It has been already revealed that the daily Solar Irradiance Data during the time period from October, 1984 to October, 2003 obtained by Earth Radiation Budget Satellite (ERBS) exhibits an Anti-persistent trend having multi-periodic phenomena. The solar irradiance time series data being a complex non linear signal in this paper we have tried to detect the irregularity and multifractality in the signal using continuous wavelet transform modulus maxima(WTMM) algorithm. Singularity spectrum of the signal has been obtained to measure the degree of multifractality of the Solar Irradiance signal.
Evidence for Long-Lasting Electrical Leader Discharges in NonSpecular Meteor ...researchinventy
Unusual, non-specular, fast-movingmeteortrail echoes are observed in the summer polar upper mesosphere near 90 km.Usually, at mid-latitudes, field-aligned irregularities cause non-specular trails, while in the polar region long-lasting irregularities are possibly sustained by charged meteor dust.The unusual meteor trails propagate downward and upward at speeds of 3.3-6.4 kms-1 along a slanted path length of 10.4 km between 87-93 km altitudes, merging in the middle and lasting for 8-10s. Here we propose that an electrical discharge is responsible for these trails. The corresponding horizontal electric field for the observed speeds is estimated up to 16.3 Vm-1 at 90 km.Both the long-lasting merging of two fast-moving plasma trails and the modest speed compared to those (~104 -105 ms -1 ) of lightning leader process and of jets (< 400 ms) occurring above thunderclouds likely suggest a new type of meteor-trail leader discharge occurring in the summer polar upper mesosphere
This document presents a novel algorithm for classifying signals (glitches) that arise in gravitational wave channels of the Laser Interferometer Gravitational-Wave Observatory (LIGO). The algorithm uses Kohonen Self Organizing Feature Maps and discrete wavelet transform coefficients to classify glitches based on their morphology and other parameters like signal-to-noise ratio and duration. This low-latency algorithm aims to help the LIGO detector characterization group identify and mitigate noise sources more quickly.
First Observation of the Earth’s Permanent FreeOscillation s on Ocean Bottom ...Sérgio Sacani
The Earth’s hum is the permanent free oscillations of the Earth recorded in the absence ofearthquakes, at periods above 30 s. We present the first observations of its fundamental spheroidaleigenmodes on broadband ocean bottom seismometers (OBSs) in the Indian Ocean. At the ocean bottom,the effects of ocean infragravity waves (compliance) and seafloor currents (tilt) overshadow the hum. In ourexperiment, data are also affected by electronic glitches. We remove these signals from the seismic traceby subtracting average glitch signals; performing a linear regression; and using frequency-dependentresponse functions between pressure, horizontal, and vertical seismic components. This reduces the longperiod noise on the OBS to the level of a good land station. Finally, by windowing the autocorrelation toinclude only the direct arrival, the first and second orbits around the Earth, and by calculating its Fouriertransform, we clearly observe the eigenmodes at the ocean bottom.
Pulsar emission amplified and resolved by plasma lensing in an eclipsing binarySérgio Sacani
Radio pulsars scintillate because their emission travels through the
ionized interstellar medium along multiple paths, which interfere
with each other. It has long been realized that, independent of their
nature, the regions responsible for the scintillation could be used
as ‘interstellar lenses’ to localize pulsar emission regions1,2
. Most
such lenses, however, resolve emission components only marginally,
limiting results to statistical inferences and detections of small
positional shifts3–5
. As lenses situated close to their source offer
better resolution, it should be easier to resolve emission regions of
pulsars located in high-density environments such as supernova
remnants6
or binaries in which the pulsar’s companion has an
ionized outflow. Here we report observations of extreme plasma
lensing in the ‘black widow’ pulsar, B1957+20, near the phase in its
9.2-hour orbit at which its emission is eclipsed by its companion’s
outflow7–9
. During the lensing events, the observed radio flux is
enhanced by factors of up to 70–80 at specific frequencies. The
strongest events clearly resolve the emission regions: they affect the
narrow main pulse and parts of the wider interpulse differently. We
show that the events arise naturally from density fluctuations in
the outer regions of the outflow, and we infer a resolution of our
lenses that is comparable to the pulsar’s radius, about 10 kilometres.
Furthermore, the distinct frequency structures imparted by the
lensing are reminiscent of what is observed for the repeating fast
radio burst FRB 121102, providing observational support for the
idea that this source is observed through, and thus at times strongly
magnified by, plasma lenses10
Wave breaking is a complex phenomenon characterized by energy dissipation and turbulence. The study analyzed wave breaking through laboratory tests using wave gauges and an acoustic Doppler velocimeter. Fifteen wave conditions were tested in a wave channel with a variable slope bottom profile designed to induce breaking. Timeseries and spectral analysis of free surface elevation data provided insights into wave propagation and breaking behavior under different conditions. Empirical formulations were also evaluated based on the experimental results.
Seismic attribute analysis using complex trace analysisSomak Hajra
The document discusses seismic attributes, which are measurements or properties obtained from seismic data that provide information about rock properties. It defines various types of attributes such as pre-stack, instantaneous, physical, and multi-trace attributes. The document also discusses the analysis of key seismic attributes like reflection strength, instantaneous phase and frequency through the use of complex trace analysis. Finally, it concludes that seismic attributes are important tools that help interpreters extract more information from seismic data for applications like hydrocarbon exploration and reservoir characterization.
This document compares methods for determining subsurface shear-wave velocity, which is important for seismic hazard assessment. It analyzes data from seismic cone penetration tests (SCPT), spectral analysis of surface waves (SASW), continuous surface wave system (CSWS), and microtremors in the Victoria, Canada area. The peak frequencies determined from SCPT measurements generally agree well with microtremor measurements, as both sample to similar depths. Surface wave methods like SASW and CSWS have more limited depth penetration and thus microtremor frequencies are sometimes lower. Combining microtremors with invasive or active non-invasive methods provides the best characterization of site response.
Evidence for Long-Lasting Electrical Leader Discharges in NonSpecular Meteor ...researchinventy
Unusual, non-specular, fast-movingmeteortrail echoes are observed in the summer polar upper mesosphere near 90 km.Usually, at mid-latitudes, field-aligned irregularities cause non-specular trails, while in the polar region long-lasting irregularities are possibly sustained by charged meteor dust.The unusual meteor trails propagate downward and upward at speeds of 3.3-6.4 kms-1 along a slanted path length of 10.4 km between 87-93 km altitudes, merging in the middle and lasting for 8-10s. Here we propose that an electrical discharge is responsible for these trails. The corresponding horizontal electric field for the observed speeds is estimated up to 16.3 Vm-1 at 90 km.Both the long-lasting merging of two fast-moving plasma trails and the modest speed compared to those (~104 -105 ms -1 ) of lightning leader process and of jets (< 400 ms) occurring above thunderclouds likely suggest a new type of meteor-trail leader discharge occurring in the summer polar upper mesosphere
This document presents a novel algorithm for classifying signals (glitches) that arise in gravitational wave channels of the Laser Interferometer Gravitational-Wave Observatory (LIGO). The algorithm uses Kohonen Self Organizing Feature Maps and discrete wavelet transform coefficients to classify glitches based on their morphology and other parameters like signal-to-noise ratio and duration. This low-latency algorithm aims to help the LIGO detector characterization group identify and mitigate noise sources more quickly.
