Unified Wind Wave Growth and Spectrum Functions for All Water Depths: Field Observations and Model Results

Wind wave development is governed by the fetch- or duration-limited growth principle that is expressed as a pair of similarity functions relating the dimensionless elevation variance (wave energy) and spectral peak frequency to fetch or duration. Combining the pair of similarity funtions the fetch or duration variable can be removed to form a dimensionless function of elevation variance and spectral peak frequency, which is interepreated as the wave enegry evolution with wave age. The relationship is initially developed for quasi-neural stability and quasi-steady wind forcing conditions. Further analyses show that the same fetch, duration, and wave age similarity functions are applicable to unsteady wind forcing conditions, including rapidly accelerating and decelerating mountain gap wind episodes and tropical cyclone (TC) wind fields. Here it is shown that with the dimensionless frequency converted to dimensionless wavenumber using the surface wave dispersion relationship, the same similarity function is applicable in all water depths. Field data collected in shallow to deep waters and mild to TC wind conditions, and synthetic data generated by spectrum model computations are assembled to illustrate the applicability. For the simulation work, the finite-depth wind wave spectrum model and its shoaling function are formulated for variable spectral slopes. Given wind speed, wave age, and water depth, the measrued and spectrum-computed significant wave heights and the associated growth parameters are in good agreement in forcing conditions from mild to TC winds and in all depths from deep ocean to shallow lake.

Application of Bayesian Super-Resolution to Spectroscopic Data for Precise Characterization of Spectral Peak Shape

The number of data points of digitally recorded spectra have been limited by the number of multichannel detectors employed, which sometimes impedes the precise characterization of spectral peak shape. Here we describe a methodology to increase the number of data points as well as the signal-to-noise (S/N) ratio by applying Bayesian super-resolution in the analysis of spectroscopic data. In our present method, first, the hyperparameters for the Bayesian super-resolution are determined by a virtual experiment imitating actual experimental data, and the precision of the super-resolution reconstruction is confirmed by the calculation of errors from the ideal values. For validation of the super-resolution reconstruction of spectroscopic data, we applied this method to the analysis of Raman spectra. From 200 Raman spectra of a reference Si substrate with a data interval of about 0.8 cm−1, super-resolution reconstruction with a data interval of 0.01 cm−1 was successfully achieved with the promised precision. From the super-resolution spectrum, the Raman scattering peak of the reference Si substrate was estimated as 520.55 (+0.12, −0.09) cm−1, which is comparable to the precisely determined value reported in previous works. The present methodology can be applied to various kinds of spectroscopic analysis, leading to increased precision in the analysis of spectroscopic data and the ability to detect slight differences in spectral peak positions and shapes.

Spectra of seismic noise at selected Indian stations

India Meteorological Department (IMD) is operating five digital seismograph systems at New Delhi (NDI),.Shillong (SHL), Pune (POO), Kodaikanal (KDK) and Dhamlsala (DHM) since last few years. The details pertaining to instrumental characteristics and software for data retrieval and processing are presented in this paper, Through PC based algorithms. noise pectra are computed and interpreted for these five stations. It is found that the maximum peak occurs at about 6Hz for Pune. Shillong and Kodaikanal while at New Delhi and Dharmsala, it is noted at about 2 Hz. The spectral peak at Shillong as deduced from the SRO system shifts to about I Hz which is in agreement with a similar observation reported at Gauribidanur seismic array.

An update on techniques to assess normal-mode behavior of rock arches by ambient vibrations

Natural rock arches are rare and beautiful geologic landforms with important cultural value. As such, their management requires periodic assessment of structural integrity to understand environmental and anthropogenic influences on arch stability. Measurements of passive seismic vibrations represent a rapid and non-invasive technique to describe the dynamic properties of natural arches, including resonant frequencies, modal damping ratios, and mode shapes, which can be monitored over time for structural health assessment. However, commonly applied spectral analysis tools are often limited in their ability to resolve characteristics of closely spaced or complex higher-order modes. Therefore, we investigate two techniques well-established in the field of civil engineering through application to a set of natural arches previously characterized using polarization analysis and spectral peak-picking techniques. Results from enhanced frequency domain decomposition and parametric covariance-driven stochastic subspace identification modal analyses showed generally good agreement with spectral peak-picking and frequency-dependent polarization analyses. However, we show that these advanced techniques offer the capability to resolve closely spaced modes including their corresponding modal damping ratios. In addition, due to preservation of phase information, enhanced frequency domain decomposition allows for direct and convenient three-dimensional visualization of mode shapes. These techniques provide detailed characterization of dynamic parameters, which can be monitored to detect structural changes indicating damage and failure, and in addition have the potential to improve numerical models used for arch stability assessment. Results of our study encourage broad adoption and application of these advanced modal analysis techniques for dynamic analysis of a wide range of geological features.

