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Notes: Abstract. Losses of nitrogen in the tile drainflow from a clay soil (Evesham series) under grazed grassland were monitored during the 1982/83 and 1983/84 drainflow seasons. In 1982/83, 40% of the discharge had a NO3− concentration 〉 11.3 mgNl−1, while in 1983/84 concentrations were always 〉 20 mgNl−1. Total N lost by leaching was 17.5 and 48.7 kg ha−1 in 1982/83 and 1983/84 respectively, which was equivalent to 9 and 43% of the fertilizer applied. The marked difference in N losses for the two seasons was attributed to differences in the quantity and timing of N fertilizer applications, the dryness of the preceding summer and the duration and density of stocking.

Notes: Abstract. Leaching losses of solutes can be calculated if two variables, the amount of water passing through the soil and the concentration of solute in that water (a flux concentration), are known. Two simple approaches, soil extraction and suction cup sampling, were used to estimate the concentration of solutes in the water moving through a silt loam soil. The results were compared with actual concentrations measured in the drainage water from a sub-surface (mole-pipe) drained soil.Seasonal leaching losses were calculated as the sum of the products of estimated monthly drainage and the estimated average monthly solute concentration in the soil solution. These results were compared with the leaching losses measured in drainage water from the mole-pipe system. For non-reactive solutes such as bromide (an applied solute) and chloride (a resident solute), the suction cup data provided better estimates of the leaching losses than did the soil extraction data. The leaching losses calculated using volume-averaged soil solution concentrations (obtained by soil extraction) overestimated the loss for the resident solute, but under-estimated the loss for the surface-applied solute. On the other hand, the data for non-reactive solutes suggest that measurements on suction cup samples may be representative of the flux concentration of a solute during leaching. For nitrate, a biologically reactive solute, there was no clear pattern in the differences between the estimated and measured leaching losses. The flux-averaged concentration in the drainage water was about midway between those measured in the suction cup samples and in the soil solution.

Notes: Abstract. Techniques for determining the probability density function (pdf) of travel times of solute molecules through a defined volume of soil, following a pulse or step-change input to the soil surface, are described. A stochastic transfer function model (TFM) based on the pdf of nitrate travel times works satisfactorily when the nitrate originates from a pulse input of soluble fertilizer to the soil surface. However, a TFM based on the pdf of a surface-applied tracer, such as chloride or tritiated water, is less satisfactory for simulating the leaching of indigenous soil nitrate. The main problems seem to be the difficulty of estimating mean nitrate concentrations because of the spatial variability of nitrate in field soils, accounting for denitrification during leaching, and the uncertain reproducibility of the soil's transport characteristics, as embodied in its operationally defined fractional transport volume, θst, Nevertheless, for many practical applications, a simplified empirical model which treats the soil's transport volume as a well mixed reactor of average initial concentration C, can provide satisfactory predictions of the quantity of nitrogen leached over extended periods. Irrespective of which model is used, a comprehensive treatment of nitrate leaching, particularly for soil generated nitrate, requires a detailed knowledge of transfers of labile nitrogen within the transport volume, and across its boundaries other than those monitored at the input and output surfaces.

Notes: Minimum variance unbiased (MVU) beamforming is a type of multichannel filtering which extracts coherent signals without distortion, whilst minimizing residual noise power. Adaptive beamforming estimates signal and noise characteristics as part of the extraction process. The adaptive beamformer used here is designed from models of primary and multiple reflection signals having parametrically specified moveout and amplitude variation with offset (MVO and AVO). Phase variation with offset (PVO) can also be included but it is not usually justified in practice. The resulting analysis provides data for input into AVO and PVO schemes for obtaining lithological information. Synthetic data examples illustrate details of implementation of parametric adaptive MVU beamforming and the response characteristics of the resultant design. Real data examples show that data-adaptive beamforming is more flexible and more effective in attenuating multiples in prestack common-midpoint seismic data than Radon transform methods. In common with other prestack multichannel processes, the advantages of beamforming are shown to best effect in data with a good signal-to-noise ratio.