First Observation of the Earth’s Permanent FreeOscillation s on Ocean Bottom ...Sérgio Sacani
The Earth’s hum is the permanent free oscillations of the Earth recorded in the absence ofearthquakes, at periods above 30 s. We present the first observations of its fundamental spheroidaleigenmodes on broadband ocean bottom seismometers (OBSs) in the Indian Ocean. At the ocean bottom,the effects of ocean infragravity waves (compliance) and seafloor currents (tilt) overshadow the hum. In ourexperiment, data are also affected by electronic glitches. We remove these signals from the seismic traceby subtracting average glitch signals; performing a linear regression; and using frequency-dependentresponse functions between pressure, horizontal, and vertical seismic components. This reduces the longperiod noise on the OBS to the level of a good land station. Finally, by windowing the autocorrelation toinclude only the direct arrival, the first and second orbits around the Earth, and by calculating its Fouriertransform, we clearly observe the eigenmodes at the ocean bottom.
Pulsar emission amplified and resolved by plasma lensing in an eclipsing binarySérgio Sacani
Radio pulsars scintillate because their emission travels through the
ionized interstellar medium along multiple paths, which interfere
with each other. It has long been realized that, independent of their
nature, the regions responsible for the scintillation could be used
as ‘interstellar lenses’ to localize pulsar emission regions1,2
. Most
such lenses, however, resolve emission components only marginally,
limiting results to statistical inferences and detections of small
positional shifts3–5
. As lenses situated close to their source offer
better resolution, it should be easier to resolve emission regions of
pulsars located in high-density environments such as supernova
remnants6
or binaries in which the pulsar’s companion has an
ionized outflow. Here we report observations of extreme plasma
lensing in the ‘black widow’ pulsar, B1957+20, near the phase in its
9.2-hour orbit at which its emission is eclipsed by its companion’s
outflow7–9
. During the lensing events, the observed radio flux is
enhanced by factors of up to 70–80 at specific frequencies. The
strongest events clearly resolve the emission regions: they affect the
narrow main pulse and parts of the wider interpulse differently. We
show that the events arise naturally from density fluctuations in
the outer regions of the outflow, and we infer a resolution of our
lenses that is comparable to the pulsar’s radius, about 10 kilometres.
Furthermore, the distinct frequency structures imparted by the
lensing are reminiscent of what is observed for the repeating fast
radio burst FRB 121102, providing observational support for the
idea that this source is observed through, and thus at times strongly
magnified by, plasma lenses10
Wave breaking is a complex phenomenon characterized by energy dissipation and turbulence. The study analyzed wave breaking through laboratory tests using wave gauges and an acoustic Doppler velocimeter. Fifteen wave conditions were tested in a wave channel with a variable slope bottom profile designed to induce breaking. Timeseries and spectral analysis of free surface elevation data provided insights into wave propagation and breaking behavior under different conditions. Empirical formulations were also evaluated based on the experimental results.
Seismic attribute analysis using complex trace analysisSomak Hajra
The document discusses seismic attributes, which are measurements or properties obtained from seismic data that provide information about rock properties. It defines various types of attributes such as pre-stack, instantaneous, physical, and multi-trace attributes. The document also discusses the analysis of key seismic attributes like reflection strength, instantaneous phase and frequency through the use of complex trace analysis. Finally, it concludes that seismic attributes are important tools that help interpreters extract more information from seismic data for applications like hydrocarbon exploration and reservoir characterization.
This document compares methods for determining subsurface shear-wave velocity, which is important for seismic hazard assessment. It analyzes data from seismic cone penetration tests (SCPT), spectral analysis of surface waves (SASW), continuous surface wave system (CSWS), and microtremors in the Victoria, Canada area. The peak frequencies determined from SCPT measurements generally agree well with microtremor measurements, as both sample to similar depths. Surface wave methods like SASW and CSWS have more limited depth penetration and thus microtremor frequencies are sometimes lower. Combining microtremors with invasive or active non-invasive methods provides the best characterization of site response.
This document analyzes wave packet propagation in weakly nonlinear acoustic metamaterials through spectro-spatial analysis. Spectro-spatial analysis uses full-scale transient analysis and signal processing techniques to reveal dispersion curves and localized solitary wave properties. The analysis finds an unusual frequency shift phenomenon in the middle-wavelength region of the optical wave branch that causes it to behave like a band gap for transient waves. This frequency shift is then used to design a direction-biased waveguide with high efficiency, as shown through numerical simulations.
Seismic methods use seismic waves created by impacts on the surface to map underground structures. The waves travel through underground layers and are reflected or refracted at boundaries between different materials. Analysis of the travel times and velocities of the waves allows determining the depth and type of geological layers. Seismic reflection techniques involve creating waves at shot points and recording them with receivers at different offsets to generate common midpoint gathers. Processing the gathers yields a seismic section that images layer boundaries like an echo sounder. Seismic refraction uses refracted head waves along interfaces to build a shallow velocity model for near-surface layers. Both methods together provide structural and physical characterization of underground features like buried valleys.
This document summarizes a study that investigated shear-wave attenuation and site response in Guerrero, Mexico using spectra from moderate earthquakes. The researchers developed a method to model spectra assuming an ω-2 source shape and exponential decay to describe attenuation. They were able to separate the spectral decay parameter into distance-dependent and site-dependent components. Comparing observed and model event spectra allowed them to estimate site response effects for different stations, independent of source and path effects. The study found weaker distance dependence of attenuation in Guerrero compared to southern California, but greater near-site attenuation. Significant amplification and deamplification was observed in site response functions for hard rock sites, with no clear correlation with local geology or topography.
1. The document discusses searches for radio transients using the Long Wavelength Array (LWA1), a radio telescope array sensitive to frequencies between 10-88 MHz.
2. No fast radio bursts (FRBs) were detected in 96 hours of observation, placing an upper limit on the FRB rate of <4.0×102 day-1 sky-1 at 38 MHz.
3. The null detection and event rate limits suggest that FRB spectra may be flatter than a assumed spectral index of -1.4, meaning their flux densities do not decrease as quickly with lower frequencies.
Filtering in seismic data processing? How filtering help to suppress noises. Haseeb Ahmed
To enhance the signal-Noise ratio different techniques are used to remove the noises.
Types of Seismic Filtering:
1- Frequency Filtering.
2- Inverse Filtering (Deconvolution).
3- Velocity Filtering.
