C.H. Mehta

Scattering theory of wave propagation in a two‐phase medium

A theory is developed for the propagation of pressure waves in a two‐phase medium where one phase consists of spherical inclusions distributed randomly in the second phase. The theory is based on an integral equation of Foldy (1945) and Twersky (1970) for the average wave which includes almost all multiple scattering processes, but it ignores correlations among inclusions. In the low‐frequency limit, this equation is solved exactly for an analytical expression for the refractive index of compressional waves in terms of elastic parameters of the matrix and the inclusions. The theory is then applied to fluid‐solid suspensions and to fluid‐saturated porous rocks. In the former case, velocities measured by Kuster and Toksoz (1974b) as a function of the concentration of inclusions are compared with theoretical predictions of seven different models. The closest agreement is obtained for the present theory. This is attributed to systematic inclusion of multiple scattering effects including near‐field scattering ...

Segmentation of well logs by maximum-likelihood estimation

A maximum-likelihood procedure for segmenting digital well-log data is presented. The method is based on a univariate state variable model in which an observed log is treated as a time-series consisting of two terms: a Gauss-Markov signal remaining constant over a segment, and an additive Gaussian, but not necessarily stationary, noise. The signal jumps by a random amount at a segment boundary. The inverse problem of log segmentation consists of detecting the segment boundaries from a given log. The problem is solved using a Bayesian approach in which the unknown parameters, the locations of segment boundaries and the jumps in the signal value, are estimated by maximizing the likelihood function for the observed data. An algorithm based on Kalman smoothing and single most likelihood replacement (SMLR) procedure is proposed. The performance of the method is illustrated with a case study comprising of multisuite log data from an exploratory well. The method is found to be rapid and robust. The resulting segments are found to be geologically consistent.

Segmentation of well logs by maximum likelihood estimation

Geologically consistent segmentation of well logs is critical to most applications in well-log analysis. Quantitative techniques in log segmentation aim at providing a measurable control on the zonation and automation of the process. A procedure for segmenting digital well-log data using maximum likelihood estimation is presented along with the algorithm and a FORTRAN-77 program.The method is based on a univariate state variable model in which the state (signal) changes by a random amount at, and only at, the segment boundary. The observed log value is the sum of the state and random noise. The noise is modeled as Gaussian, but not necessarily stationary. The inverse problem of log segmentation is one of detecting the segment boundaries, and estimating the signal within the segment from a given log. These are solved by an iterative application of Kalman filtering and Single Most Likelihood Replacement (SMLR) techniques of Estimation theory.The technique is illustrated with a case study comprising of multisuite log data from an exploratory well. Different experiments on the performance of the algorithm are discussed. The method is robust and the resulting segments are determined to be geologically consistent.

The problem of the relation between double pomeron exchange in inclusive and exclusive experiments

Abstract The pionization region of the inclusive single-particle spectrum is accounted for by double pomeron exchange in the absorptive part of a six-point amplitude. In this paper a multiperipheral model for the six-point amplitude with double pomeron exchange is used for continuation by crossing and analyticity to the physical region of the exclusive two particle → four particle production process. The cross section for π − p → π − ( π + π − )p in the double-Regge region is then calculated and compared with the experimental analysis of Lipes, Zweig and Robertson which sets an upper bound to the strength of the double pomeron exchange coupling. This upper bound, coupled with the model for continuation to the inclusive cross section, is shown to give too small a magnitude for the double pomeron exchange in the pionization region. Further avenues for investigation are discussed.

Minimum phase wavelet by ARMA factorization

An algorithm is presented for computing a minimum phase wavelet, given only the causal part of its autocorrelation function r/sup +/ (k),k>or=0. The algorithm falls in the category of spectral factorization techniques, with the difference that instead of factoring the symmetric autocorrelation, its ARMA model is factored, and the ARMA model for symmetric autocorrelation is obtained directly from that of r/sup +/ (k) via a simple identity. It is found that, at least in seismic context, this procedure works better than the conventional spectral factorization as it involves ARMA polynomials which are of much lower order than MA polynomials. The algorithm is supported by two theorems and a detailed numerical example. The treatment is essentially deterministic. >

Double-Pomeron decoupling and the relation of exclusive to inclusive experiments with the dual resonance model

Abstract The double-pomeron coupling strength in the dual resonance model is found in both the inclusive and exclusive regions by comparison with experiments. Double-pomeron coupling occurs in inclusive experiments in the Mueller diagram for the central plateau region. Its strength can also be bounded from its non-observation in the two-particle to four-particle exclusive experiments. The dual resonance model is used to perform the analytic continuation of a six-point amplitude between these regions. The results show that the coupling strength for two forward pomerons in the exclusive region must be less than 1 300 of that in the inclusive region. This is experimental evidence for substantial forward double-pomeron decoupling in exclusive processes.