High-resolution seismic signals from band-limited data using scaling laws of wavelet transforms

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. WA143-WA152 ◽  
Author(s):  
K. R. Devi ◽  
Herb Schwab
Keyword(s):  
High Resolution ◽  
Power Law ◽  
Seismic Data ◽  
Wavelet Transforms ◽  
Scaling Laws ◽  
Scaling Law ◽  
Well Log ◽  
Seismic Signals ◽  
Local Scaling ◽  
Seismic Wavelet

Time-scale spectra, obtained from seismic data wavelet transforms, are useful in analyzing local scaling properties of seismic signals. In particular, the wavelet transform modulus maxima (WTMM) spectra, obtained by following the local extrema of wavelet transforms along a constant phase line, describe characteristics of discontinuities such as interfaces. They also show a smooth behavior as a function of scale and thus allow us to derive local scaling laws. We use scaling behavior of WTMM spectra to enhance the bandwidth of seismic data. An analysis of well-log scaling behaviors and the seismic data shows that, whereas the WTMM spectrum of well logs at each interface exhibits a power-law behavior as a function of scale, the corresponding seismic signal spectrum shows a more complicated behavior, arising from seismic wavelet effects. Under the assumption that local well-log power-law behavior holds in general, a scaling law for seismic signals can be derived in terms of parameters that describe subsurface scaling effects and the seismic wavelet. A stable estimation of these parameters can be carried out simultaneously, as a function of time and over the seismic bandwidth, using the modified scaling law. No well-log information is needed to derive the seismic wavelet. Then wavelet transforms can be corrected for seismic wavelet effects and a high-resolution signal reconstructed. This reconstructed high-resolution signal can be used to map features that might not be obvious in the original seismic data, such as small faults, fractures, and fine-scale variations within channel margins.

scholarly journals Applicataion of ormsby wavelet for generation of synthetic seismic signals

2018 ◽  
Vol 7 (2.7) ◽  
pp. 794
Author(s):  
E Sai Sumanth ◽  
V Joseph ◽  
Dr K S Ramesh ◽  
Dr S Koteswara Rao
Keyword(s):  
Wavelet Transform ◽  
Seismic Data ◽  
Wavelet Transforms ◽  
Seismic Signal ◽  
Core Structure ◽  
Seismic Signals ◽  
Seismic Reflections ◽  
Input Wave

Investigation of signals reflected from earth’s surface and its crust helps in understanding its core structure. Wavelet transforms is one of the sophisticated tools for analyzing the seismic reflections. In the present work a synthetic seismic signal contaminated with noise is synthesized  and analyzed using Ormsby wavelet[1]. The wavelet transform has efficiently extracted the spectra of the synthetic seismic signal as it smoothens the noise present in the data and upgrades the flag quality of the seismic data due to termers. Ormsby wavelet gives the most redefined spectrum of the input wave so it could be used for the analysis of the seismic reflections. 

Scaling Laws for the Peak Overpressure of a Cannon Blast

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Robert A. Carson ◽  
Onkar Sahni
Keyword(s):  
Power Law ◽  
Scaling Laws ◽  
Near Field ◽  
Scaling Law ◽  
Radial Distance ◽  
Polar Angle ◽  
Model Parameters ◽  
Far Field ◽  
Simulation Data ◽  
Angle Dependence

For large cannons, blast overpressure can have a detrimental effect on the crew in the near field (i.e., within a distance of 50 tube diameters or calibers from the muzzle center) as well as on the support personnel and equipment in the far field (i.e., at a distance greater than 50 calibers). Therefore, an efficient method to determine the peak overpressure due to a cannon blast is highly desired. In this study, we investigate scaling laws for the peak overpressure, due to the primary blast of a large cannon, with the aim that they can be applied as an efficient method to evaluate the peak overpressure in the far field. We explore two types of scaling laws; each type is based on a power-law model involving a prefactor and an exponent as model parameters. The two types of the power-law models differ in the way they incorporate the polar angle dependence. The first type was proposed by Fansler and Schmidt (1983, “The Prediction of Gun Muzzle Blast Properties Utilizing Scaling,” U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, Report No. ARBRL-TR-02504). They developed a muzzle-center based scaling law (MCSL) in which the polar angle dependence was incorporated through a reference length scale to define a nondimensional or scaled radial distance from the muzzle center and the model parameters were independent of the polar angle. They calibrated the parameters by employing least-squares fit to a wide range of experimental data. In this study, we recalibrated or updated the parameters for the current cannon by using the numerical simulation data for the cannon blast in the near field. Additionally, we developed a second type of scaling law in which the radial distance is defined from the blast center (in contrast to the muzzle center) and scaled using the inner tube diameter. In this model, the angular dependence is incorporated directly into the model parameters. For this model too, we calibrated the parameters by using the numerical simulation data. We observe that both the modified version of the muzzle-center based scaling law as well as the blast-center based scaling law (BCSL) show a significantly closer fit to the numerical and experimental data and achieve a similar level of accuracy. This indicates that the current form or structure of the two types of power-law based scaling models is able to fit well with the near-field data; however, the current methodology requires a calibration process for a given cannon of interest. In the future, with far field data, we plan to evaluate predictions in the far field.

scholarly journals Single-block rockfall dynamics inferred from seismic signal analysis