Application of Bayesian Super-Resolution to Spectroscopic Data for Precise Characterization of Spectral Peak Shape

The number of data points of digitally recorded spectra have been limited by the number of multi-channel detectors employed, which sometimes inhibits the precise characterization of spectral peak shape. Here we describe a methodology to increase the number of data points as well as the signal-to-noise (S/N) ratio by applying Bayesian super-resolution in the analysis of spectroscopic data. In our present method, first the hyperparameters for the Bayesian super-resolution are determined by a virtual experiment imitating actual experimental data, and the precision of the super-resolution reconstruction is confirmed by the calculation of errors from the ideal values. For validation of the super-resolution reconstruction of spectroscopic data, we applied this method to the analysis of Raman spectra. From 200 Raman spectra of a reference Si substrate with a data interval of about 0.8 cm-1, super-resolution reconstruction with a data interval of 0.01 cm-1 was successfully achieved with the promised precision. From the super-resolution spectrum, the Raman scattering peak of the reference Si substrate was estimated as 520.55 (+0.12, -0.09) cm-1, which is comparable to the precisely determined value reported in previous works. The present methodology can be applied to various kinds of spectroscopic analysis, leading to increased precision in the analysis of spectroscopic data and the ability to detect slight differences in spectral peak positions and shapes.

Wavelet Analysis of Red Noise and Its Application in Climate Diagnosis

Signals are often destroyed by various kinds of noises. A common way to statistically assess the significance of a broad spectral peak in signals and the synchronization between signals is to compare with simple noise processes. At present, wavelet analysis of red noise is studied limitedly and there is no general formula on the distribution of the wavelet power spectrum of red noise. Moreover, the distribution of the wavelet phase of red noise is also unknown. In this paper, for any given real/analytic wavelet, we will use a rigorous statistical framework to obtain the distribution of the wavelet power spectrum and wavelet phase of red noise and apply these formulas in climate diagnosis.

MNLS simulations of surface wave groups with directional spreading in deep and finite depth waters

We simulate focusing surface gravity wave groups with directional spreading using the modified nonlinear Schrödinger (MNLS) equation and compare the results with a fully-nonlinear potential flow code, OceanWave3D. We alter the direction and characteristic wavenumber of the MNLS carrier wave, to assess the impact on the simulation results. Both a truncated (fifth-order) and exact version of the linear dispersion operator are used for the MNLS equation. The wave groups are based on the theory of quasi-determinism and a narrow-banded Gaussian spectrum. We find that the truncated and exact dispersion operators both perform well if: (1) the direction of the carrier wave aligns with the direction of wave group propagation; (2) the characteristic wavenumber of the carrier wave coincides with the initial spectral peak. However, the MNLS simulations based on the exact linear dispersion operator perform significantly better if the direction of the carrier wave does not align with the wave group direction or if the characteristic wavenumber does not coincide with the initial spectral peak. We also perform finite-depth simulations with the MNLS equation for dimensionless depths ($$k_{\text {p}}d$$ k p d ) between 1.36 and 5.59, incorporating depth into the boundary conditions as well as the dispersion operator, and compare the results with those of fully-nonlinear potential flow code to assess the finite-depth limitations of the MNLS.

Enhanced Static Modulated Fourier Transform Spectrometer for Fast Approximation in Field Application

We discuss the data sampling frequency, the spectral resolution, and the limit for non-aliasing in the static modulated Fourier transform spectrometer based on a modified Sagnac interferometer. The measurement was performed in a very short 4 ms, which is applicable for real time field operation. The improved spectrometer characteristics were used to investigate the spectral properties of an InGaAs light emitting diode. In addition, The measured spectral peak was shifted from 6420 cm−1 to 6365 cm−1, as the temperature increased from 25 °C to 40 °C, when the operating current is fixed to be 0.55 A. As the applied current increased from 0.30 A to 0.55 A at room temperature, the spectral width was broadened from 316 cm−1 to 384 cm−1. Compared to the conventional Fourier transform spectrometer, the measured spectral width by the static modulated Fourier transform spectrometer showed a deviation less than 10%, and the spectral peak shift according to the temperature rise showed a difference within 2%.

Dimension-Selective Attention and Dimensional Salience Modulate Cortical Tracking of Acoustic Dimensions

Some theories of auditory categorization suggest that auditory dimensions that are strongly diagnostic for particular categories - for instance voice onset time or fundamental frequency in the case of some spoken consonants - attract attention. However, prior cognitive neuroscience research on auditory selective attention has largely focused on attention to simple auditory objects or streams, and so little is known about the neural mechanisms that underpin dimension-selective attention, or how the relative salience of variations along these dimensions might modulate neural signatures of attention. Here we investigate whether dimensional salience and dimension-selective attention modulate cortical tracking of acoustic dimensions. In two experiments, participants listened to tone sequences varying in pitch and spectral peak frequency; these two dimensions changed at systematically different rates. Inter-trial phase coherence (ITPC) and EEG signal amplitude at the rates of pitch and spectral change allowed us to measure cortical tracking of these dimensions. In Experiment 1, tone sequences varied in the size of the pitch intervals, while the size of spectral peak intervals remained constant. Neural entrainment to pitch changes was greater for sequences with larger compared to smaller pitch intervals, with no difference in entrainment to the spectral dimension. In Experiment 2, participants selectively attended to either the pitch or spectral dimension. Neural entrainment was stronger in response to the attended compared to unattended dimension for both pitch and spectral dimensions. These findings demonstrate that bottom-up and top-down attentional mechanisms enhance the cortical tracking of different acoustic dimensions within a single sound stream.