2 to −1.9. The average value of the exponent −3 is consistent with a low-frequency slope caused by IGWs in turbulent spectra in the lower SBL.

Gifts from anomalies: Exact results for Landau phase transitions in metals

Non-Fermi liquid phenomena arise naturally near critical points of Landau ordering transitions in metallic systems, where strong fluctuations of a bosonic order parameter destroy coherent quasiparticles. Despite progress in developing controlled perturbative techniques, much of the low energy physics of such metallic quantum critical points remains poorly understood. We demonstrate that exact, non-perburbative results can be obtained for both optical transport and static susceptibilities in “Hertz-Millis” theories of Fermi surfaces coupled to critical bosons. Such models possess a large emergent symmetry and anomaly structure, which we leverage to fix these quantities. In particular, we show that in the infrared limit, the boson self energy at zero wave vector, \mathbf{q}=0𝐪=0, is a constant independent of frequency, and the real part of the optical conductivity, \sigma(\omega)σ(ω), is purely a delta function Drude peak with no other corrections. Therefore, further frequency dependence in the boson self energy or optical conductivity can only come from irrelevant operators in a clean system. Exact relations between Fermi liquid parameters as the critical point is approached from the disordered phase are also obtained. The absence of a universal, power law frequency dependence in the boson self energy contrasts with previous perturbative calculations, and we explain the origin of this difference.

Diamond surface electric-field noise detection using shallow nitrogen-vacancy centers

Detection of diamond surface electric-field noise is of importance for studying the coherence properties of shallow nitrogen-vacancy (NV) centers. Using the double quantum relaxation method, we demonstrated that the noise has a power-law frequency dependence, and it increases slowly from 295 K to 420 K but reduces quickly at higher temperatures. As the Dutta-Horn model described, the noise is created by ensembles of two-level systems with activation energies ranging from 0.3 eV to 0.6 eV. For diamond surface passivation, we found that the solid covering material (PMMA) outperforms the liquid one (glycerol) in reducing the electric-field noise, which was attributed to the presence of surface-modified phononic coupling noise. We anticipate that our findings will contribute to a better understanding of the origins of surface 1/f electric-field noise, as well as identify optimal covering materials for enhancing the coherence time of near-surface NV centers.

Test-retest reproducibility of in vivo oscillating gradient and microscopic anisotropy diffusion MRI in mice at 9.4 Tesla.

Microstructure imaging with advanced diffusion MRI (dMRI) techniques have shown increased sensitivity and specificity to microstructural changes in various disease and injury models. Oscillating gradient spin echo (OGSE) dMRI, implemented by varying the oscillating gradient frequency, and microscopic anisotropy (μA) dMRI, implemented via tensor valued diffusion encoding, may provide additional insight by increasing sensitivity to smaller spatial scales and disentangling fiber orientation dispersion from true microstructural changes, respectively. The aims of this study were to characterize the test-retest reproducibility of in vivo OGSE and μA dMRI metrics in the mouse brain at 9.4 Tesla and provide estimates of required sample sizes for future investigations. Twelve adult C57Bl/6 mice were scanned twice (5 days apart). Each imaging session consisted of multifrequency OGSE and μA dMRI protocols. Metrics investigated included μA, linear diffusion kurtosis, isotropic diffusion kurtosis, and the diffusion dispersion rate (Λ), which explores the power-law frequency dependence of mean diffusivity. The dMRI metric maps were analyzed with mean region-of-interest (ROI) and whole brain voxel-wise analysis. Bland-Altman plots and coefficients of variation (CV) were used to assess the reproducibility of OGSE and μA metrics. Furthermore, we estimated sample sizes required to detect a variety of effect sizes. Bland-Altman plots showed negligible biases between test and retest sessions. ROI-based CVs revealed high reproducibility for most metrics (CVs < 15%). Voxel-wise CV maps revealed high reproducibility for μA (CVs ~ 10%), but low reproducibility for OGSE metrics (CVs ~ 50%). Most of the μA dMRI metrics are reproducible in both ROI-based and voxel-wise analysis, while the OGSE dMRI metrics are only reproducible in ROI-based analysis. Given feasible sample sizes (10-15), μA metrics and OGSE metrics may provide sensitivity to subtle microstructural changes (4-8%) and moderate changes (> 6%), respectively.