The document summarizes the observation of gravitational waves from a binary black hole merger detected by the LIGO detectors on September 14, 2015. The key points are:
1) LIGO detected a transient gravitational-wave signal that matches predictions from general relativity for the inspiral and merger of two black holes.
2) Analysis of the signal determines that the initial black hole masses were about 36 and 29 solar masses, which merged into a final black hole of about 62 solar masses over 0.2 seconds.
3) This is the first direct detection of gravitational waves as well as the first observation of a binary black hole merger, confirming predictions from Einstein's theory of general relativity.
The document summarizes initial measurements of mesospheric gravity waves over McMurdo, Antarctica using infrared imaging. Over 300 gravity wave events were observed and analyzed over the 2012 season. The observed horizontal wavelengths averaged 22 km, phase speeds averaged 53.3 m/s. Wave propagation directions varied seasonally, with northwest in fall, isotropic in winter, and southwest in spring. Comparisons show similar wave characteristics to other Antarctic sites, but McMurdo exhibits a wider range of phase speeds. Ongoing analysis will help understand pan-Antarctic gravity wave climatology.
A highly magnetized twin-jet base pinpoints a supermassive black holeSérgio Sacani
Supermassive black holes (SMBH) are essential for the production of jets in radio-loud active galactic nuclei (AGN). Theoretical
models based on (Blandford & Znajek 1977, MNRAS, 179, 433) extract the rotational energy from a Kerr black hole, which could
be the case for NGC1052, to launch these jets. This requires magnetic fields on the order of 103 G to 104 G. We imaged the vicinity
of the SMBH of the AGN NGC1052 with the Global Millimetre VLBI Array and found a bright and compact central feature that is
smaller than 1.9 light days (100 Schwarzschild radii) in radius. Interpreting this as a blend of the unresolved jet bases, we derive the
magnetic field at 1 Schwarzschild radius to lie between 200 G and 8:3 104 G consistent with Blandford & Znajek models.
1) Geophysics uses remote sensing to determine subsurface conditions by analyzing seismic and radar signals that travel through and reflect off underground materials.
2) There are four main modes of signal propagation: vertical reflection, wide angle reflection, critical refraction, and direct waves. Precisely measuring the travel times of these signals allows subsurface structures to be interpreted.
3) Reflection seismology analyzes reflected signals to determine depth to interfaces by relating travel time, distance between source and receiver, and velocity, while refraction seismology uses travel times of critically refracted signals to determine shallow subsurface velocity structure.
This document summarizes a research paper on using discrete wavelet transform (DWT) and empirical mode decomposition (EMD) to remove "ghosting effects" from seismic signals. It begins with an introduction to earthquakes and how they are recorded via seismographs. It then describes existing filtering methods and their limitations. The proposed method uses 1D convolutional filtering and vibration analysis with DWT and EMD to enhance noisy seismic wave signals. It involves steps like magnitude spectrum estimation, windowing, phase estimation, noise variance prediction, and directional estimation. The method is able to attenuate coherent noise and improve seismic wave detection, separation and tracking. In conclusion, time-scale directional filters are a powerful tool for seismic data
Successful search for ether drift in a modified michelson morley experiment u...Võ Hồng Quý
This modified Michelson-Morley experiment directly measured the travel times of light using GPS clocks placed along the arms, instead of indirectly measuring fringe shifts. It detected differences in travel times for light moving east-west, consistent with the Earth's rotational motion causing ether drift, but no differences north-south. This provides evidence for the existence of ether drift in a way not subject to the length contraction effects that obscured results of previous experiments. The GPS clocks precisely confirmed the light travel times predicted by ether theory for the changing speed of light due to the apparatus moving through the ether as the Earth rotates.
The document presents a new technique called Full Spectrum Inversion (FSI) for analyzing radio occultation signals. FSI uses a Fourier transform of the entire occultation signal to determine the arrival times and frequencies of different signal components. This provides high vertical resolution and can disentangle signals in multipath regions. The method works by assuming the Fourier transform can be evaluated using the method of stationary phase. This allows the Fourier spectrum to be interpreted as the instantaneous frequencies contained in the signal. The arrival times are then found by taking the derivative of the Fourier transform phase. FSI is demonstrated to work for idealized occultation signals, and its performance is assessed using simulated signals.
Seismic surveys use seismic waves to image the subsurface. There are two main types: refraction surveys use refracted waves to determine shallow layer velocities, while reflection surveys use reflected waves to image deeper geological structures and boundaries between rock layers. Reflection surveys require more receivers and sources to adequately image the subsurface, making the data acquisition and processing more complex but able to image deeper targets compared to refraction surveys.
The document discusses common pitfalls in 3D seismic interpretation and provides recommendations to improve interpretations. It notes that interpreters often rely too heavily on workstation tools rather than thoughtful geological analysis, and fail to properly understand data defects, phase and polarity, resolution limits, and amplitude information. The document emphasizes the importance of integrating seismic data with well data on character, using autotracking tools appropriately, questioning attribute selections, and differentiating between horizon and windowed amplitudes.
The document summarizes research on using seismic methods to detect and characterize a sinkhole in Doha, Qatar. A seismic survey was conducted along the edge of the sinkhole opening. The recorded seismic data revealed a distinct resonance peak at 70 Hz above the sinkhole. Numerical modeling showed that this peak is indicative of a karst side wall separating rock, karst border, and roof. The data were inverted in the frequency domain and fit using a model with low velocity and density parameters in the sinkhole layer, representing the complex geometry of karst.
This document summarizes a study of mesospheric gravity waves over McMurdo Station, Antarctica using infrared imaging:
1) Over 400 short-period gravity waves were observed between March-September 2012, with average horizontal wavelength of 22 km, phase speed of 42 m/s, and period of 12 minutes.
2) Waves exhibited seasonal variations in propagation direction, with northwest in fall expanding to northeast and southwest in winter and more isotropic propagation in late winter.
3) Analysis of 73 continuous hours in June revealed over 40 gravity wave events with characteristics consistent with full season results. Diurnal and semidiurnal tides were also observed.
4) Later season observations in August showed higher average phase
This document discusses turbulence, mass loss, and Hα emission in the hypergiant star ρ Cassiopeiae. It summarizes the star's extreme properties like high luminosity, irregular pulsations, and variable mass loss rate. It proposes that a stochastic field of shock waves can explain the observed mass loss rate, high microturbulent velocity, and Hα line profile. The document finds that adopting a Kolmogorov spectrum of shock waves characterized by a single parameter - the maximum Mach number - can successfully model these observed properties of the star.
What do you means by seismic resolutionHaseeb Ahmed
Seismic resolution refers to the ability to differentiate between two seismic features. Vertical resolution is the ability to resolve two vertically stacked seismic horizons, and depends on factors like frequency and wavelength. Higher frequencies and shorter wavelengths improve vertical resolution but are attenuated at greater depths. Lateral resolution is the ability to resolve two horizontally separated features, and depends on factors like frequency, velocity, aperture, and whether pre-stack or post-stack migration is used. Both vertical and lateral resolution decrease with depth due to attenuation of higher frequencies. Increasing bandwidth, using phase rotation techniques, and migration can help enhance seismic resolution.
