Spectral Density Level Research Articles

Sea Surface Height Wavenumber Spectrum from Airborne Interferometric Radar Altimeter

The proposed “Guanlan” ocean science satellite, led by China’s Laoshan Laboratory, includes an interferometric radar altimeter (IRA) as a key payload. As an integral part of its development, an airborne IRA experiment was conducted on 6 November 2021, with a flight path of approximately 90 km in the South China Sea. This study investigates the IRA’s ability to observe ocean sea surface height (SSH) across scales ranging from meters to mesoscale. The sea surface height anomaly (SSHA) of the IRA is aligned with the SSHA of the AVISO at scales greater than 30 km, but also demonstrates the ability to capture small-scale SSHA changes in two dimensions. We analyzed wavenumber spectra of SSHA obtained from the airborne IRA, ICESat-2, and SARAL/AltiKa satellite for this region. The results show a good agreement in power spectral density (PSD) levels between ICESat-2, SARAL/AltiKa and IRA at scales larger than 30 km. Within the submesoscale range of 1–10 km, the IRA SSHA spectrum exhibits a distinctly negative slope and the lowest energy level. The minimum PSD level of the IRA fell in the range of 10−4–10−3 m2/cycle/km, at scales around 1 km, which is more than an order of magnitude lower than that of ICESat-2, forming a spectral gap that is in agreement with the theoretical expectation. Furthermore, IRA-derived wave direction and significant wave height matched well with the MFWAM wave data. The results of this study underscore the considerable potential of airborne IRA in capturing SSHA across a range of scales, from oceanic waves to submesoscale.

Data-driven prediction of aerodynamic noise of transonic buffeting over an airfoil

Accurately predicting buffet frequency and aerodynamic noise level is crucial in transonic buffet noise reduction studies. In this study, the Random Forest (RF) algorithm is employed to predict the Power Spectral Density (PSD) and Overall Sound Pressure Level (OASPL) distribution over the supercritical airfoil RAE2822. The study indicates that the RF algorithm exhibits greater advantages over the Multi-Layer Perceptron (MLP). This algorithm does not suffer from the problems of high-frequency divergence or inflection distortion, maintaining a reduction in prediction errors for OASPL and PSD by approximately three to four orders of magnitude. Additionally, this paper proposes a priori criterion for evaluating the accuracy of PSD prediction. When there is a strong correlation between PSD at adjacent points, a data-driven modeling approach can achieve higher prediction accuracy. However, when the root mean square error of the cross-correlation functions, auto-correlation functions, and the PSD between adjacent points are both high, the generalization ability of pure data-driven modeling is insufficient, necessitating the additional monitoring points to ensure prediction accuracy.

Temporary Seismic Network in the Metropolitan Area of Rome (Italy): New Insight on an Urban Seismology Experiment

Abstract This study presents data and preliminary analysis from a temporary seismic network (SPQR), which was deployed in the urban area of Rome (Italy) for three months in early 2021. The network was designed to investigate the city’s subsurface while evaluating the feasibility of a permanent urban seismic network, and consisted of 24 seismic stations. Despite significant anthropogenic noise, the SPQR network well recorded earthquake signals, revealing clear spatial variability referable to site effects. In addition, the network’s continuous recordings allowed the use of seismic noise and earthquake signals to derive spectral ratios at sites located in different geological and lithological settings. During the experiment, there were periods of activity restrictions imposed on citizens to limit the spread of COVID-19. Although the observed power spectral density levels at stations may not show visible noise reductions, they do cause variations in calculated spectral ratios across measurement sites. Finally, a statistical noise analysis was conducted on continuous seismic station data to evaluate their performance in terms of detection threshold for earthquakes. The results indicate that all network stations can effectively record earthquakes with a good signal-to-noise ratio (≥5 for P and S phases) in the magnitude range of 1.9–3.3 at distances of 10 km and 80 km, respectively. In addition, the network has the potential to record earthquakes of magnitude 4 up to 200 km, covering areas in Central Italy that are far from the city. This analysis shows that it is possible to establish urban observatories in noisy cities such as Rome, where hazard studies are of particular importance due to the high vulnerability (inherent fragility of its monumental heritage) and exposure.