Superconductivity of incoherent electrons in the Yukawa Sachdev-Ye-Kitaev model

We study a model of $N$ fermions in a quantum dot, coupled to $M$ bosons by a disorder-induced complex Yukawa coupling (Yukawa-SYK model), in order to explore the interplay between non-Fermi liquid and superconductivity in a strongly coupled, (quantum-)critical environment. We analyze the phase diagram of the model for an arbitrary complex interaction and arbitrary ratio of $N/M$, with special focus on the two regimes of non-Fermi-liquid behavior: an SYK-like behavior with a power-law frequency dependence of the fermionic self-energy and an impurity-like behavior with frequency independent self-energy. We show that the crossover between the two. can be reached by varying either the strength of the fermion-boson coupling or the ratio $M/N$. We next argue that in both regimes the system is unstable to superconductivity if the strength of time-reversal-symmetry-breaking disorder is below a certain threshold. We show how the corresponding onset temperatures vary between the two regimes. We argue that the superconducting state is highly unconventional with an infinite set of minima of the condensation energy at $T=0$, corresponding to topologically different gap functions. We discuss in detail similarities and differences between this model and the model of dispersion-full fermions tuned to a metallic quantum-critical point, with an effective singular dynamical interaction $V(\Omega) \propto 1/|\Omega|^\gamma$ (the $\gamma-$model).

Electrical and dielectric properties of rare earth substituted hard-soft ferrite (Co0.5Ni0.5Ga0.01Gd0.01Fe1.98O4)x/(ZnFe2O4)y nanocomposites

ZnFe2O4 (ZFO) NPs (nanoparticles), Co0.5Ni0.5Ga0.01Gd0.01Fe1.98O4 (CNGaGdFO) NPs and hard-soft spinel ferrite (H/S) (CNGaGdFO)x/(ZFO)y (x:y = 1:1, 1:2, 1:3, 2:1, 3:1 and 4:1) NCs (nanocomposites) were synthesized via a one-pot sol–gel auto combustion route. X-ray powder diffraction (XRD) analyses confirmed the purity of ZFO NPs, CNGaGdFO NPs and H/S (H/S) (CNGaGdFO)x/(ZFO)y (x:y = 1:1, 1:2, 1:3, 2:1, 3:1 and 4:1) (absence of any second phase). The crystallite size of NCs was between 39 and 52 nm. The cubic morphology was observed for ZFO NPs, CNGaGdFO NPs and all H/S NCs by the help of scanning electron microscopy (SEM) and transmission electron microscopy (TEM) analyses. Energy dispersive X-Ray analysis (EDX) also confirmed the chemical formula of all the NC samples. Electrical and dielectric properties of ZFO NPs, CNGaGdFO NPs and H/S NCs were explored with an impedance analyzer with f ≤ 3.0 MHz, where f stands for frequency, and within the temperature range between 20 and 120 °C. Electric and dielectric parameters such as AC conductivity as well as DC conductivity, activation energy, dielectric constant, dielectric loss in addition to the dissipation parameter relevant to the electrical energy due to different physical processes were measured for each of the given compositional ratios. The AC conductivity was found to follow the frequency-dependent power law in general, being mainly reliant on the compositional ratios and the measured temperatures especially at lower frequencies. This study has shown that CoNiGaGdFeO-ZnFe2O4 H/S NCs carry out conduction mechanisms, which can be predominantly credited to grain–grain boundaries for various compositional ratios. The dielectric constant of (CNGaGdFO)x/(ZFO)y (x:y = 1:1, 1:2, 1:3, 2:1, 3:1 and 4:1) H/S NCs indicates common dielectric behaviours with frequency, largely dependent on compositional rates of the hard to soft spinel ferrites. It is observed that hard ferrite is dominant in the formation of the semicircles, and the diameter of the semicircles shows a drop as the temperature rises, suggesting a temperature-dependent relaxation mechanism. Consequently, the observed variation of the studied dielectric parameters with frequency can be explained by the conduction mechanism in most composition ratios of hard to soft spinel ferrites, which can be explained by a phenomenological method with Koop's model.