Application of Low Frequency Passive Seismic Method for Hydrocarbon Detection...Andika Perbawa
Passive seismic survey is a geophysical method that utilizes a spectral frequency from seismicity data to identify subsurface reservoir fluids. Rock pores that contain hydrocarbon fluids show higher low-frequency amplitude between 2-4 Hz compared with those that contain water. This paper shows the feasibility study that has been done in S Field, South Sumatra Basin. Four wells were used to validate the result of the spectral data. This method is also considered as a prospect ranking tool in the vicinity of the S field.
Eighteen measurement points were collected and grouped into 6 clusters. Four clusters are located near S-1, S-2, S-3, and S-4 wells. One cluster is located on prospect K and the other one on prospect G. Standard signal processing flows were conducted such as band-pass filter, FFT, and moving average.
The result shows that the maximum amplitude low-frequency between 2-4 Hz of K and S-1 is less than 0.017. On the other hand, S-2, S-3, S-4 and G show a relatively high amplitude of more than 0.02 which indicates a greater possibility of hydrocarbon accumulation when compared with K and S-1. This result was confirmed by gas production in S-2 and oil production in S-3. S-4 has not been tested yet, but the refined well correlation it indicates that there is a limestone reservoir of about 60 feet above OWC. S-1 shows a low amplitude which indicates low potential. The completion log confirmed that the well did not penetrate the reservoir target. Prospect G which has a high amplitude of low-frequency anomaly is more interesting than prospect K.
To conclude, low-frequency passive seismic method was successful in distinguishing between water or no hydrocarbons. It is feasible to employ this methodology as a tool for hydrocarbon detection and also as a tool to help in prospect ranking.
This document summarizes research on identifying spin-wave eigen-modes in a circular spin-valve nano-pillar using Magnetic Resonance Force Microscopy (MRFM). Key findings include:
1) Distinct spin-wave spectra are observed depending on whether the nano-pillar is excited by a uniform in-plane radio-frequency magnetic field or by a radio-frequency current perpendicular to the layers, indicating different excitation mechanisms.
2) Micromagnetic simulations show the azimuthal index φ is the discriminating parameter, with only φ=0 modes excited by the uniform field and only φ=+1 modes excited by the orthogonal current-induced Oersted field.
3) Three indices are used to label resonance
Identification of the Memory Process in the Irregularly Sampled Discrete Time...idescitation
This poster paper analyzes the memory process in the irregularly sampled daily solar radio flux signal between 1972-2013. The authors apply Savitzky-Golay filtering to denoise the signal, then use Finite Variance Scaling Method and Hurst exponent analysis to investigate the memory pattern. Their analysis finds the signal exhibits short memory behavior, suggesting it may have multi-periodic or pseudo-periodic characteristics. This provides insight into the internal dynamics and particle acceleration processes of the Sun.
1) The document discusses remote sensing and provides definitions and explanations of key concepts such as the electromagnetic spectrum, atmospheric interaction with electromagnetic waves, and atmospheric windows.
2) It describes the seven elements of remote sensing including the energy source, interaction with the atmosphere and target, sensor recording, processing, interpretation, and application.
3) The electromagnetic spectrum is divided into regions including radio waves, microwaves, infrared, visible light, ultraviolet, and others. Certain regions have high atmospheric transmittance and are considered atmospheric windows for remote sensing.
This document analyzes wave packet propagation in weakly nonlinear acoustic metamaterials through spectro-spatial analysis. Spectro-spatial analysis uses full-scale transient analysis and signal processing techniques to reveal dispersion curves and localized solitary wave properties. The analysis finds an unusual frequency shift phenomenon in the middle-wavelength region of the optical wave branch that causes it to behave like a band gap for transient waves. This frequency shift is then used to design a direction-biased waveguide with high efficiency, as shown through numerical simulations.
Seismic methods use seismic waves created by impacts on the surface to map underground structures. The waves travel through underground layers and are reflected or refracted at boundaries between different materials. Analysis of the travel times and velocities of the waves allows determining the depth and type of geological layers. Seismic reflection techniques involve creating waves at shot points and recording them with receivers at different offsets to generate common midpoint gathers. Processing the gathers yields a seismic section that images layer boundaries like an echo sounder. Seismic refraction uses refracted head waves along interfaces to build a shallow velocity model for near-surface layers. Both methods together provide structural and physical characterization of underground features like buried valleys.
This document summarizes a study that investigated shear-wave attenuation and site response in Guerrero, Mexico using spectra from moderate earthquakes. The researchers developed a method to model spectra assuming an ω-2 source shape and exponential decay to describe attenuation. They were able to separate the spectral decay parameter into distance-dependent and site-dependent components. Comparing observed and model event spectra allowed them to estimate site response effects for different stations, independent of source and path effects. The study found weaker distance dependence of attenuation in Guerrero compared to southern California, but greater near-site attenuation. Significant amplification and deamplification was observed in site response functions for hard rock sites, with no clear correlation with local geology or topography.
1. The document discusses searches for radio transients using the Long Wavelength Array (LWA1), a radio telescope array sensitive to frequencies between 10-88 MHz.
2. No fast radio bursts (FRBs) were detected in 96 hours of observation, placing an upper limit on the FRB rate of <4.0×102 day-1 sky-1 at 38 MHz.
3. The null detection and event rate limits suggest that FRB spectra may be flatter than a assumed spectral index of -1.4, meaning their flux densities do not decrease as quickly with lower frequencies.
Filtering in seismic data processing? How filtering help to suppress noises. Haseeb Ahmed
To enhance the signal-Noise ratio different techniques are used to remove the noises.
Types of Seismic Filtering:
1- Frequency Filtering.
2- Inverse Filtering (Deconvolution).
3- Velocity Filtering.
The document summarizes the observation of gravitational waves from a binary black hole merger detected by the LIGO detectors on September 14, 2015. The key points are:
1) LIGO detected a transient gravitational-wave signal that matches predictions from general relativity for the inspiral and merger of two black holes.
2) Analysis of the signal determines that the initial black hole masses were about 36 and 29 solar masses, which merged into a final black hole of about 62 solar masses over 0.2 seconds.
3) This is the first direct detection of gravitational waves as well as the first observation of a binary black hole merger, confirming predictions from Einstein's theory of general relativity.
The document summarizes initial measurements of mesospheric gravity waves over McMurdo, Antarctica using infrared imaging. Over 300 gravity wave events were observed and analyzed over the 2012 season. The observed horizontal wavelengths averaged 22 km, phase speeds averaged 53.3 m/s. Wave propagation directions varied seasonally, with northwest in fall, isotropic in winter, and southwest in spring. Comparisons show similar wave characteristics to other Antarctic sites, but McMurdo exhibits a wider range of phase speeds. Ongoing analysis will help understand pan-Antarctic gravity wave climatology.
