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  • 1
    facet.materialart.
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    In:  Geophysical Prospecting, Washington, D.C., AGU, vol. 32, no. 6B, pp. 871-891, pp. B01308, (ISSN: 1340-4202)
    Publication Date: 1984
    Keywords: Seismic stratigraphy
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  • 2
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    In:  Geophys. Pros, Kunming, China, D. Reidel Publishing Company, vol. 22, no. 30, pp. 627-651, pp. L09303, (ISSN: 1340-4202)
    Publication Date: 1974
    Keywords: Inversion
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  • 3
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 21 (1973), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: A seismic trace recorded with suitable gain control can be treated as a stationary time series. Each trace, χj(t), from a set of traces, can be broken down into two stationary components: a signal sequence, αj(t) *s(t—τj), which correlates from trace to trace, and an incoherent noise sequence, nj(t), which does not correlate from trace to trace. The model for a seismic trace used in this paper is thus χj(t) =αj(t) * s(t—τj) +nj(t) where the signal wavelet αj(t), the lag (moveout) of the signal τj, and the noise sequence nj(t) can vary in any manner from trace to trace. Given this model, a method for estimating the power spectra of the signal and incoherent noise components on each trace is presented.The method requires the calculation of the multiple coherence function γj(f) of each trace. γj(f) is the fraction of the power on traced at frequency f that can be predicted in a least-square error sense from all other traces. It is related to the signal-to-noise power ratio ρj(f) by 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR660:GPR_660_mu1"/〉 where Kj(f) can be computed and is in general close to 1.0. The theory leading to this relation is given in an Appendix.Particular attention is paid to the statistical distributions of all estimated quantities. The statistical behaviour of cross-spectral and coherence estimates is complicated by the presence of bias as well as random deviations. Straightforward methods for removing this bias and setting up confidence limits, based on the principle of maximum likelihood and the Goodman distribution for the sample multiple coherence, are described.Actual field records differ from the assumed model mainly in having more than one correctable component, components other than the required sequence of reflections being lumped together as correlated noise. When more than one correlatable component is present, the estimate for the signal power spectrum obtained by the multiple coherence method is approximately the sum of the power spectra of the correlatable components. A further practical drawback to estimating spectra from seismic data is the limited number of degrees of freedom available. Usually at least one second of stationary data on each trace is needed to estimate the signal spectrum with an accuracy of about 10%. Examples using synthetic data are presented to illustrate the method.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 32 (1984), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: A synthetic seismogram that closely resembles a seismic trace recorded at a well may not be at all reliable for, say, stratigraphic interpretation around the well. The most accurate synthetic seismogram is, in general, not the one that displays the smallest errors of fit to the trace but the one that best estimates the noise on the trace. If the match is confined to a short interval of interest or if the seismic reflection wavelet is allowed to be unduly long, there is considerable danger of forcing a spurious fit that treats the noise on the trace as part of the seismic reflection signal instead of making a genuine match with the signal itself. This paper outlines tests that allow an objective and quantitative evaluation of the accuracy of any match and illustrates their application with practical examples.The accuracy of estimation is summarized by the normalized mean square error (NMSE) in the estimated reflection signal, which is shown to be(/n)(PN/PS)where PS/PN is the signal-to-noise power ratio and n is the spectral smoothing factor. That is, the accuracy varies directly with the ratio of the power in the signal (taken to be the synthetic) to that in the noise on the seismic trace, and the smoothing acts to improve the accuracy of the predicted signal. The construction of confidence intervals for the NMSE is discussed. Guidelines for the choice of the spectral smoothing factor n are given.The variation of wavelet shape due to different realizations of the noise component is illustrated, and the use of confidence intervals on wavelet phase is recommended.Tests are described for examining the normality and stationarity of the errors of fit and their independence of the estimated reflection signal.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 22 (1974), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: A seismic trace after application of suitable amplitude recovery may be treated as a stationary time-series. Such a trace, or a portion of it, is modelled by the expression 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR627:GPR_627_mu1"/〉 where j represents trace number on the record, t is time, αj is a time delay, α (t) is the seismic wavelet, s(t) is the reflection impulse response of the ground and nj is uncorrelated noise. With the common assumption that s(t) is white, random, and stationary, estimates of the energy spectrum (or auto-correlation function) of the pulse α(t) are obtained by statistical analysis of the multitrace record. The time-domain pulse itself is then reconstituted under the assumption of minimum-phase. Three techniques for obtaining the phase spectrum have been evaluated: (A) use of the Hilbert transform, (B) Use of the z-transform, (C) a fast method based on inverting the least-squares inverse of the wavelets, i.e. inverting the normal time-domain deconvolution operator. Problems associated with these three methods are most acute when the z-transform of α(t) has zeroes on or near the unit circle. Such zeroes result from oversampling or from highly resonant wavelets. The behaviour of the three methods when the energy spectra are perturbed by measurement errors is studied. It is concluded that method (A) is the best of the three. Examples of reconstituted pulses are given which illustrate the variability from trace-to-trace, from shot-to-shot, and from one shot-point medium to another. There is reasonable agreement between the minimum-phase pulses obtained by this statistical analysis of operational records and those estimated from measurements close to the source. However, this comparison incorporates a “fudge-factor” since an allowance for absorption has to be made in order to attenuate the high frequencies present in the pulse measured close to the shot.