Forward problem, inverse problem কী?

Let a model of the Earth be described by a vector $\mathbf m$ of $M$ parameters and the observations by a vector $\mathbf d$ of $N$ data. The forward problem is to compute the data $\mathbf d = g(\mathbf m)$ that a given model would produce, by a physical theory. The inverse problem is to estimate the model from data that carry errors, $\mathbf d = g(\mathbf m) + \mathbf e$, and to say how well each part of the model is determined. The problem is linear when $g(\mathbf m) = \mathsf G\mathbf m$ for a fixed $N\times M$ matrix $\mathsf G$, the kernel.