2017 ◽  
Author(s):  
Clément Hibert ◽  
Jean-Philippe Malet ◽  
Franck Bourrier ◽  
Floriane Provost ◽  
Frédéric Berger ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Scaling Laws ◽  
Scaling Law ◽  
Soft Rock ◽  
Signal Amplitude ◽  
Seismic Signal ◽  
Seismic Signals ◽  
Video Cameras ◽  
The Impact

Abstract. We conducted controlled releases of single blocks within a soft-rock (black marls) gully of the Rioux Bourdoux torrent (French Alps). 28 blocks, with masses ranging from 76 kg to 472 kg, were used for the experiment. An instrumentation combining video cameras and seismometers was deployed along the traveled path. The video cameras allow to reconstruct the trajectories of the blocks and to estimate their velocities at the time of the different impacts with the slope. These data are compared to the recorded seismic signals. As the distance between the falling block and the seismic sensors at the time of each impact is known, we were able to determine the associated seismic signal amplitude corrected from propagation and attenuation effects. We compared the velocity, the loss of potential energy, the kinetic energy and the momentum of the block at each impact to the true amplitude and the energy of the corresponding part of the seismic signal. Our results suggest that the amplitude of the seismic signal scales with the momentum of the block at the impact. We also found a scaling law between the potential energy lost, the kinetic energy and the energy of the seismic radiation generated by the impacts. By combining these scaling laws, we inferred the mass and the velocity before impact of each block directly from the seismic signal. Despite high uncertainties, the values found are close to the true values of the mass and the velocities of the blocks. These relationships also provide new insights to understand the source of high-frequency seismic signals generated by rockfalls.

scholarly journals The velocity-curvature power law in Drosophila larval locomotion

2016 ◽  
Author(s):  
Myrka Zago ◽  
Francesco Lacquaniti ◽  
Alex Gomez-Marin
Keyword(s):  
Power Law ◽  
Scaling Laws ◽  
Scaling Law ◽  
Fruit Fly ◽  
Pattern Generation ◽  
Geometric Constraints ◽  
Muscle Properties ◽  
Wide Range ◽  
The Law ◽  
Almost All

AbstractWe report the discovery that the locomotor trajectories generated by crawling fruit fly larvae follow the same power law relationship between speed and curvature previously found in the human motor control of hand-drawing, walking, eye movements and speech. Using high resolution behavioral tracking of individual flies in different sensory environments, we tested the power law by making maggots trace different trajectory types in naturalistic conditions, from reaching-like movements to scribbles. In all these conditions, we found that the law holds, and also that the exponent of the larval scaling law approaches 3/4, rather than the usual 2/3 exponent found in almost all human situations. This is consistent with recent findings on humans drawing ellipses on water, where dynamic effects related to medium viscosity have been shown to increase the exponent that would emerge from purely kinematic-geometric constraints. To our knowledge, the speed-curvature power law has only been studied in human and non-human primates, our work then being the first demonstration of the speed-curvature scaling principle in other species. As there are still different competing hypotheses for the origin of such law in humans (one invoking complex cortical computations in primates; another postulating its emergence from the coupling of viscoelastic muscle properties with simple central pattern generation) our findings in the larva demonstrate that the law is possible in an animal with a nervous system orders of magnitude simpler than that of humans, thus supporting the latter view. Given that our discovery is in Drosophila (amenable to precise genetic manipulations, electron microscopy reconstruction of neural circuits, imaging in behaving animals, electrophysiology, and other techniques) this opens great potential for uncovering the mechanistic implementation of the velocity-curvature power law. Such scaling laws might exist because natural selection favors processes that remain behaviorally efficient across a wide range of contexts in distantly related species. Our work is an effort to search for shared principles of animal behavior across phyla.

scholarly journals Jet Dynamics Associated with Drop Impact on Micropillared Substrate

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 155
Author(s):  
Brooklyn Asai ◽  
Anayet Ullah Siddique ◽  
Hua Tan
Keyword(s):  
Time Dependence ◽  
Power Law ◽  
High Speed ◽  
Scaling Laws ◽  
Scaling Law ◽  
Droplet Impact ◽  
Dimensionless Time ◽  
Cavity Collapse ◽  
Bubble Bursting ◽  
Jet Breakup

The jetting phenomenon associated with droplet impact upon a hydrophilic micropillared substrate was analyzed in detail using a high-speed camera. Viscosities of the fluids were varied using differing concentrations of glycerol in deionized water. This paper aims to connect similarities between this form of capillary jetting and another well-known jetting phenomenon from the bubble bursting. Both experience a cavity collapse when opposing fluid fronts collide which causes a singularity at the liquid surface, thus leading to the occurrence of jetting. Following processes used to define scaling laws for bubble bursting, a similar approach was taken to derive scaling laws for the dimensionless jet height, jet radius, base height, and radius of the jet base with respect to dimensionless time for the jetting phenomenon associated with the droplet impact. The development of a top droplet before the breakup of the jet also allows the examination of a scaling law for the necking diameter. We find that with the proper scaling factors, the evolution of the jet profile can collapse into a master profile for different fluids and impact velocities. The time dependence of the necking diameter before the jet breakup follows the power law with an exponent of ~2/3. Contrastingly, for other jet parameters such as the radius and height, the power law relationship with time dependence was not found to have a clear pattern that emerged from these studies.

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

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