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical prospecting 32 (1984), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: Frequency-dependent attenuation of compressional waves within the earth has been estimated in the vicinity of wells from〈list xml:id="l1" style="custom"〉1spectral power ratios of the coherent events in separate time gates on the seismic section2matching a broadband synthetic trace with seismic data at the well, and3determining the operator that transforms one down(up) going pulse recorded in the well into another recorded at a deeper (shallower) level.The accuracy of estimation of all three methods was insufficient to estimate attenuation over small depth intervals, and it was not possible to distinguish between the contribution due to internal multiples and that of genuine absorption with much confidence. Spectral ratios from (1) showed a smoother variation with frequency—and one more consistent with other estimates—when they were compensated for the spectra of the reflectivities over the time gates employed, but they did not provide more than a broad indication of attenuation over a substantial depth interval. Approach (2) was hampered by the restricted durations over which synthetic trace and seismic data can be reliably matched; approach (3) gave the best results. Here matching is a much more powerful tool than the spectral-ratio techniques that are commonly applied since it can yield the form of the attenuation operator, i.e., both its amplitude and phase response, together with properly defined measures of its accuracy, while at the same time it minimizes the influence of noise and local interference effects at each recording level.For seismic target depths where internal multiple activity was low the logarithms of the amplitude responses of the estimated attenuation operators decreased approximately linearly with frequency and the phase responses showed no significant dispersion. Application of approach (3) to downgoing and upgoing waves estimated from a vertical seismic profile revealed the importance of changes in frequency-dependent geophone coupling and their effect on values of Q determined from downgoing pulses only.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Biochemistry 49 (1980), S. 315-356 
    ISSN: 0066-4154
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Chemistry and Pharmacology , Biology
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 385 (1982), S. 0 
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 225 (1970), S. 1156-1158 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Our object here is briefly to summarize some interesting new findings with gannets (Sula bassana); a full account is in the press3. The interesting features are that the usual frequency-time parameters were of little use in analysing individual vocal features; instead, changes in the amplitude ...
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Plant and soil 36 (1972), S. 427-447 
    ISSN: 1573-5036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The relative yield response and phosphate uptake ofS. humilis, P. atropurpureus andD. intortum, grown on a very deficient soil, enriched with phosphate, were measured at four successive harvests during 42 days growth under controlled environmental conditions. Except at the first harvest (19–21 days), the relative yields ofS. humilis andP. atropurpureus at P0 were identical, and slightly greater than that ofD. intortum; the relative response to applied phosphate was similar for the three species, up to the maximum yield attained. The higher relative yield ofD. intortum, at harvest 1, reflected the influence of a higher initial phosphate concentration in the small Desmodium seedling, compared toS. humilis andP. atropurpureus. The mean absorption rate for phosphate $$\overline {\left( {AR} \right)} $$ ofD. intortum, and to a lesser degreeS. humilis andP. atropurpureus, showed two distinct maxima: an initial peak at low soil activities (0.3 — 3µM P), and a second at higher soil activities (37–43µM P) when maximum yield had been attained, and luxury accumulation of phosphate appear to occur. The initial peak in $$\overline {AR} $$ was followed by a decline (significant (P=0.05) forD. intortum) at soil phosphate activities corresponding to maximum yield, suggesting that the rate of absorption by the roots was influenced by the demand for phosphate created within the growing plant. Mean absorption rates and relative growth rates $$\overline {\left( {RGR} \right)} $$ , averaged over all phosphate levels, fell in the orderD. intortum 〉S. humilis 〉P. atropurpureus. Conversely, the efficiency of phosphate utilization by the plant, which may be expected to be greater in plants of low RGR, fell in the orderP. atropurpureus 〉S. humilis 〉D. intortum, and so counteracted the lower $$\overline {AR} $$ ofP. atropurpureus, and to a lesser extent,S. humilis. However,S. humilis had the advantage of a lower retention of phosphate in the root system, compared toP. atropurpureus, due to a relatively greater shortage of nitrogen in the tops when grown on symbiotically-fixed nitrogen.
    Type of Medium: Electronic Resource
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