A highly magnetized twin-jet base pinpoints a supermassive black holeSérgio Sacani
Supermassive black holes (SMBH) are essential for the production of jets in radio-loud active galactic nuclei (AGN). Theoretical
models based on (Blandford & Znajek 1977, MNRAS, 179, 433) extract the rotational energy from a Kerr black hole, which could
be the case for NGC1052, to launch these jets. This requires magnetic fields on the order of 103 G to 104 G. We imaged the vicinity
of the SMBH of the AGN NGC1052 with the Global Millimetre VLBI Array and found a bright and compact central feature that is
smaller than 1.9 light days (100 Schwarzschild radii) in radius. Interpreting this as a blend of the unresolved jet bases, we derive the
magnetic field at 1 Schwarzschild radius to lie between 200 G and 8:3 104 G consistent with Blandford & Znajek models.
1) Geophysics uses remote sensing to determine subsurface conditions by analyzing seismic and radar signals that travel through and reflect off underground materials.
2) There are four main modes of signal propagation: vertical reflection, wide angle reflection, critical refraction, and direct waves. Precisely measuring the travel times of these signals allows subsurface structures to be interpreted.
3) Reflection seismology analyzes reflected signals to determine depth to interfaces by relating travel time, distance between source and receiver, and velocity, while refraction seismology uses travel times of critically refracted signals to determine shallow subsurface velocity structure.
This document summarizes a research paper on using discrete wavelet transform (DWT) and empirical mode decomposition (EMD) to remove "ghosting effects" from seismic signals. It begins with an introduction to earthquakes and how they are recorded via seismographs. It then describes existing filtering methods and their limitations. The proposed method uses 1D convolutional filtering and vibration analysis with DWT and EMD to enhance noisy seismic wave signals. It involves steps like magnitude spectrum estimation, windowing, phase estimation, noise variance prediction, and directional estimation. The method is able to attenuate coherent noise and improve seismic wave detection, separation and tracking. In conclusion, time-scale directional filters are a powerful tool for seismic data
Successful search for ether drift in a modified michelson morley experiment u...Võ Hồng Quý
This modified Michelson-Morley experiment directly measured the travel times of light using GPS clocks placed along the arms, instead of indirectly measuring fringe shifts. It detected differences in travel times for light moving east-west, consistent with the Earth's rotational motion causing ether drift, but no differences north-south. This provides evidence for the existence of ether drift in a way not subject to the length contraction effects that obscured results of previous experiments. The GPS clocks precisely confirmed the light travel times predicted by ether theory for the changing speed of light due to the apparatus moving through the ether as the Earth rotates.
The document presents a new technique called Full Spectrum Inversion (FSI) for analyzing radio occultation signals. FSI uses a Fourier transform of the entire occultation signal to determine the arrival times and frequencies of different signal components. This provides high vertical resolution and can disentangle signals in multipath regions. The method works by assuming the Fourier transform can be evaluated using the method of stationary phase. This allows the Fourier spectrum to be interpreted as the instantaneous frequencies contained in the signal. The arrival times are then found by taking the derivative of the Fourier transform phase. FSI is demonstrated to work for idealized occultation signals, and its performance is assessed using simulated signals.
Seismic surveys use seismic waves to image the subsurface. There are two main types: refraction surveys use refracted waves to determine shallow layer velocities, while reflection surveys use reflected waves to image deeper geological structures and boundaries between rock layers. Reflection surveys require more receivers and sources to adequately image the subsurface, making the data acquisition and processing more complex but able to image deeper targets compared to refraction surveys.
The document discusses common pitfalls in 3D seismic interpretation and provides recommendations to improve interpretations. It notes that interpreters often rely too heavily on workstation tools rather than thoughtful geological analysis, and fail to properly understand data defects, phase and polarity, resolution limits, and amplitude information. The document emphasizes the importance of integrating seismic data with well data on character, using autotracking tools appropriately, questioning attribute selections, and differentiating between horizon and windowed amplitudes.
The document summarizes research on using seismic methods to detect and characterize a sinkhole in Doha, Qatar. A seismic survey was conducted along the edge of the sinkhole opening. The recorded seismic data revealed a distinct resonance peak at 70 Hz above the sinkhole. Numerical modeling showed that this peak is indicative of a karst side wall separating rock, karst border, and roof. The data were inverted in the frequency domain and fit using a model with low velocity and density parameters in the sinkhole layer, representing the complex geometry of karst.
This document summarizes a study of mesospheric gravity waves over McMurdo Station, Antarctica using infrared imaging:
1) Over 400 short-period gravity waves were observed between March-September 2012, with average horizontal wavelength of 22 km, phase speed of 42 m/s, and period of 12 minutes.
2) Waves exhibited seasonal variations in propagation direction, with northwest in fall expanding to northeast and southwest in winter and more isotropic propagation in late winter.
3) Analysis of 73 continuous hours in June revealed over 40 gravity wave events with characteristics consistent with full season results. Diurnal and semidiurnal tides were also observed.
4) Later season observations in August showed higher average phase
This document discusses turbulence, mass loss, and Hα emission in the hypergiant star ρ Cassiopeiae. It summarizes the star's extreme properties like high luminosity, irregular pulsations, and variable mass loss rate. It proposes that a stochastic field of shock waves can explain the observed mass loss rate, high microturbulent velocity, and Hα line profile. The document finds that adopting a Kolmogorov spectrum of shock waves characterized by a single parameter - the maximum Mach number - can successfully model these observed properties of the star.
What do you means by seismic resolutionHaseeb Ahmed
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Investigatng MultIfractality of Solar Irradiance Data Through Wavelet Based MultIfractal Spectral Analysis
1. K. Mofazzal Hossain, Dipendra N. Ghosh and Koushik Ghosh
Signal Processing: An International Journal (SPIJ) Volume (3): Issue (4) 83
Investigating Multifractality of Solar Irradiance Data through
Wavelet Based Multifractal Spectral Analysis
K. Mofazzal Hossain email: hossainkm_1976@yahoo.co.in
Assistant Professor,
Department of Electronics & Instrumentation Engineering
Dr.B.C.Roy Engineering College, Durgapur
Durgapur-713206,West Bengal, India
Dipendra N. Ghosh email: ghoshdipen2003@yahoo.co.in
Associate Professor, Department of Mathematics
Dr.B.C.Roy Engineering College, Durgapur
Durgapur-713206, West Bengal, India
Koushik Ghosh email: koushikg123@yahoo.co
Lecturer, Department of Mathematics
University Institute of Technology, University of Burdwan
Burdwan-713104, West Bengal, India
Abstract
It has been already revealed that the daily Solar Irradiance Data during the time
period from October, 1984 to October, 2003 obtained by Earth Radiation Budget
Satellite (ERBS) exhibits an Anti-persistent trend having multi-periodic
phenomena. The solar irradiance time series data being a complex non linear
signal in this paper we have tried to detect the irregularity and multifractality in
the signal using continuous wavelet transform modulus maxima (WTMM)
algorithm. Singularity spectrum of the signal has been obtained to measure the
degree of multifractality of the Solar Irradiance signal. The qualitative measure of
the degree of multifractality of the Solar Irradiance signal will help us to decide
the nature of the signal processing tools that can be used to extract the features
of the signal in our future work. This may also give an input to the research work
of researchers on the solar physics and geophysics.
