We have a group of observations
$$y = f(x_1, x_2, x_3) \enspace .$$
We have also a forward model $y = f(x_1, x_2)$. The forward model does not include $x_3$ because $x_3$ might include dozens of parameters which we do not understand clearly.
First, we inverted parameter $x_1$ with the forward model $y = f(x_1, 0)$ embedded in our inversion strategy. The best model can fit 80% of the observed data sets. Then we inverted both parameters $x_1$ and $x_2$ with the forward model $y = f(x_1, x_2)$. However, the misfit did not reduce and the inverted $x_2$ is always quite close to zero.
Based on previous laboratory and numerical experiments, $x_2$ should have significant effects on the observation and its value is obvious larger than zero. So we fix $x_2$ as the experimental observed value and inverted for the optimized model. The misfit from the best inverted model is larger than that with $x_2$ fixed at zero. How can we understand these inversion results? Do they mean that $x_2$ is balanced by $x_3$ or that there was overfitting in inversions with $x_1$ only?