Switching of antiferromagnetic states in LiCoPO4 as investigated via the magnetoelectric effect

The linear magnetoelectric (ME) effect allows for the selection or switching between two antiferromagnetic (AFM) states via the application of large electric ($E$) and magnetic ($H$) fields. Once an AFM state is selected, it is preserved by an energy barrier, even when the fields are removed. Using a simple phenomenological model, we find that this energy barrier, needed to switch the AFM state, is proportional to the product of the $E$ and $H$ coercive fields $(EH)_{\rm C}$. We measured the field and temperature dependence of $(EH)_{\rm C}$ in LiCoPO$_4$ for two different field configurations, and the data show the temperature variation of $(EH)_{\rm C}\sim(T_{\rm N}-T)^{3/2}$ in good agreement with the model. We also investigated the dynamics of the AFM domain switching using pulsed $E$-field measurements. It was found that the coercive field $(EH)_{\rm C}$ follows a power-law frequency dependence and is well described in the framework of Ishibashi-Orihara model, implying 1-dimensional character of domain wall propagation.

Numerical analysis of a wave equation for lossy media obeying a frequency power law

Abstract We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency-dependent power law. First we prove the existence of a unique solution to this equation with particular attention paid to the handling of the fractional derivative. Then we derive an explicit time-stepping scheme based on the finite element method in space and a combination of convolution quadrature and second-order central differences in time. We conduct a full error analysis of the mixed time discretization and in turn the fully space-time discretized scheme. Error estimates are given for both smooth solutions and solutions with a singularity at $t = 0$ of a type that is typical for equations involving fractional time derivatives. A number of numerical results are presented to support the error analysis.

Focused fields of ultrashort radially polarized laser pulses having low-order spatiotemporal couplings

We present a detailed study of the fields and propagation characteristics around the focus of ultrashort radially-polarized laser beams (RPLBs) having low-order spatio-temporal couplings (STCs). The three STCs considered are the focusing of the different frequencies to different positions along the longitudinal coordinate, the focusing of the frequencies to different positions along one transverse coordinate, and the beam waist or Rayleigh range having a power-law frequency dependence. The STCs considered are deemed low-order because they are generally linear in frequency. The combination of a low-order vector beam, ultrashort pulse duration, and the three different STCs shows promise for exotic applications in dielectric or charged particle manipulation and potentially other strong-field phenomena. The STCs presented are all developed in a standard frequency-domain model where each case involves a different chromatic term. We present the results unique to the vector nature of the RPLBs and compare them to the linearly polarized cases, opening up opportunities for control of the electric field around the focus with the additional element of polarization.

Impedance spectroscopy and conduction mechanism of a BiFe0.95Mn0.05O3 thin film

Dielectric response and conduction mechanism were investigated for a multiferroic BiFe0.95Mn0.05O3 epitaxial thin film. A contribution from a thermally activated interface (0.37 eV) and the bulk of the film on the dielectric response were observed through the comparison between experimental results and equivalent circuit model. The low frequency interface relaxation signatures strongly suggest a Maxwell-Wagner space charge origin. The alternative current conductivity deduced from the model follows a power law frequency dependence suggesting a polaronic hopping mechanism while the low frequency limit is in perfect agreement with the direct current conduction mechanism. The current-voltage characteristics were indeed correlated with Schottky-Simmons interface limited transport with activation energy of 0.36 eV, close to the one extracted from the impedance analysis. Such analysis of the electrostatic landscape and dielectric behaviour may help to further understanding the anomalous photo-induced properties in the BiFeO3 system.

NMR T1 dispersion of crude oils from 10 kHz to 20 MHz

In this article T1 dispersion measurements on a set of crude oils that span a viscosity range of 0.7 cP up to 2·104 cP are reported. Larmor frequencies were varied from 10 kHz up to 20 MHz. The relaxation dispersion measurements are interpreted in terms of the threshold viscosity model, which allows model applicability tests presented in literature to be extended to Larmor frequencies below 1 MHz. It is shown that the measurements can be equally well described by assuming a proton-proton interaction process as by assuming proton-electronic spin interactions. A power-law frequency dependence of the threshold viscosity parameter is observed for both types of spin interactions. Modifications to the description of rotational diffusion in the threshold viscosity model are suggested that may account for the observed frequency dependence in the threshold viscosity parameter. Without modifications, the threshold viscosity model is shown to have a limited application range of η ≥ 40 cP and ω0/2π ≥ 700 kHz, in which model parameters have a physically justifiable order of magnitude for the set of crude oils studied. Outside this range, the threshold viscosity model can still be applied as a parametrization of T1 dispersion effects for the complete set of experiments presented in this study. This explicit viscosity and Larmor frequency dependent parametrization may be used as first-order approximation to T1 dispersion in crude oils for which only oil viscosity is known and may be applied to polarization level and pulse sequence simulations in low field NMR relaxometry studies up to 20 MHz for a wide range of crude oil viscosities, and in particular for better interpretation of NMR flow measurements on crude oils.

