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Gaussian processes refer to stochastic processes whose realization consists of normally distributed random variables, with the additional property that any finite collection of these random variables have a multivariate normal distribution. The machinery of Gaussian processes can be employed in regression and classification problems.

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What does it mean that a variogram keeps increasing with distance?

You likely have a trend in you data. So as locations get further apart the variance increases. Try to detrend the data and then do again.
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