Small-Scale Heterogeneity Models

The ssh1d, ssh2d, and ssh3d modules generate fractional perturbations with zero mean and a user-specified sample standard deviation before local tapering.

Models

von Karman

The default model. It uses correlation length -C and Hurst exponent -U. The default Hurst exponent is 0.15. This is the preferred default for geophysical applications.

Gaussian

A smooth correlated model controlled by -C.

Exponential

A rougher correlated model controlled by -C.

White noise

Uncorrelated samples. Correlation length and Hurst exponent are not used here.

Anisotropy

One correlation length produces isotropic statistics. A length for each coordinate dimension produces axis-aligned anisotropy. Rotated anisotropy is not yet implemented.

Multiple fields

Shared -D, -C, and -U values apply to every selected field. Repeatable field/value forms override one parameter. Multidimensional SSH modules use a shared underlying Gaussian realization by default so equivalent statistics produce equivalent patterns apart from scale. The independent seed modifier creates a separate realization for each field.

Application

In application mode a model value m becomes m(1 + epsilon). The same taper is used for all selected fields, while each field may retain distinct statistical parameters.