ALBERT

Notes: Replacement of native deep-rooted grasses by shallow-rooted ones has resulted in greater losses of water and nitrogen by drainage. To counter this effect we have tested the hypothesis that liming, and the conversion of annual grass pastures to perennial grass pastures, could improve the sustainability of grazing systems in the high rainfall zone (〉 600 mm per annum) in southeastern Australia, through better use of water and nitrogen. A field experiment consisting of sixteen 0.135 ha (30 m × 45 m) grazed paddocks representing four pasture combinations (annual pasture (mainly Lolium rigidum) without lime (AP–); annual pasture with lime (AP+); perennial pasture (mainly Phalaris aquatica) without lime (PP–), and perennial pasture with lime (PP+)) was carried out from 1994 to 1997 on an acid Sodosol (Aquic Hapludalf) in southern New South Wales, Australia. Measurements were made of surface runoff, subsurface flow (on top of the B horizon) and soil water content. The results showed that perennial grass pastures, especially PP+, extracted approximately 40 mm more soil water each year than the annual grass pastures. As a result, surface runoff, subsurface flow and deep drainage were at least 40 mm less from the perennial pastures. These measurements were further supported by a simulation of soil water deficit and deep drainage for AP– and PP+ paddocks, using 10 years' past meteorological records. Overall, the results suggested that well-grown, phalaris-based pastures could reduce recharge to groundwater and make pastoral systems more sustainable in the high rainfall zone.

Notes: Mineral N accumulates in autumn under pastures in southeastern Australia and is at risk of leaching as nitrate during winter. Nitrate leaching loss and soil mineral N concentrations were measured under pastures grazed by sheep on a duplex (texture contrast) soil in southern New South Wales from 1994 to 1996. Legume (Trifolium subterraneum)-based pastures contained either annual grass (Lolium rigidum) or perennial grasses (Phalaris aquatica and Dactylis glomerata), and had a control (soil pH 4.1 in 0.01 m CaCl2) or lime treatment (pH 5.5). One of the four replicates was monitored for surface runoff and subsurface flow (the top of the B horizon), and solution NO3– concentrations.The soil contained more mineral N in autumn (64–133 kg N ha−1 to 120 cm) than in spring (51–96 kg N ha−1), with NO3– comprising 70–77%. No NO3– leached in 1994 (475 mm rainfall). In 1995 (697 mm rainfall) and 1996 (666 mm rainfall), the solution at 20 cm depth and subsurface flow contained 20–50 mg N l−1 as NO3– initially but 〈 1 mg N l−1 by spring. Nitrate-N concentrations at 120 cm ranged between 2 and 22 mg N l−1 during winter. Losses of NO3– were small in surface runoff (0–2 kg N ha−1 year−1). In 1995, 9–19 kg N ha−1 was lost in subsurface flow. Deep drainage losses were 3–12 kg N ha−1 in 1995 and 4–10 kg N ha−1 in 1996, with the most loss occurring under limed annual pasture. Averaged over 3 years, N losses were 9 and 15 kg N ha−1 year−1 under control and limed annual pastures, respectively, and 6 and 8 kg N ha−1 year−1 under control and limed perennial pastures. Nitrate losses in the wet year of 1995 were 22, 33, 13 and 19 kg N ha−1 under the four respective pastures. The increased loss of N caused by liming was of a similar amount to the decreased N loss by maintaining perennial pasture as distinct from an annual pasture.

Notes: This paper presents some results from an investigation into the utility of pattern recognition methods in seismic interpretation. The seismic instantaneous attributes of amplitude, phase and frequency provide a way of quantifying the character of a simple reflection. Measures of character can be developed from cross-plots and cluster analysis of these attributes. It is demonstrated that such seismic character can produce better-defined maps than a single attribute. These procedures can be extended to attributes derived from seismic trace segments, such as trace energy and centre frequency, and to multitrace attributes, but more effort is then needed to analyse the attributes and search out useful ones.An introduction is given to projection pursuit which has proved a useful exploratory tool for the anlysis of attribute relationships.It is important to stress that pattern recognition techniques simply help bring relationships and patterns in the data to the attention of the interpreter and the most persistent problem in applying these techniques is the evaluation of potentially interesting patterns. The decision on what use can be made of them is highly interpretive and their calibration is difficult. Well control is vital but it normally allows only very limited supervision of a seismic classifier. An example is presented to illustrate these problems.