Keywords: ERBS, Wavelet transform, WTMM, scaling exponent, multifractal
dimension, Hölder exponent, singularity spectrum
1. INTRODUCTION
Total solar irradiance describes the electromagnetic radiant energy emitted by the sun over all
wavelengths that falls each second on 1 square meter outside the earth's atmosphere. Solar
refers to electromagnetic radiation in the spectral range of approximately 1–9ft (0.3–3m), where
the shortest wavelengths are in the ultraviolet region of the spectrum, the intermediate
wavelengths in the visible region, and the longer wavelengths are in the near infrared. Total solar
irradiance means that the solar flux has been integrated over all wavelengths to include the
contributions from ultraviolet, visible, and infrared radiation. The solar irradiance had been
monitored with absolute radiometers since November 1978, on board six spacecraft (Nimbus-7,
2. K. Mofazzal Hossain, Dipendra N. Ghosh and Koushik Ghosh
Signal Processing: An International Journal (SPIJ) Volume (3): Issue (4) 84
SMM, UARS, ERBS, EURECA, and SOHO), outside the terrestrial atmosphere (Fröhlich and
Lean, 1998). Before measuring it from space, this quantity was thought to be constant, because
the precision of the ground-based instruments at that time was not high enough to detect such a
small variation. It consequently got the name of “solar constant”, which had a value of only 1,353
W/m
2
, as a part of the solar radiation is absorbed by the Earth’s atmosphere. But from the data
sent by the mentioned spacecraft it reveals that the solar irradiance varies about a small fraction
of 0.1% over solar cycle being higher during maximum solar activity conditions. [1]
It is suggested that the solar variability is due to the perturbed nature of the solar core and this
variability is provided by the variability of the solar neutrino flux from the solar neutrino detectors
i.e., Homestake, Superkamiokande, SAGE and GALLEX-GNO. A major part of the Solar
Irradiance variation is explained as a combined effect of the sunspots blocking and the
intensification due to bright faculae and plages, with a slight dominance of the bright features
effect during the 11-year solar cycle maximum. Solar Irradiance variation within solar cycle is
thought to be due to the changing emission of bright magnetic elements, including faculae and
the magnetic network. [2]
It has been revealed that the variation of the solar irradiance is anti-persistent and shows multi-
periodicity. [3] The periods of the solar irradiance variation detected are 9.08-9.35, 13.53-14.03,
27.50-28.17, 30.26, 35.99-36.37, 51.14-51.52, 68.27-68.60, 101.15, 124.85, 150.63-153.98,
659.90, 729.37, 1259.82, 3464.50 and 4619.33 days.[4]. In this paper we would like to
characterize the complex behaviour of the solar irradiance fluctuation by i) tracing the existence
of multifractality and ii) scanning the singularities of the time series signal. Here we have
computed the signal parameters like scaling exponents τ (q), multifractal scaling exponents h(q)
and generalized multifractal dimensions D(q) which quantifies the multifractality of the signal. For
tracking the singularities in the time series signal we have computed the singularity strength or
Hölder exponent (α) and obtained the Hausdorff dimension or singularity spectrum f (α). The use
of monofractal methods to extract quantitative information from signals is well known.
Monofractals are homogeneous objects, in the sense that they have the same scaling properties,
characterized by a single singularity exponent. Generally, there exist many observational signals
which do not present a simple monofractal scaling behaviour. The need for more than one scaling
exponent can derive from the existence of a crossover timescale, which separates regimes with
different scaling behaviours. Different scaling exponents could be required for different segments
of the same time series, indicating a time variation of the scaling behaviour. Furthermore,
different scaling exponents can be revealed for many interwoven fractal subsets of the time
series; in this case the process is not a monofractal but multifractal. Thus, multifractals are
intrinsically more complex and inhomogeneous than monofractals and characterize systems
featured by very irregular dynamics, with sudden and intense bursts of high-frequency
fluctuations. The simplest type of multifractal analysis is given by the standard partition function
multifractal formalism, developed to characterize multifractality in stationary measures. This
method does not correctly estimate the multifractal behaviour of signal affected by trends or non-
stationarities. But the solar irradiance time series signal is non stationary in nature. To analyze
non-stationary signal wavelet transform based tool are more suitable compared to the traditional
Fourier based tools [5]. Hence to characterize the multifractality of non-stationary signals another
multifractal method based on the wavelet analysis named as Wavelet Transform Modulus
Maxima (WTMM) method is being used in this paper. [6, 7] This method involves tracing the
maxima lines in the continuous wavelet transform over all scales. WTMM allows one to detect
scaling by means of the maxima lines of the continuous wavelet transform on different scales.
2. THEORY
CONTINUOUS WAVELET TRANSFORM
The continuous wavelet transform (WT) is a mathematical technique introduced in signal
analysis in the early 1980s. Since then, it has been the subject of considerable theoretical
developments and practical applications in a wide variety of fields. The WT has been early
recognized as a mathematical microscope that is well adapted to reveal the hierarchy that
governs the spatial distribution of singularities of multifractal measures. The wavelet transform is
3. K. Mofazzal Hossain, Dipendra N. Ghosh and Koushik Ghosh
Signal Processing: An International Journal (SPIJ) Volume (3): Issue (4) 85
a convolution product of the data sequence (a function f(x), where x, referred to as “position”, is
usually a time or space variable. In this study x is referred as time (t) and hence the data
sequence is time series) with the scaled and translated version of the mother wavelet, ψ(x). The
scaling and translation are performed by two parameters; the scale parameter s stretches (or
compresses) the mother wavelet to the required resolution, while the translation parameter b
shifts the analyzing wavelet to the desired location:
)1(,)(
1
),( ∫
∞
∞−
−
= dx
s
bx
xf
s
bsWf ψ
where s, b are real, s > 0 for the continuous version (CWT). ),( bsWf are the wavelet transform
coefficients .The wavelet transform acts as a microscope: it reveals more and more details while
going towards smaller scales, i.e. towards smaller s values [8].