Attenuation of High-Frequency P and S Waves in the Crust of Central and Western Tien Shan

In order to better understand the attenuation characteristics in the crust of the central and western Tien Shan orogenic belt, we investigate both Qp and Qs values by applying the extended coda-normalization method. We estimate the frequency-dependent attenuation of both P and S waves in the frequency band of 1.0–20.0 Hz using data from local networks. The average frequency relations of Qp and Qs have been derived as Qp = (61 ± 9) × f(1.21±0.08) and Qs = (77 ± 6) × f(1.11±0.04) by fitting a power-law frequency dependence model for the study region. The low Q0 and high η values indicate that the central and western Tien Shan is a tectonically and seismically active region. We also find lateral variations of both Qp,s and Qs/Qp values, reflecting complex tectonic structures in the study area. In general, the relatively high-attenuation areas corresponding to tectonically active regions are found beneath mountainous ranges in the central Tien Shan whereas the relatively low-attenuation areas are associated with stable regions, such as Fergana Basin and Issyk-Kul Lake. Besides, regions in the central Tien Shan with Qs/Qp > 1 are likely partially saturated with fluids or rich in scattering heterogeneities, whereas regions in the western Tien Shan display Qs/Qp < 1, possibly suggesting almost complete fluid saturation.

Diffusion dispersion imaging: Mapping oscillating gradient spin-echo frequency dependence in the human brain.

Oscillating gradient spin-echo (OGSE) diffusion MRI provides information about the microstructure of biological tissues by means of the frequency dependence of the apparent diffusion coefficient (ADC). ADC dependence on OGSE frequency has been explored in numerous rodent studies, but applications in the human brain have been limited and have suffered from low contrast between different frequencies, long scan times, and a limited exploration of the nature of the ADC dependence on frequency. Multiple frequency OGSE acquisitions were acquired in healthy subjects at 7T to explore the power-law frequency dependence of ADC, the "diffusion dispersion." Furthermore, a method for optimizing the estimation of the ADC difference between different OGSE frequencies was developed, which enabled the design of a highly efficient protocol for mapping diffusion dispersion. For the first time, evidence of a linear dependence of ADC on the square root of frequency in healthy human white matter was obtained. Using the optimized protocol, high-quality, full-brain maps of apparent diffusion dispersion rate were also demonstrated at an isotropic resolution of 2 mm in a scan time of 6 min. This work sheds light on the nature of diffusion dispersion in the healthy human brain and introduces full-brain diffusion dispersion mapping at clinically relevant scan times. These advances may lead to new biomarkers of pathology or improved microstructural modeling.

Resolution Limits in Photoacoustic Imaging Caused by Acoustic Attenuation.

In conventional photoacoustic tomography, several effects contribute to the loss of resolution, such as the limited bandwidth and the finite size of the transducer, or the space-dependent speed of sound. They can all be compensated (in principle) technically or numerically. Frequency-dependent acoustic attenuation also limits spatial resolution by reducing the bandwidth of the photoacoustic signal, which can be numerically compensated only up to a theoretical limit given by thermodynamics. The entropy production, which is the dissipated energy of the acoustic wave divided by the temperature, turns out to be equal to the information loss, which cannot be compensated for by any reconstruction method. This is demonstrated for the propagation of planar acoustic waves in water, which are induced by short laser pulses and measured by piezoelectric acoustical transducers. It turns out that for water, where the acoustic attenuation is proportional to the squared frequency, the resolution limit is proportional to the square root of the distance and inversely proportional to the square root of the logarithm of the signal-to-noise ratio. The proposed method could be used in future work for media other than water, such as biological tissue, where acoustic attenuation has a different power-law frequency dependence.

Impedance spectroscopy of Bi-rich BiFeO3: Twin thermal-activations

Transport measurements data are presented on bismuth-rich BiFeO3 ceramic, synthesized by a solid state method. Conductivity isotherms were analyzed using Jonscher’s empirical power-law frequency dependence. Monotonically increasing frequency-exponent n(T) over 413–593 K indicates a small polaron tunnelling mechanism for the charge transport. Distinct linear regimes observed in the Arrhenius σdc vs. T−1 plot suggest that two different charge-carriers/conductivity-relaxations prevail above and below ∼490 K. Twin Arrhenius regimes of ac-conductivity also exhibit a sharp “transition” at 510 K, from the pinned-dipole/hopping-anion dynamics to the free-dipole/oscillating-ions response at higher temperatures. Furthermore, a concurrent behavior-change of the locus traced out by the charge-hopping frequency ωh [with σ(ωh) = 2σdc] also designates 510 K as delineating two different transport characteristics in the adjacent temperature regimes.