Notes: A crucial step in the use of synthetic seismograms is the estimation of the filtering needed to convert the synthetic reflection spike sequence into a clearly recognizable approximation of a given seismic trace. In the past the filtering has been effected by a single wavelet, usually found by trial and error, and evaluated by eye. Matching can be made more precise than this by using spectral estimation procedures to determine the contribution of primaries and other reflection components to the seismic trace. The wavelet or wavelets that give the least squares best fit to the trace can be found, the errors of fit estimated, and statistics developed for testing whether a valid match can be made.If the composition of the seismogram is assumed to be known (e.g. that it consists solely of primaries and internal multiples) the frequency response of the best fit wavelet is simply the ratio of the cross spectrum between the synthetic spike sequence and the seismic trace to the power spectrum of the synthetic spike sequence, and the statistics of the match are related to the ordinary coherence function. Usually the composition cannot be assumed to be known (e.g. multiples of unknown relative amplitude may be present), and the synthetic sequence has to be split into components that contribute in different ways to the seismic trace. The matching problem is then to determine what filters should be applied to these components, regarded as inputs to a multichannel filter, in order to best fit the seismic trace, regarded as a noisy output. Partial coherence analysis is intended for just this problem. It provides fundamental statistics for the match, and it cannot be properly applied without interpreting these statistics.A useful and concise statistic is the ratio of the power in the total filtered synthetic trace to the power in the errors of fit. This measures the overall goodness-of-fit of the least squares match. It corresponds to a coherent (signal) to incoherent (noise) power ratio. Two limits can be set on it: an upper one equal to the signal-to-noise ratio estimated from the seismic data themselves, and a lower one defined from the distribution of the goodness-of-fit ratios yielded by matching with random noise of the same bandwidth and duration as the seismic trace segment. A match can be considered completely successful if its goodness-of-fit reaches the upper limit; it is rejected if the goodness-of-fit falls below the lower one.

Notes: Filters for migrated offset substacks are designed by partial coherence analysis to predict ‘normal’ amplitude variation with offset (AVO) in an anomaly free area. The same prediction filters generate localized prediction errors when applied in an AVO-anomalous interval. These prediction errors are quantitatively related to the AVO gradient anomalies in a background that is related to the minimum AVO anomaly detectable from the data. The prediction-error section is thus used to define a reliability threshold for the identification of AVO anomalies. Coherence analysis also enables quality control of AVO analysis and inversion. For example, predictions that are non-localized and/or do not show structural conformity may indicate spatial variations in amplitude–offset scaling, seismic wavelet or signal-to-noise (S/N) ratio content. Scaling and waveform variations can be identified from inspection of the prediction filters and their frequency responses. S/N ratios can be estimated via multiple coherence analysis.AVO inversion of seismic data is unstable if not constrained. However, the use of a constraint on the estimated parameters has the undesirable effect of introducing biases into the inverted results: an additional bias-correction step is then needed to retrieve unbiased results. An alternative form of AVO inversion that avoids additional corrections is proposed. This inversion is also fast as it inverts only AVO anomalies. A spectral coherence matching technique is employed to transform a zero-offset extrapolation or near-offset substack into P-wave impedance. The same technique is applied to the prediction-error section obtained by means of partial coherence, in order to estimate S-wave velocity to P-wave velocity (VS/VP) ratios. Both techniques assume that accurate well ties, reliable density measurements and P-wave and S-wave velocity logs are available, and that impedance contrasts are not too strong. A full Zoeppritz inversion is required when impedance contrasts that are too high are encountered. An added assumption is made for the inversion to the VS/VP ratio, i.e. the Gassmann fluid-substitution theory is valid within the reservoir area. One synthetic example and one real North Sea in-line survey illustrate the application of the two coherence methods.