Using the soundscape to monitor vessel visitation at an Australian fur seal (Arctocephalus pusillus doriferus) breeding colony

Marine vessel traffic is a significant source of anthropogenic noise pollution and a major source of disturbance for many marine species. Despite Seal Rocks (Victoria, Australia) being the largest Australian fur seal breeding colony, and subject to a high volume of visitation, particularly during the breeding season, there has been no long-term effort to monitor visitation and its potential impact on seals. Autonomous passive acoustic recorders were deployed at Seal Rocks to monitor vessel visitation during both low visitation (off-peak) and the breeding (peak) season. Proportion of time vessels present in the area was calculated from visual inspection of long-term spectral averages (LTSA). Soundscape metrics were calculated to determine broadband sound pressure level (BL) and percentiles of power spectral density (PSD). Visitation was higher in the peak season, as was BL, particularly during daylight hours. While there were periods of high winds and heavy swell during both deployment seasons, vessel noise was still a regular and loud contributor to the soundscape. From these results, the airborne noise received by seals can also be estimated. These results will contribute towards the development of an impact model to assess noise impacts at Seal Rocks and other sensitive marine sites.

Deep learning and beamforming comparison of source ranging in a laboratory tank

Deep learning has been shown to be useful for ocean acoustics applications, such as source ranging. The variable nature of the ocean causes difficulty when attempting to apply trained models to new datasets. To explore ways to train supervised deep learning models that are robust to environmental variability, laboratory tank measurements can be used. A laboratory tank presents a system where uncertainty in the acoustic environment can be adjusted in a more controlled manner. In this work, recordings of ultrasonic chirps (50–200 kHz) are obtained at different source-receiver positions. Time-averaged spectral density levels are used to train one-dimensional convolutional neural networks that predict source-receiver range. The trained networks are tested on data obtained under different conditions. Data augmentation techniques are applied to increase the models’ robustness in the presence of limited uncertainty. Metrics such as root mean-squared error and mean absolute percent error are used to quantify the model’s performance. The results from deep learning with single channel recordings and multi-channel recordings are compared with traditional beamforming methods on the multi-channel data. [Work supported by the Office of Naval Research.]

(Invited) In-Depth Understanding of the Key Contributors to the Total Flicker Noise in Advanced Logic Devices

The aim of this work is to perform an in-depth analysis in order to identify the key contributors to the total flicker noise in advanced MOSFET technologies, e.g. UTBOX, Gate-all-around (GAA) nanowire or nanosheet FET devices. For all investigated devices of these technologies an increase of the flat-band noise power spectral density level with the increase of the applied gate voltage was observed. This may be related to the correlated carrier number and mobility fluctuations noise mechanisms and/or with additional access resistances noise contributions. Different existing models have been applied in order to identify the key 1/f noise mechanism. However, a discrepancy in the obtained 1/f noise contributors is highlighted, and leads to some questioning about which employed model is most accurate and gives good indications on the key contributors and estimated parameters of the total flicker noise.

Hybrid synthesizer with two PLLs and DDS Part 2. Fine tuning circuit and main PLL

The use of a direct digital synthesizer (DDS) with a frequency converter in the frequency shift circuit of a hybrid synthesizer of high-frequency oscillations can significantly reduce its phase noise. This version of the frequency synthesizer (FS) has not been previously considered in known publications. There is a need to perform an analysis of existing circuits of hybrid FS with PLL to identify the elements that make the greatest contribution to the phase noise of the output oscillations, develop and experimentally test a FS with a low level of phase noise power spectral density. The performed calculations and experiments show that the use of a frequency shift circuit with frequency conversion based on a DDS operating in the first Nyquist zone in a hybrid frequency synthesizer makes it possible to minimize the effect of DDS phase noises on the FS phase noises. In this case, at frequencies of detuning from the carrier, where the flicker noise of the PFD of PLL circuits in cascade connection prevails, the contribution of the flicker noise of the PLL chips to the noise of the output oscillation of the FS will be equivalent. It is convenient to estimate the phase noise of the FS at the equivalent frequency, determined by the frequency of the phase detector and the division factor in the feedback circuit of the second (main) PLL ring. Taking into account the results of the first part of this work, the calculated relations obtained allow us to design hybrid frequency synthesizers with DDS and PLL with a low level of phase noise. The expressions obtained in the work for the phase noise of a hybrid FS and its components also make it possible to estimate the potentially achievable levels of FS phase noise and can be used in calculating the characteristics of oscillation sources and signal synthesizers.

