Leon E. Borgman

Three-Dimensional, Frequency-Domain Simulations of Geological Variables

Layered three-dimensional, frequency-domain computer simulations have many advantages an an alternative to the turning band method, for certain geological problems. Computer speed and even, accurate duplication of statistical properties are the main advantages. Limitations in the permitted extent in the third dimension are the primary disadvantages of the method.

A note on the asymptotic distribution of the sample variogram

tion. These articles deal with a variogram assumed to be associated with an underlying random function Z(x). However, it has been shown (Matheron, 1965, reemphasized by Journel and Huijbregts, 1978) that only the local variogram has any practical importance for linear geostatistics. The local variogram is a function of the regionalized variable and is not a function of the probabilistic model Z(x). Therefore, any article dealing with the statistical properties of the variogram is esoteric when viewed from the reference of linear geostatistics. Such examinations may represent interesting statistical questions but provide no real benefit to the practitioner. Further, Matheron (1965) has made a thorough examination of the properties of the variogram under the hypotheses of linear geostatistics. That does not mean such investigations are without value. Nonlinear geostatistical procedures such as lognormal kriging (Journel, 1980) depend on the random function or assumed stochastic model, Z(x). In light of nonlinear procedures, examination of the properties of the experimental variogram with respect to the underlying model do have meaning. The development that follows is presented in such a spirit. For the .linear case, it represents only an exercise in large sample theory. For the nonlinear case, the results may have practical consequences for a given application. Before continuing we present some fundamental notation and some assumptions.

Directional Wave Spectra from Wave Sensors

The measurement of directional ocean wave spectra with in situ instruments in the ocean environment requires arrays consisting of relatively few sensors. More elaborate systems are difficult and costly to maintain.

Some exact sampling distributions for variogram estimators

AbstractFor equally spaced observations from a one-dimensional, stationary, Gaussian random function, the characteristic function of the usual variogram estimator

MAXIMUM WAVE HEIGHT PROBABILITIES FOR A RANDOM NUMBER OF RANDOM INTENSITY STORMS

\hat \gamma k

Spectral-type simulation of spatially correlated fracture set properties

for a fixed lag k is derived. Because the characteristic function and the probability density function form a Fourier integral pair, it is possible to tabulate the sampling distribution of a function of a

Maximum-Entropy and Data-Adaptive Procedures in the Investigation of Ocean Waves

\hat \gamma k