Coda Q before and after the eruptions of 13 November 1985, and 1 September 1989, at Nevado del Ruiz Volcano, Colombia

 Coda Q^–1 was calculated at Nevado del Ruiz Volcano (NRV) before and after two phreatomagmatic eruptions (November 1985, September 1989) and for a period of stability (May 1987) using a functional form for coda derived from a single scattering model (Sato 1977). Substantial changes were found before and after the eruptions. The highest value of Q^–1 was found during the November 1985 eruption, an intermediate value for the September 1989 eruption, and the lowest value for May 1987. It seems that the changes in coda Q^–1 at NRV have a still-unknown relationship with the volume or magnitude of the eruption. A relatively strong frequency dependence was found for all periods. Also Q^–1 clearly changed with time, suggesting that the scattering was strong for the eruption of November 1985 and decreased for the eruption of September 1989, and that the intrinsic absorption probably increased. This suggests the possibility that crystallization is taking place in the NRV magma. The clear change of coda Q^–1 before and after the eruptions at NRV also suggests the possibility that coda Q^–1 is a premonitory tool of activity at this volcano. Received: 25 October 1996 / Accepted: 21 January 1998     

A note on smoothness measures for space–time surfaces

The differentiability of a random field has a direct relationship with the differentiability of its covariance function. We review the concept of differentiability of space–time covariance models and random fields, and its implications on predictions. We analyze the change of behavior of the covariance function at the origin and at different space–time lags away from the origin, by using the concept of smoothness which can be considered the geometrical view of the differentiability. We propose a way to measure the smoothness of any covariance function, and apply it to purely spatial and space–time covariance functions.     

Asymptotic Dykstra�CParsons Distribution, Estimates and Confidence Intervals

The sample Dykstra?CParsons (DP) coefficient, the most popular heterogeneity static measure among petroleum engineers, may exhibit significant sampling errors. Moreover, approximations of its probability distributions (uncertainty estimates) are only available for specific families of permeability models (e.g., log-normal). The cited probability distributions allow for the specification of confidence intervals and other inferences for the theoretical DP, which will be useful for reservoir screening purposes, or to establish if a more detailed study is justified. This paper presents the development of an asymptotic approximation of the distribution of the sample Dykstra?CParsons coefficient, which is independent of the permeability probability distribution. The effectiveness (bias and confidence intervals) of the proposed approach is demonstrated using analytical and field case studies and by comparing the results gleaned with those obtained using a well-known parametric approximation, under different scenarios of reservoir maturity levels (i.e., number of wells) and different degrees of deviation from the log-normal probability density function assumption. The results show that, in the vast majority of the case studies, the proposed approach outperformed the parametric approximation; in particular, our approach resulted in a significant reduction of the bias and the confidence intervals always including the theoretical DP coefficient. In addition, an excellent agreement was observed between the asymptotic cumulative distribution of the DP coefficient and the corresponding empirical distribution for sample sizes as small as one hundred, which suggests that high success rates can be obtained when reservoirs are classified according to the asymptotic DP coefficient.     

Transport of suspended sediment under the dam‐break flow on an inclined plane bed of arbitrary slope

The problem of transport of suspended sediment after the break of a dam on an inclined bed is considered. To that end we use the shallow‐water approximation for arbitrary, constant slopes of the bottom, taking into consideration the effect of friction. The numerical technique and the frictional model are validated by comparison with available experimental data and asymptotic analytical solutions, with special attention to the numerical solution near the wetting front. The transport of suspended sediment down the inclined bed is obtained and discussed as a function of the slope of the bed for different values of the parameters characterizing the sediment and its transport properties. For sufficiently large times we always find the formation of roll waves near the water front, which affects the transport of sediments significantly. These strong oscillations are accurately computed with the numerical method used. The relative importance of the bed load (to the suspended load) sediment transport is also discussed as a function of the size of the sediment particles and the slope of the bed for different models on the initiation of sediment suspension from bed load. We also check the dilute sediment approach and characterize the conditions for its failure. Finally, the results of the present simplified model are intended to be used as tests of more complex numerical models. Copyright © 2007 John Wiley & Sons, Ltd.