Apparent attenuation from short‐period multiples and intrinsic absorption in the seismic wavelet model

2002 ◽  
Author(s):  
Albena Mateeva ◽  
Douglas Hart ◽  
Scott MacKay
Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2775-2783 ◽  
Author(s):  
N. C. Banik ◽  
I. Lerche ◽  
J. R. Resnick ◽  
R. T. Shuey

We describe filtering by short‐period multiples in one dimension using a combination of the O’Doherty‐Anstey (1971) formula with a stochastic model in which the autocorrelation of acoustic impedance decreases exponentially with lag [Formula: see text] while the spectrum of reflection coefficients rises with frequency up to a corner, then is approximately constant, [Formula: see text] An impedance log with these statistics is a generalization of the classic random telegraph wave. The parameter [Formula: see text], the mean‐square fractional fluctuation of impedance, is typically less than 1 percent, although we show an example where it is as high as 13 percent. The corner frequency [Formula: see text] is inversely related to average bed thickness. Typical values are 50–100 Hz, at the upper end of the normal seismic band. The cyclic stratification discussed by O’Doherty and Anstey (1971) and others corresponds to [Formula: see text] above the seismic band. Some logs have more reflection power at low frequencies than predicted from high frequencies by this model. We describe in both frequency and time domains the filtering of a seismic wavelet by multiples in such a stratigraphic sequence. The impulse response has a direct arrival, followed by a long tail of multiply scattered energy. The greater the impedance fluctuations or the longer the traveltime, the more amplitude is transferred from the primary to the multiples. We discuss in less detail several other models, including periodic and nearly periodic bedding. We also include two numerical applications of the O’Doherty‐Anstey formula; we show on a specific logged interval the formula’s remarkable accuracy for both attenuation and time delay; and we describe the reduction in computed time delay due to coarser sampling of the log.


Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2768-2774 ◽  
Author(s):  
N. C. Banik ◽  
l. Lerche ◽  
R. T. Shuey

We present a new and more detailed derivation of the formula due to O’Doherty and Anstey (1971) for filtering a transmitted wavelet by short‐period multiples. We use a continuous rather than discrete formulation and regard the impedance as a random variable. The mean pressure represents the downgoing wavelet as progressively modified by short‐period multiples, while the deviations from the mean field are essentially the upcoming reflections. Standard procedures and approximations lead to the dispersion relation of the mean pressure field. To describe the stratigraphic filtering, we introduce a dimensionless complex quantity F such that a wavelet which has traveled a time ΔT is modified by the filter [Formula: see text]. From the Kramers‐Kronig relation appropriate for a causal earth, F has real and imaginary parts [Formula: see text] and [Formula: see text] Where Q and δt define the apparent attenuation and time delay, both of which may depend upon frequency, R is the spectrum of reflection coefficients, and [Formula: see text] is the spectrum of the impedance fluctuations. The first equation means that the apparent attenuation depends only on the impedance fluctuations with spatial period half the seismic wavelength; the second means that the stratigraphic filter is minimum‐phase. We also show that changes of impedance on a spatial scale much larger than a seismic wavelength modify the amplitude so as to conserve energy, but they do not filter the waveform.


1962 ◽  
Vol 14 ◽  
pp. 133-148 ◽  
Author(s):  
Harold C. Urey

During the last 10 years, the writer has presented evidence indicating that the Moon was captured by the Earth and that the large collisions with its surface occurred within a surprisingly short period of time. These observations have been a continuous preoccupation during the past years and some explanation that seemed physically possible and reasonably probable has been sought.


1974 ◽  
Vol 22 ◽  
pp. 193-203
Author(s):  
L̆ubor Kresák

AbstractStructural effects of the resonance with the mean motion of Jupiter on the system of short-period comets are discussed. The distribution of mean motions, determined from sets of consecutive perihelion passages of all known periodic comets, reveals a number of gaps associated with low-order resonance; most pronounced are those corresponding to the simplest commensurabilities of 5/2, 2/1, 5/3, 3/2, 1/1 and 1/2. The formation of the gaps is explained by a compound effect of five possible types of behaviour of the comets set into an approximate resonance, ranging from quick passages through the gap to temporary librations avoiding closer approaches to Jupiter. In addition to the comets of almost asteroidal appearance, librating with small amplitudes around the lower resonance ratios (Marsden, 1970b), there is an interesting group of faint diffuse comets librating in characteristic periods of about 200 years, with large amplitudes of about±8% in μ and almost±180° in σ, around the 2/1 resonance gap. This transient type of motion appears to be nearly as frequent as a circulating motion with period of revolution of less than one half that of Jupiter. The temporary members of this group are characteristic not only by their appearance but also by rather peculiar discovery conditions.


