sfcausint implements an operation of causal numerical integration. This is a simple operation, which mathematically amounts to recursion
$$yn = y{n-1} + x_n$$
or to inversion of a simple bidiagonal matrix. See Geophysical Image Estimation by Example for more explanation.

The only parameter in sfcausint is adj=, the flag for adjoint computation. The adjoint operation applies recursion backwards
$$x{n-1} = xn + y_{n-1}$$

The following example from gee/ajt/causint illustrates forward and ajoint causal integration with sfcausint: