For a damping parameter ε>0, the damped least squares estimate is the model that minimises
Φε(m)=χ2(m)+ε2∥m∥2,mε=(N+ε2I)−1GTCd−1d.
The trade-off curve is the curve traced, as ε varies, by the pair (size of the model ∥mε∥, misfit χ2(mε)): small damping fits the data closely with a large, rough model, large damping gives a small model and a poor fit.