Notes: Methods of minimum entropy deconvolution (MED) try to take advantage of the non-Gaussian distribution of primary reflectivities in the design of deconvolution operators. Of these, Wiggins’(1978) original method performs as well as any in practice. However, we present examples to show that it does not provide a reliable means of deconvolving seismic data: its operators are not stable and, instead of whitening the data, they often band-pass filter it severely. The method could be more appropriately called maximum kurtosis deconvolution since the varimax norm it employs is really an estimate of kurtosis. Its poor performance is explained in terms of the relation between the kurtosis of a noisy band-limited seismic trace and the kurtosis of the underlying reflectivity sequence, and between the estimation errors in a maximum kurtosis operator and the data and design parameters.The scheme put forward by Fourmann in 1984, whereby the data are corrected by the phase rotation that maximizes their kurtosis, is a more practical method. This preserves the main attraction of MED, its potential for phase control, and leaves trace whitening and noise control to proven conventional methods. The correction can be determined without actually applying a whole series of phase shifts to the data. The application of the method is illustrated by means of practical and synthetic examples, and summarized by rules derived from theory. In particular, the signal-dominated bandwidth must exceed a threshold for the method to work at all and estimation of the phase correction requires a considerable amount of data.Kurtosis can estimate phase better than other norms that are misleadingly declared to be more efficient by theory based on full-band, noise-free data.

Notes: Optimum stacking filters based on estimates of trace signal-to-uncorrelated noise ratios are assessed and compared in performance with conventional straight stacking. It is shown that for the trace durations and signal bandwidths normally encountered in seismic reflection data the errors in estimating signal/noise ratios largely counteract the theoretical advantages of the optimum filter. The more specific the filter (e.g. the more frequency components included in its design) the more this is true. Even for a simple weighted stack independent of frequency, the performance is likely to be better than a straight (equal weights) stack only for relatively high signal/noise ratios, when the performance is not critical anyway.

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: In many branches of science, techniques designed for use in one context are used in other contexts, often with the belief that results which hold in the former will also hold or be relevant in the latter. Practical limitations are frequently overlooked or ignored. Three techniques used in seismic data analysis are often misused or their limitations poorly understood: (1) maximum entropy spectral analysis; (2) the role of goodness-of-fit and the real meaning of a wavelet estimate; (3) the use of multiple confidence intervals.It is demonstrated that in practice maximum entropy spectral estimates depend on a data-dependent smoothing window with unpleasant properties, which can result in poor spectral estimates for seismic data.Secondly, it is pointed out that the level of smoothing needed to give least errors in a wavelet estimate will not give rise to the best goodness-of-fit between the seismic trace and the wavelet estimate convolved with the broadband synthetic. Even if the smoothing used corresponds to near-minimum errors in the wavelet, the actual noise realization on the seismic data can cause important perturbations in residual wavelets following wavelet deconvolution.Finally the computation of multiple confidence intervals (e.g. at several spatial positions) is considered. Suppose a nominal, say 90%, confidence interval is calculated at each location. The confidence attaching to the simultaneous use of the confidence intervals is not then 90%. Methods do exist for working out suitable confidence levels. This is illustrated using porosity maps computed using conditional simulation.

Notes: A new approach has been developed for the design of cross-equalization filters by the least-squares method. The filters estimated by this new exact method are subject to only two types of error: bias and random error. Cross-equalization filters estimated by a more conventional least-squares method are further subject to “transient error”. This type of error becomes important when designing filters from a data gate of a length comparable with the length of the filter, i.e., less than four times the length of the filter.The effect of altering various design parameters has been investigated for the new method. It has been found that the proportion of bias in the filter decreases as the effective filter length increases, whereas the random error in the filter decreases with increase in either the signal-to-noise ratio of the data or the ratio of the data duration to the filter length. The level of whitening applied to the auto-correlation matrix before inversion was not found to be a critical design parameter. Also, two techniques have been tested for reducing any anomalous d.c. component in the calculated filter.

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.