  This paper considers a generalization of Gaussian random field with
covariance function of Whittle-Mat$\acute{\text{e}}$rn family. Such a random
field can be obtained as the solution to the fractional stochastic differential
equation with two fractional orders. Asymptotic properties of the covariance
functions belonging to this generalized Whittle-Mat$\acute{\text{e}}$rn family
are studied, which are used to deduce the sample path properties of the random
field. The Whittle-Mat$\acute{\text{e}}$rn field has been widely used in
modeling geostatistical data such as sea beam data, wind speed, field
temperature and soil data. In this article we show that generalized
Whittle-Mat$\acute{\text{e}}$rn field provides a more flexible model for wind
speed data.