Interrelation between ferroelectric properties and defects based on low-frequency noise analysis of HZO ferroelectric capacitor

Switching characteristics of ferroelectrics depend on the fabrication conditions and phase-transition results of each fabrication recipe. Here, the pulsed I–V and positive-up negative-down plots of hafnium zirconium oxide ferroelectric capacitors (FeCaps) are analyzed using low-frequency noise (LFN), an electrical method to investigate defects including oxygen vacancies that are key elements influencing polarization properties. This is a new trial at adopting the LFN method for analysis of FeCaps to find interrelation ferroelectric characteristics and defects depending on the annealing conditions. Increasing power spectral density (PSD) levels are observed with increasing annealing temperature and time. Moreover, the nature of the defects reflected in the PSD is examined via x-ray photoelectron spectroscopy. Correlations are observed between the defects, including oxygen vacancies and ZrOx defects, and FeCap properties. High intrinsic polarization is observed when the density of defects is large; this shows that oxygen vacancies and ZrOx defects in FeCaps may enhance the orthorhombic phase by inducing lattice strain. These findings are expected to facilitate LFN studies of ferroelectrics and the fundamental understanding of their electrical properties from defects and oxygen vacancy analyses.

A real-time underwater soundscape classification system

The study of underwater soundscapes, pioneered by Dr. Jeff Nystuen, includes information about geophonic, biological, and anthropogenic processes, many of which have distinct spectral characteristics. The contributors to the underwater ambient sound field can be quantified and classified using knowledge of these spectra. Long-term acoustic data recordings from a wide variety of depths and locations with high sampling frequencies have been analyzed to develop a robust soundscape classification algorithm based on Dr. Nystuen’s methods. Each one-minute of data has been evaluated to classify the soundscape into wind, rainfall, drizzle, heavy shipping, light shipping, other vessel activity, and biological phenomena. The power spectral density (PSD) level at twelve frequencies in the range of 0.03–30 kHz, as well as the spectral slope for the frequency range between 8 and 15kHz and kurtosis are used for the passive classification algorithm. After classification, the wind speed was quantified as a cubic function of PSD at 6 kHz and recording depth. The wind speed estimated from the acoustics compared very well to satellite data for speeds lower than 15 m/s. The classification algorithms are being embedded on a processor using Xilinx’s Zynq System-on-Chip that produces a 32-kHz hybrid millidecade spectrum in real-time on a logarithmic scale.

Effects of multiple subcavities with floor subcavity in supersonic cavity flow

Experimental and computational analysis has been carried out by many researchers on supersonic cavity flow, but detailed analysis based on Rossiter's model still requires some insight. In the current study an open rectangular cavity with a length to depth ratio of 2 (L/D = 2) and Mach number at the inlet as 1.71, was considered as a baseline configuration for experimental analysis. Statistical techniques such as power spectral density (PSD), correlation, and overall sound pressure level (OASPL) were carried out on the unsteady pressure data, to analyze the aero-acoustic flow physics. High-speed schlieren images were processed to obtain spatially coherent modes by proper orthogonal decomposition (POD). The analysis was extended for different dimensions of subcavities on the aft, floor, and front wall. This detailed analysis of these configurations with different dimensions and combinations revealed the various flow features and mode frequencies in supersonic cavity. As the front wall subcavity act as a passive control device, reducing the overall sound pressure level inside the cavity whereas, the aft wall subcavity acts as a passive resonator with distinct harmonic fluid-resonant modes, a similar phenomenon was observed for floor subcavity at different locations. A novel method was employed to analyze Rossiter's model and its applicability in estimating experimental modes was verified, as it accurately predicted the dominant frequencies with a maximum of 2.74% uncertainty among all the configurations.