The mother wavelet ψ(x) is generally chosen to be well localized in space (or time) and
frequency. Usually, ψ(x) is only required to be of zero mean, but for the particular purpose of
multifractal analysis ψ(x) is also required to be orthogonal to some lower order polynomials, up to
the degree n:
)2(0,,0)( nmmdxxxm
<≤∀=∫ ψ
Thus, while filtering out the trends, the wavelet transform can reveal the local characteristics of a
signal, and more precisely its singularities. The Hölder exponent can be understood as a global
indicator of the local differentiability of a function.
By preserving both scale and location (time, space) information, the CWT is an excellent tool for
mapping the changing properties of non-stationary signals. A class of commonly used real-valued
analyzing wavelets, which satisfies the above condition (2), is given by the successive derivatives
of the Gaussian function:
)3()( 2)(
2
x
n
n
n
e
dx
d
x
−
=ψ
Note that the WT of a signal )(xf with )()(
xn
ψ in Eq. (3) takes the following simple expression:
)4(),(
,)(
1
),( )(
bsWf
dx
d
s
dx
s
bx
xf
s
bsWf
n
n
n
n
=
−
= ∫
∞
∞−
ψ
Equation (4) shows that the WT computed with )()(
xn
ψ at scale s is nothing but the n
th
derivative
of the signal )(xf smoothed by a dilated version )/()0(
sxψ of the Gaussian function. This
property is at the heart of various applications of the WT microscope as a very efficient multi-
scale singularity tracking technique. Thus, the higher derivatives, the more vanishing moments,
that is, the local polynomial trends of higher order would be eliminated. We choose the third
derivative of a Gaussian
)5()( 2
3
3
)3(
2
x
e
dx
d
x
−
=ψ
which is insensitive to trends up to a quadratic one.
WAVELET TRANSFORM MODULUS MAXIMA (WTMM)
The WTMM method inherits the advantages of the wavelet transform analysis and was developed
to deal with strongly non-stationary data. It has an important ability to reveal hierarchical structure
of singularities and therefore proves useful in analyzing self-similar structures like fractals. In
4. K. Mofazzal Hossain, Dipendra N. Ghosh and Koushik Ghosh
Signal Processing: An International Journal (SPIJ) Volume (3): Issue (4) 86
small-scale levels s of wavelet transform, sharp hidden transitions (singularities) in Solar
Irradiance dynamics would be extracted.
The continuous wavelet transform described in Eq. (1) is an extremely redundant representation,
too expensive for most practical applications. To characterize the singular behaviour of functions,
it is sufficient to consider the values and position of the Wavelet Transform Modulus Maxima
(WTMM). The wavelet modulus maxima is a point (s0, x0) on the scale-position (or time) plane, (s,
x), where |Wf(s0, x)| is locally maximum for x in the neighborhood of x0. These maxima are
disposed on connected curves in the scale position (s, x) (or scale-time) half-plane, called
maxima lines. An important feature of these maxima lines, when analyzing singular functions, is
that there is at least one maxima line pointing towards each singularity The WTMM
representation has been used for defining the partition function based multifractal formalism.
Let {un(s)}, where n is an integer, be the position (time) of all local maxima at a fixed scale s. By
summing up the q’s power of all these WTMM, we obtain the partition function Z:[9]
∑=
n
q
nusWfsqZ )6(|),(|),(
where q can be any real value except zero.
TRACING SINGULARITIES
The rapid changes in a time series f(x) are called singularities and a characterization of their
strength is obtained with the Hölder exponents. The strength of the singularity of a function
)(xf at point x0 is given by the Hölder exponent α, i.e., the largest exponent such that )(xf is
Lipchitz at x0 .There exists a polynomial )( 0xxPn − of order n and a constant C, so that for any
point x in a neighborhood of x0, one has:
)7(|||)()(| 00
α
xxCxxPxf n −≤−−
where is )( 0xn α≤ and 0>C .
The Hölder exponent measures the degree of irregularity of )(xf at the point x0.When a broad
range of exponents is found, signals are considered as multifractal. A narrow range implies
monofractality. Let us assume that according to Eq.(7), )(xf has, at the point x0, a local scaling
(Hölder) exponent )( 0xα ; then, assuming that the singularity is not oscillating, one can easily
prove that the local behaviour of )(xf is mirrored by the WT which locally behaves as per the
power law:
)8(,~),( )(
0
0x
sxsWf α
Taking the log-log plot on both sides of the Eq. (8) Hölder exponent α can be estimated. A very
important point (at least for practical purpose) rose by Mallat and Hwang is that the local scaling
exponent )( 0xα can be equally estimated by looking at the value of the WT modulus along a
maxima line converging towards the point x0. Indeed one can prove that Eqs. (8) still holds when
following a maxima line from large down to small scales. Depending on the value of )( 0xα at
every x0 we can scan the points of irregularity (opposite of regularity) or singularity.
If )( 0xα is Regularity of
)(xf at x0
Singularity of
)(xf at x0
Higher More Less
Lower Less More
5. K. Mofazzal Hossain, Dipendra N. Ghosh and Koushik Ghosh
Signal Processing: An International Journal (SPIJ) Volume (3): Issue (4) 87
MULTIFRACTAL ANALYSIS
A natural way of performing a multifractal analysis of a function lies in generalizing the multifractal
formalism using wavelets. From the deep analogy that links the multifractal formalism to
thermodynamics [10], one can define the scaling exponent )(qτ from the power-law behavior of
the partition function as given in Eqs (6):
)9(~),( )(q
ssqZ τ
Here we have varied the value of q from -20 to 20 with an increment of 0.2.Taking the log of the
Eq.(9), )(qτ is being estimated for each value of q. The singularity spectrum )(αf is related
to )(qτ by Legendre Transform as follows: a) from the plot of )(qτ vs. q the Hölder exponents α
as a function of q can be determined from the relationship:
)10(
)(
)(
dq
qd
q
τ
α =
b) Singularity spectrum )(αf is calculated from the equation
)11()()( qqf ταα −=
From the properties of the Legendre transform, it is easy to see that homogeneous mono-fractal
functions that involve singularities of unique Hölder exponent )(qα are characterized by a
)(qτ spectrum which is a linear function of q. On the contrary, a nonlinear )(qτ curve is the
signature of non-homogeneous functions that exhibit multifractal properties, in the sense that the
Hölder exponent )(qα is a fluctuating quantity. The singularity spectrum )(αf of a multifractal
function displays a single humped shape that characterizes intermittent fluctuations
corresponding to Hölder exponent values spanning a whole interval[ ]maxmin ,αα , where minα and
maxα are the Hölder exponents of the strongest and weakest singularities respectively.