Stability of Random Processes with the 1/f α Spectrum

Extreme fluctuations have been modeled based on point nonpotential and potential systems of stochastic equations, in which white noise induces random processes with a power-law frequency dependence of the power spectra. The distribution of extreme fluctuations corresponds to the maximum of statistical entropy, which indicates their stability. The stability of fluctuation processes with 1/f α power spectra has been analyzed based on the principle of maximum information entropy.

Effect of concentration, temperature, pH, co-solutes on the rheological properties of Hyptis suaveolens L. mucilage dispersions

The rheological behavior of mucilage dispersions obtained from Hyptis suaveolens L. seeds was characterized. The apparent viscosity showed a non-Newtonian shear-thinning behavior in a range of shear rate 0.1–300 s−1 at 25 °C and pH 6.5. The Cross and Herschel-Bulkley parameters (r2 > 0.9923) indicated that more physical entanglements arise with increasing concentration (0.1–0.75% w/v). Mechanical spectra were obtained by frequency sweep measurement (0.01–10 Hz) at 0.1% deformation and 25 °C. A G´-G´´ cross-over point was observed (1 Hz) for a 0.1% mucilage dispersion, suggesting a molecular transition from random coil to an entangled conformation. The tan(δ) performance for mucilage dispersion with 0.25–0.75% (w/v) concentrations, with values between 0.2 and 0.3, classified into an intermediate behavior between weak and elastic gel. The G´ values were well characterized by power-law frequency dependence (r2≥0.9628). The mucilage dispersion exhibited temperature stability between 20 and 60 °C, and activation energies with values between 7.20 and 12.85 kJmol-1 indicated that more energy was required to disrupt the formed entanglements and to induce viscous flow. For 0.5% mucilage dispersion, the NaCl addition (0–250 mM) generate more aggregates which disruption became more shear dependence as salt concentration growth, and the formed entanglements were less flexible from neutral to alkaline conditions. The sucrose addition (1, 3, 5, 10, and 20% w/v) into 0.5% mucilage dispersion produced a less shear-thinning behavior, giving a stabilizing effect and enhancing the biopolymer gel strength. These results suggest that mucilage could be applied in many food applications, such as stabilizing, thickening and gelling agents.

Estimation and applicability of attenuation characteristics for source parameters and scaling relations in the Garhwal Kumaun Himalaya region, India

Source parameters of the small to moderate earthquakes are significant for understanding the dynamic rupture process, the scaling relations of the earthquakes and for assessment of seismic hazard potential of a region. In this study, the source parameters were determined for 58 small to moderate size earthquakes (3.0 ≤ Mw ≤ 5.0) occurred during 2007–2015 in the Garhwal-Kumaun region. The estimated shear wave quality factor (Qβ(f)) values for each station at different frequencies have been applied to eliminate any bias in the determination of source parameters. The Qβ(f) values have been estimated by using coda wave normalization method in the frequency range 1.5–16 Hz. A frequency-dependent S wave quality factor relation is obtained as Qβ(f) = (152.9 ± 7) f(0.82±0.005) by fitting a power-law frequency dependence model for the estimated values over the whole study region. The spectral (low-frequency spectral level and corner frequency) and source (static stress drop, seismic moment, apparent stress and radiated energy) parameters are obtained assuming ω−2 source model. The displacement spectra are corrected for estimated frequency-dependent attenuation, site effect using spectral decay parameter “Kappa”. The frequency resolution limit was resolved by quantifying the bias in corner frequencies, stress drop and radiated energy estimates due to finite-bandwidth effect. The data of the region shows shallow focused earthquakes with low stress drop. The estimation of Zúñiga parameter (ε) suggests the partial stress drop mechanism in the region. The observed low stress drop and apparent stress can be explained by partial stress drop and low effective stress model. Presence of subsurface fluid at seismogenic depth certainly manipulates the dynamics of the region. However, the limited event selection may strongly bias the scaling relation even after taking as much as possible precaution in considering effects of finite bandwidth, attenuation and site corrections. Although, the scaling can be improved further with the integration of large dataset of microearthquakes and use of a stable and robust approach.