Influence of emotional tension on tremor parameters in the writing process

Background. The influence of emotional tension on writing is actively studied in the aspect of its influence on kinematic characteristics. Such approaches as machine learning, exploratory and handwriting research prevail. There are currently no studies which take into account the relationship between kinetic characteristics of writing and emotional tension. The proposed study fills the gap in this area and is part of the dissertation research. Purpose. To study the method of tensotremorography as an indicator of the presence of emotional tension in the process of writing. Methods. The spectral power of applied force, obtained by Welch's method, was analyzed during the process of writing of the prepared phrase during the presentation of the COMPASS emotional image and sound stimuli, exceeding the level of comfort, according to the kinetic characteristics of 50 subjects. Result. Noticeable significant difference between the powers at stress-inducing stimuli and non-stress-inducing stimuli. The differences between the 10th and 90th percentile of emotionally relevant stimuli is virtually indistinguishable from each other and are at the same level of spectral density (about 370 000–400 000 mN2/Hz). This supports the assumption that the response to stimulation by emotionally significant stimuli is nonspecific. Conclusion. The results of the study show that the spectral power at a frequency of 8–16 Hz is significantly higher when emotional stimuli are presented than in the absence of stimuli, or when a neutral stimulus is presented. This technique has prospects for use in the detection of hidden information, determination of emotional tension in the educational environment and medicine as a means of determining motor and nervous system diseases.

Controllable acoustic deterrent based on the warning signals generated by nonel detonators

Acoustic deterrents are a practical strategy to mitigate the impact of underwater noise on marine mammals. However, their safety and effectiveness are still debatable. This study proposes a controllable acoustic deterrence method to protect marine mammals threatened by underwater blasting noise. The method creates strong-randomness warning signals using nonel detonators and establishes an escape time for animals protected. Combining the BELLHOP ray-based acoustic model with the marine environmental parameters and animals' auditory characteristics, we built a prediction model to establish a link between the acoustic fields and the adjustable source parameters, and provide a Risk zone and Deterrent zone for animals. The simulation and experimental results demonstrated that the root mean squared error between the simulated and measured sound pressure spectral density levels did not exceed 4.5 dB and the coefficient of determination remained at approximately 0.8, indicating that the new deterrent is an effective method with good controllable performances.

Potential therapeutic mechanism of deep brain stimulation of the nucleus accumbens in obsessive-compulsive disorder.

Deep brain stimulation (DBS) of the nucleus accumbens (NAc) (NAc-DBS) is an effective solution to refractory obsessive-compulsive disorder (OCD). However, evidence for the neurobiological mechanisms of OCD and the effect of NAc-DBS is still lacking. One hypothesis is that the electrophysiological activities in the NAc are modulated by DBS, and another hypothesis is that the activities of neurotransmitters in the NAc are influenced by DBS. To investigate these potential alterations, rats with quinpirole (QNP)- induced OCD were treated with DBS of the core part of NAc. Then, extracellular spikes (SPK) and local field potentials (LFP) in the NAc were recorded, and the levels of relevant neurotransmitters and related proteins were measured. Analysis of SPK revealed that the firing rate was decreased and the firing pattern was changed after NAc-DBS, and analysis of LFP showed that overall power spectral density (PSD) levels were reduced after NAc-DBS. Additionally, we found that the relative powers of the theta band, alpha band and beta band were increased in OCD status, while the relative powers of the delta band and gamma band were decreased. This pathological pattern of power distribution was reformed by NAc-DBS. Furthermore, we found that the local levels of monoamines [dopamine (DA) and serotonin (5-HT)] and amino acids [glutamate (Glu) and gamma-aminobutyric acid (GABA)] in the NAc were increased in OCD status, and that the expression of the two types of DA receptors in the NAc exhibited an opposite change. These abnormalities could be reversed by NAc-DBS. These findings provide a more comprehensive understanding about the function of the NAc in the pathophysiology of OCD and provide more detailed evidence for the potential effect of NAc-DBS.

Modern Solutions to Improve the Energy Efficiency of Radio Lines for the Technical Renewal of Radio Stations of Integrated Communication Systems

Promising tasks for improving radio equipment with increased energy efficiency, related to in-depth preliminary study and efficiency research using the stand of the chief designer, are considered. Initially, a theoretical factor analysis of the interference radio terminal energy efficiency with respect to evenly distributed over the spectrum is given. The problem of choosing a variant of digital modulation and parameters of a noise-resistant code from the condition of obtaining the least energy for the transmission of one bit of information at a given error probability per bit and the level of spectral noise density is examined. With regard to broadband signals, energy-efficient linearly frequency-modulated signals are allocated. In the case of narrowband signals, cognitive technologies for improving energy efficiency for radio paths with partially filled spectrum, tuning radio lines to the 'windows of the best transparency' of the spectrum, are studied. Their importance for VHF radio lines and HF radio systems with tuning to the optimal frequency by regular ionosphere sounding is noted. The features of cognitive radio networks development to improve the energy efficiency of radio facilities are considered. The ways of algorithms design for modem and noise-resistant encoder energy effective tuning to a given radio line conditions for testing in the stand of the Chief Designer are discussed. Priority tasks for improving radio equipment with increased energy efficiency have been specified. Urgent specific subtasks for elaboration at the stand of the Chief Designer are highlighted.

