ALBERT

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.

Notes: Summary The rate of accumulation of phosphorus in the roots, and its transport to the shoots, of whole plants grown in very dilute nutrient solutions, did not conform to the kinetic models derived from studies with excised roots or tissue slices. The demand for phosphorus associated with the rate of plant growth, or the level of metabolic activity within the tissues, appeared to have a marked influence on the rate of phosphorus uptake at deficient to optimum (1 to 10 μM P) levels of supply. A hypothesis is presented whereby the rate of influx of orthophosphate into the root cortical cells is regulated by the turn-over rate of the pool of inorganic phosphate in the cytoplasm, and by the rate of transport of inorganic phosphate to the shoot. The turn-over rate of this labile pool depends on inherent factors, such as the relative growth rate of the species, and on environmental factors, including the supply of essential nutrients such as nitrogen. re]19720502