1999 ◽  
Vol 173 ◽  
pp. 381-387
Author(s):  
M. Królikowska ◽  
G. Sitarski ◽  
S. Szutowicz

AbstractThe nongravitational motion of five “erratic” short-period comets is studied on the basis of published astrometric observations. We present the precession models which successfully link all the observed apparitions of the comets: 21P/Giacobini-Zinner, 31P/Schwassmann-Wachmann 2, 32P/Comas Solá, 37P/Forbes, and 43P/Wolf-Harrington. We used the Sekanina's forced precession model of the rotating cometary nucleus to include the nongravitational terms into equations of the comet's motion. Values of six basic parameters (four connected with the rotating comet nucleus and two describing the precession of spin-axis of the nucleus) have been determined along the orbital elements from positional observations of the comets. The solutions were derived with additional assumptions which introduce instantaneous changes of modulus of reactive force,Aand of maximum of cometary activity with respect to perihelion time. The present precession models impose some contraints on sizes and rotational periods of cometary nuclei. According to our solutions the nucleus of 21P/Giacobini-Zinner with oblateness along the spin-axis of about 0.32 (equatorial to polar radius of 1.46) is the most oblate among five investigated comets.


1999 ◽  
Vol 173 ◽  
pp. 365-370
Author(s):  
Kh.I. Ibadinov

AbstractFrom the established dependence of the brightness decrease of a short-period comet dependence on the perihelion distance of its orbit it follows that part of the surface of these cometary nuclei gradually covers by a refractory crust. The results of cometary nucleus simulation show that at constant insolation energy the crust thickness is proportional to the square root of the insolation time and the ice sublimation rate is inversely proportional to the crust thickness. From laboratory experiments resulted the thermal regime, the gas productivity of the nucleus, covering of the nucleus by the crust, and the tempo of evolution of a short-period comet into the asteroid-like body studied.


1999 ◽  
Vol 173 ◽  
pp. 327-338 ◽  
Author(s):  
J.A. Fernández ◽  
T. Gallardo

AbstractThe Oort cloud probably is the source of Halley-type (HT) comets and perhaps of some Jupiter-family (JF) comets. The process of capture of Oort cloud comets into HT comets by planetary perturbations and its efficiency are very important problems in comet ary dynamics. A small fraction of comets coming from the Oort cloud − of about 10−2− are found to become HT comets (orbital periods < 200 yr). The steady-state population of HT comets is a complex function of the influx rate of new comets, the probability of capture and their physical lifetimes. From the discovery rate of active HT comets, their total population can be estimated to be of a few hundreds for perihelion distancesq <2 AU. Randomly-oriented LP comets captured into short-period orbits (orbital periods < 20 yr) show dynamical properties that do not match the observed properties of JF comets, in particular the distribution of their orbital inclinations, so Oort cloud comets can be ruled out as a suitable source for most JF comets. The scope of this presentation is to review the capture process of new comets into HT and short-period orbits, including the possibility that some of them may become sungrazers during their dynamical evolution.


1999 ◽  
Vol 173 ◽  
pp. 289-293 ◽  
Author(s):  
J.R. Donnison ◽  
L.I. Pettit

AbstractA Pareto distribution was used to model the magnitude data for short-period comets up to 1988. It was found using exponential probability plots that the brightness did not vary with period and that the cut-off point previously adopted can be supported statistically. Examination of the diameters of Trans-Neptunian bodies showed that a power law does not adequately fit the limited data available.


1999 ◽  
Vol 173 ◽  
pp. 243-248
Author(s):  
D. Kubáček ◽  
A. Galád ◽  
A. Pravda

AbstractUnusual short-period comet 29P/Schwassmann-Wachmann 1 inspired many observers to explain its unpredictable outbursts. In this paper large scale structures and features from the inner part of the coma in time periods around outbursts are studied. CCD images were taken at Whipple Observatory, Mt. Hopkins, in 1989 and at Astronomical Observatory, Modra, from 1995 to 1998. Photographic plates of the comet were taken at Harvard College Observatory, Oak Ridge, from 1974 to 1982. The latter were digitized at first to apply the same techniques of image processing for optimizing the visibility of features in the coma during outbursts. Outbursts and coma structures show various shapes.


Sign in / Sign up

Export Citation Format

Share Document