The use of instantaneous velocity in uplift investigations

Uplift and the accompanying reduction in overburden result in anomalously high velocity in the uplifted rock unit relative to its current depth. The present work utilizes the non‐uniqueness of the parameters of instantaneous velocity versus depth functions as an effective tool for uplift studies. The linear function with its two parameters, V₀ and k, is a very simple function and is used as the illustrative vehicle. In the parameter space, i.e. in a plot where one axis represents V₀ and the other axis represents k, non‐uniqueness can be represented by contours of equal goodness‐of‐fit values between the observed data and the fitted function. The contour delimiting a region of equivalent solutions in the parameter space is called a ‘solution trough’. Uplift corresponds to a rotation of the solution trough in the parameter space. It is shown that, in terms of relative depth changes, there are five possible configurations (five cases) of uplift in a given area (the mobile location) relative to another area (the reference location). The cases depend on whether the uplifted location had attained a (pre‐uplift) maximum depth of burial that was greater than, similar to, or smaller than the maximum depth of burial at the reference location. Interpretation of the relationships between the solution troughs corresponding to the different locations makes it possible to establish which of the five cases applies to the uplifted location and to estimate the amount of uplift that the unit had undergone at that location. The difficulty in determining the reduction in velocity due to decompaction resulting from uplift is a main source of uncertainty in the estimate of the amount of uplift. This is a common problem with all velocity‐based methods of uplift estimation. To help around this difficulty, the present work proposes a first‐order approximation method for estimating the effect of decompaction on velocity in an uplifted area.