Mitigation of turbulent noise sources by riblets

A feasibility study is presented on the application of riblets to suppress turbulent pressure sources leading to a reduction in the generation of aerofoil self-noise. It is shown that riblets can reduce skin friction as well as the turbulence intensity inside the boundary layer. In addition, near-wall turbulence structures were found to be dissipated quite rapidly when crossing the riblets surface. It is found that riblets (1) slightly reduce the wall fluctuating pressure power spectral density level at the low and high frequency ranges, but cause an increase at the mid frequency range, and (2) reduce the lateral turbulence coherence length scale across a large frequency range. As a result, riblets have the potential to reduce trailing edge noise at the low and high frequency regions. The fundamental mechanism by which riblets reduce the turbulent intensity level inside the boundary layer is investigated by studying the spatio-temporal evolution of turbulent spots, which are commonly regarded as the building blocks of a turbulent boundary layer. In this paper two mechanisms are proposed. First, the enhanced momentum achieved at the becalmed region of each turbulent spot will lead to a reduction in the overall turbulence intensity obtained when turbulent spots merge downstream. Second, the internal turbulence level at the rear part of a turbulent spot can be reduced directly by an enhanced re-laminarisation effect.

Градієнтна оптимізація двопараметричної віконної функції Найквіста для зменшення позасмугогово випромінювання в OFDM системі

The relationship between Nyquist pulses in the time domain and Nyquist window functions used in orthogonal frequency division multiplexing (OFDM) technology has been investigated. One of the ways to approximate the transition region of Nyquist window functions using piecewise linear functions has been analyzed. This method allowed increasing the number of degrees of signal freedom through the introduction of two additional parameters. The spectral density of the selected two-parameter Nyquist window function has been determined. Optimization of the synthesized signal by the criterion of minimum energy in the first side lobes of its spectral density has been performed. To solve the optimization problem, the gradient descent method with minimization of the function at each stage of the iteration by the golden section method is chosen. In the MATLAB programming environment, program has been created that works according to the selected optimization algorithm. With the maximum allowable relative error ε =10–3, the number of iterations of the gradient search method is 2 iterations. It is established that at the optimal values of the signal parameters the amount of energy concentrated in the first three side lobes of its spectral density is 12.6 dB less than for the rectangular window function. The graphs for the synthesized window function with optimal parameters in time and frequency domain are given in this paper. The use of the two-parameter Nyquist window function with reduced level of spectral density of the side lobes allows reducing the level of out-of-band radiation of the OFDM signal and increasing the resistance of the system with many subcarriers to frequency offsets caused by the mutual movement of the transmitter and receiver. It should be noted that the chosen gradient search algorithm is universal and can be used to optimize the Nyquist window functions by different criteria and regardless of the number of signal parameters.

Interference-Fading-Suppressed Pulse-Coding Φ-OTDR Using Spectrum Extraction and Rotated-Vector-Sum Method

With phase-sensitive optical time-domain reflectometry (Φ-OTDR), an optic fiber can be used as a distributed vibration sensor to perceive the external disturbance along the fiber through the phase variation of the Rayleigh backscatter light. However, due to the inevitable interference fading phenomenon, the signal-to-noise ratio (SNR) of Rayleigh backscatter light at certain points is insufficient, thus affecting the fidelity of vibration sensing. In this paper, we propose the spectrum extraction and the rotated-vector-sum (SERVS) method to suppress the interference fading in the pulse-intensity-coding Φ-OTDR, which applies Golay complementary sequence through acousto-optic modulator (AOM). Benefited from the easier implementation, the experimental results demonstrate that the percentage of fading points can be reduced from 2.98% to 0.33% significantly and the standard deviation of differential phase is also decreased from 0.6556 rad to 0.2901 rad. Also the minimum level of averaged power spectral density (PSD) of the differential phase at whole locations along the fiber is reduced about 6 dB/Hz effectively. For the demodulated disturbance signal, no influence on the SNR is observed thus it maintains a SNR improvement of 8.6 dB compared to the traditional single pulse Φ-OTDR system, achieving a noise floor of 2.38 pϵ/√Hz.