Other than the signal parameters like scaling exponent )(qτ , Hölder exponents )(qα and
singularity spectrum )(αf as described above, multifractality can also be detected from the
multifractal scaling exponent or generalized Hurst exponent )(qh and the generalized
multifractal dimension )(qD . Both )(qh and )(qD can be calculated from the scaling exponent
)(qτ as below:
)12(0,
)(1
)( ≠
+
= q
q
q
qh
τ
and
)13(1,
1
1)(
1
)(
)( ≠
−
−
=
−
= q
q
qqh
q
q
qD
τ
For monofractal time series )(qh is independent of q whereas )(qD depends on q. But for
multifractal time series there is significant dependence of )(qh on q. If q is positive, large
fluctuations are characterized by a smaller values of )(qh ) for multifractal time series. And, for
negative q values, small fluctuations are usually characterized by larger values of )(qh .
From Eq.10, 11 and 12 Hölder exponent )(qα and Singularity spectrum )(αf can also be
expressed in terms of the multifractal scaling exponent )(qh as follows:
)14(
)(
)(
dq
qdh
qqh +=α
and
6. K. Mofazzal Hossain, Dipendra N. Ghosh and Koushik Ghosh
Signal Processing: An International Journal (SPIJ) Volume (3): Issue (4) 88
)15(1)]([)( +−= qhqf αα
Here we like to mention that multifractal scaling exponent or generalized Hurst exponent )(qh is
related to Hurst exponent H by the equation
)16(1)2( −== qhH
3. RESULTS
Fig.1 represents the original signal of the daily Solar Irradiance from October, 1984 to October,
2003 obtained by ERBS after simple exponential smoothing which is being denoised using
DWT thresholding and the denoised signal is obtained as in fig.2.[3].
1360
1361
1362
1363
1364
1365
1366
1367
1368
10/25/198410/25/198510/25/198610/25/198710/25/198810/25/198910/25/199010/25/199110/25/199210/25/199310/25/199410/25/199510/25/199610/25/199710/25/199810/25/199910/25/200010/25/200110/25/2002
Year ----->
SolarIrradiance
(Watts/Sqr.mtr)
Fig.1:Daily TS I data from October 1984 to October 2003
7. K. Mofazzal Hossain, Dipendra N. Ghosh and Koushik Ghosh
Signal Processing: An International Journal (SPIJ) Volume (3): Issue (4) 89
CWT, ),( bsWf of this data is being taken. The absolute values of the coefficients i.e.
|),(| bsWf is plotted with color coding, independently at each scale s , using 128 colors from
deep brown ( 0|),(| =bsWf ) to white ( |),(|max bsWf ) as shown in fig.3. Scale and time are on
the vertical and horizontal axis, respectively. The plot was obtained by using the “Wavelet
toolbox” of Matlab software.
Fig.4 represents the WT skeleton defined by the set of all maxima lines.
The plot of )(qτ vs q for the scale, s=3, 65,127 are being shown in fig.5
8. K. Mofazzal Hossain, Dipendra N. Ghosh and Koushik Ghosh
Signal Processing: An International Journal (SPIJ) Volume (3): Issue (4) 90
The singularity spectrum i.e αα .)( vsf for the scales s=3, 65, 127 is represented in fig.6.
9. K. Mofazzal Hossain, Dipendra N. Ghosh and Koushik Ghosh
Signal Processing: An International Journal (SPIJ) Volume (3): Issue (4) 91
Fig.7 represents the D(q) vs.q curve for the scales s=3,65 and 127 as shown below.
Fig.8 represents the h(q) vs.q curve for the scales s=3,65 and 127 as shown below.
10. K. Mofazzal Hossain, Dipendra N. Ghosh and Koushik Ghosh
Signal Processing: An International Journal (SPIJ) Volume (3): Issue (4) 92
The plot of D (h) vs. h for the scale, s=3, 65,127 are being shown in fig.9.
Fig.10: )(qα vs.q curve for the scales s=3,65 and 127 as shown below
11. K. Mofazzal Hossain, Dipendra N. Ghosh and Koushik Ghosh
Signal Processing: An International Journal (SPIJ) Volume (3): Issue (4) 93
4. CONCLUSIONS
WTMM method allows us to determine the multifractal characterization of the nonstationary solar
irradiance time series. The concept of WTMM of the solar irradiance time series is used here to
have a deeper insight into the process occurring in nonstationary dynamical system such as
multi-periodic fluctuation in solar irradiance values. The dependency of the )(qτ and )(qh on q as
observed in fig.5 and fig.8, indicates that the solar irradiance variation has multifractal behavior.
This behavior of exhibiting multifractal characteristics can be more established from the
singularity spectrum as in fig.6. The multifractal analysis gives information about the relative
importance of various fractal exponents present in the series. In particular, the width of the
singularity spectrum indicates the range of present exponents. To get the quantitative
characterization of multifractal spectra, the singularity spectrum is fitted to a quadratic
function around the position of its maximum at α0, i.e. f(a) = A(α - α0)
2
+ B(α - α0) + C. The
coefficients can be obtained by an ordinary least-squares procedure. [11]In this fitting the additive
constant C = f(α0) . With low α0, the process becomes correlated; for example if the process had
the tendency to move upward in the past, it will move upward with a probability larger than 1/2 in
the next time step. Roughly speaking, a small value of α0 means that the underlying process is
more regular in appearance. From the fig.6 we observe that the value of α0 is very high for lower
scales and decreases with increase in the scale. It means that the signal is correlated at higher
scales.
To obtain an estimate of the range of possible fractal exponents, we measured the width of the
singularity spectrum, extrapolating the fitted curve to zero. The width of the spectrum was then
defined as minmax αα −=W with 0)()( minmax == αα ff . The width of the spectrum W is a
measure of how wide the range of fractal exponents found in the signal and thus it measures the
degree of multifractality of the series. The wider the range of possible fractal exponents, the
`richer' is the process in structure. From the fig.6 we observe that W is decreasing with increase
in the scale size i.e. solar irradiance signal is richer in structure at lower scales.
Finally, parameter B serves as an asymmetry parameter, which is zero for symmetric shapes,
positive or negative for a left- or right-skewed (centered) shape, respectively. B captures the
dominance of low- or high-fractal exponents with respect to the other. A right-skewed spectrum
indicates relatively strongly weighted low-fractal exponents, and for left-skewed spectrum
indicates relatively strongly weighted high-fractal exponents. From fig.6 we observe that for scale
65 and 127 the singularity spectrum is left skewed whereas for scale 3 the singularity spectrum is
more or less symmetrical. Hence we can say that with increasing scales the signal is found to
have high fractal exponents. The parameter scale(s) in the wavelet analysis also has a significant
role. The high scales correspond to a non-detailed global view (of the signal), whereas the low
scales correspond to a detailed view. Similarly, in terms of frequency, low frequencies (high
scales) correspond to a global information of a signal (that usually spans the entire signal),
whereas high frequencies (low scales) correspond to a detailed information of a hidden pattern in
the signal (that usually lasts a relatively short time).So the above discussion regarding the values
of α0, W, B at various scales give a measure of the detailed or non-detailed global view of the
signal.
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Signal Processing: An International Journal (SPIJ) Volume (3): Issue (4) 94
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