Adaptive Lp inversion to recover both blocky and smooth features

Inversion based on L2 norm has been widely used in geophysical problems. However, L2 inversion is only capable of recovering smooth features. To obtain sharp boundaries, non-L2 inversion has been used successfully. In reality, however, both smooth and blocky features can be present in the subsurface physical property or interfaces to be recovered. To deal with this situation, we propose a new method to adaptively apply L2 and non-L2 norm to different parts of the same model. This method first detects the smoothness or blockiness of different regions of a model and then applies appropriate Lp model norm with different p values to complete the final inversion. We test this method in an example of crosshole seismic traveltime inversion.