Aero-acoustic feedback mechanisms in supersonic cavity flow with subcavity

An open rectangular cavity with a length to depth ratio of 2 (L/D = 2) and inlet Mach number 1.71 was considered as a baseline configuration for an unsteady computational analysis. Fast Fourier transform using power spectral density, correlation, and overall sound pressure level (OASPL) was carried out on the unsteady pressure data, to analyze the flow dynamics. Many flow visualization techniques were employed such as density gradient-based numerical schlieren, vorticity contour, and streamlines for revealing major features associated with the flow. Vortex shedding visualization was carried out in terms of the Lambda 2 (λ2) criterion, where the vortex core can be observed moving downstream in the shear layer. In the acoustic pressure contours and OASPL contours, the characteristics of the acoustic waves can be distinctly observed traversing within the cavity. The analysis was extended for different flow conditions and configurations. The front wall subcavity with a ratio of subcavity length (l) to cavity length (L) l/L = 0.20 has already been established as a passive control device experimentally whereas the aft wall subcavity with l/L = 0.20 was found to behave like a passive resonator with distinct harmonic fluid-resonant modes. A more detailed investigation of these configurations with different dimensions and combinations resulted in a comparative and better understanding of the flow features, mode frequencies, and fluid-resonant oscillations in a supersonic cavity flow. Further, a method for designing front wall subcavity for passive control device has been applied to a variety of test cases and has been proven effective in suppressing the oscillations for cavity configurations with longitudinal oscillation mechanisms.

Measurements of open-water arctic ocean noise directionality and transport velocity.

Measurements from bottom-mounted acoustic vector sensors, deployed seasonally between 2008 and 2014 on the shallow Beaufort Sea shelf along the Alaskan North Slope, are used to estimate the ambient sound pressure power spectral density, acoustic transport velocity of energy, and dominant azimuth between 25 and 450 Hz. Even during ice-free conditions, this region has unusual acoustic features when compared against other U.S. coastal regions. Two distinct regimes exist in the diffuse ambient noise environment: one with high pressure spectral density levels but low directionality, and another with lower spectral density levels but high directionality. The transition between the two states, which is invisible in traditional spectrograms, occurs between 73 and 79 dB re 1 μPa2/Hz at 100 Hz, with the transition region occurring at lower spectral levels at higher frequencies. Across a wide bandwidth, the high-directionality ambient noise consistently arrives from geographical azimuths between 0° and 30° from true north over multiple years and locations, with a seasonal interquartile range of 40° at low frequencies and high transport velocities. The long-term stability of this directional regime, which is believed to arise from the dominance of wind-driven sources along an east-west coastline, makes it an important feature of arctic ambient sound.

Землетрясение 12 декабря 2020 г. в Анапской зоне с Mw=3.8, I0=4–5 баллов

The article presents instrumental and macroseismic data on the earthquake on 12.12.2020 at 14:54 with Mw=3.8, h=30 km. The epicenter and parameters of the earthquake were deter-mined using instrumental data from the network of regional seismic stations in the western zone of the North Caucasus of the EGS RAS. This earthquake occurred in the shelf zone of the Eastern Black Sea coast near the resort town of Anapa, in the Anapa seismically active area. This area tectonically is the conjunction of the northern side of the Tuapse trough and the thrust front of the Greater Caucasus. The focal mechanism for the earthquake was calcu-lated. The solution of the focal mechanism was obtained from the polarization in P-waves at 29 seismic stations. From the focal follows the type of source up thrust-thrust movement. The GS RAS organized a macroseismic survey in the Anapa and Novorossiysk regions on the “VKontakte” social network a day after the earthquake. According to the results of the study, 144 respondents in 15 settlements in 7 days were interviewing. The maximum observed in-tensity was I=4-5 points in Su-Psekh and Varvarovka according to the results of the macro-seismic survey, a map of the distribution of intensity points was create. The SEISAN software package calculated the spectral parameters of the source: seismic moment, corner frequency, spectral density level and spectral magnitude Mw.