Sentences with phrase «spherical harmonics»
Spherical harmonics are mathematical functions that describe the way things behave on a sphere. They are like building blocks that can be used to represent various patterns or vibrations on a spherical surface, such as the Earth or a ball. By combining and manipulating these harmonics, we can understand and analyze things like sound, light, or magnetic fields in different regions of a sphere. Full definition
Regarding the family of spherical harmonic models, CALS10k.1 b is substantially improved compared to the previous CALS7K.2, which suffered from a lack of intensity information prior to about 1000 BC.
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It has a higher effective resolution on the order of spherical harmonic degree 5 and around 100 years in time.
To elaborate on the question at the end of my above comment — among all other considerations and obstacles, how practical would it be to go back over the past 100 + years and compute monthly anomalies of globally averaged SST using spherical harmonic functions?
The presented models display comparable power in low spherical harmonic degrees with strong drop of power for higher degrees (see, e.g., Fig. 10 of Korte et al. 2009), but it is clear that the choice of regularisation factors remains somewhat subjective and a model is far from a unique solution to the data inversion.
Field intensity distribution at the Earth surface predicted by spherical harmonic field models averaged over 400 years (a) model gufm1, 3 kyrs (b) model CALS3k.4, 7 kyrs (c), outdated model CALS7K.2 and 10 kyrs (d) model CALS10k.1 b.
Gridded data on a sphere can instead be represented by a series of spherical harmonic functions.
Dipole moment predicted by spherical harmonic field models CALS10k.1 b (red), CALS3k.4 (blue), CALS3k.3 (light blue), CALS7K.2 (grey) and by the archeomagnetic VADM reconstructions by Knudsen et al. (2008)(black) and Genevey et al. (2008)(brown) with uncertainty estimates (dashed lines and error bars) as provided by the authors, see text for details.
Graphics are said to be «more photorealistic than ever, with such advancements like changeable weather conditions, physical lighting model, Spherical Harmonics based Indirect Lighting, and Atmospheric Scattering.»
Estimates are from spherical harmonic models CALS10k.1 b (red with bootstrap uncertainty estimates as dashed lines), CALS3k.4 (blue), CALS7K.2 (grey) and the VGP reconstruction DEFNBKE (black with uncertainty estimates as dashed lines).
If I talk about spherical harmonics or a thin - plate spline, clinicians don't have a grasp of what is biologically meaningful about that.»
Dr Miroshnichenko's insight came while trying to reconcile differences between two different mathematical descriptions of radiation; one based on Cartesian multipoles and the other on vector spherical harmonics used in a Mie basis set.
The global field reconstructions of the CALSxk series (Continuous models based on Archeomagnetic and Lake Sediment data spanning the past x kyrs) are regularised spherical harmonic models.
Here we review several spherical harmonic models and compare their dipole field predictions to reconstructions based on virtual axial dipole moments and virtual geomagnetic poles.
Recent spherical harmonic models for the past 3 and 10 kyrs have improved considerably compared to earlier versions.
We then review recently developed millennial - scale spherical harmonic geomagnetic field models and compare their dipole predictions to virtual axial dipole and virtual geomagnetic pole (VGP) reconstructions, discussing uncertainties in absolute values and variations.
«When we try to analyze the global shape of the moon using spherical harmonics, the craters are like gaps in the data,» Garrick - Bethell said.
However, we might have to wait for a good distribution of southern hemisphere archeomagnetic data to definitely settle the question whether VADMs give a regionally biased overestimate or spherical harmonic models underestimate the dipole moment during these times.
Spherical harmonics are the natural choice for representing patterns on a sphere, but the oceans don't cover the whole of the sphere and the physical processes that govern changes in SST might mean that harmonics aren't the most natural set of patterns for efficiently capturing that variability.
The present - day dipole tilt might seem exceptionally large particularly compared to the spherical harmonic model predictions.
At first glance they seem more robust than spherical harmonic models, which have more degrees of freedom so that inconsistent data might lead to some dispersion of large - scale power towards higher spherical harmonic degrees.
Nevertheless, the spherical harmonic and VGP reconstructions agree well in predicting a comparatively strong tilt between 6500 and 5500 BC and in the variations predicted from about 1000 BC to present.
Continuous, spherical harmonic models of the geomagnetic field are convenient representations for many purposes.
The degree of the spherical harmonic expansion and the knot - point spacing of the splines are chosen to be higher than the spatial and temporal resolution expected from the data.
The spherical harmonic models do not only provide estimates of the past dipole evolution, as will be discussed in the next section, but also give information about regional differences in magnetic field strength.
In general, however, the VADM results tend to be higher than the spherical harmonic estimates, which could be consistent with VADMs that are biased towards Eurasia (Korte & Constable 2005b) for recent times.
Different dipole axis reconstructions appear to converge at least for the recent three millennia, but a notable discrepancy remains among dipole moment estimates, where VADMs give consistently higher values than spherical harmonic models.
Spherical harmonic and VADM reconstructions agree, perhaps surprisingly, well between 4000 and 1500 BC, around 0 AD and after 1000 AD.
Some groups, instead of dividing the planet's surface into a grid of thousands of square cells, took to dividing it into a tier of segments — hemispheres, quadrants, eighths, sixteenths, etc. («spherical harmonics»).