MohoIso: A MATLAB program to determine crustal thickness by an isostatic and a global gravitational model

This paper focuses on the modeling of the boundary between Earthʹs crust and upper mantle using a gravimetric–isostatic model. Here a MATLAB code is presented based on the gravimetric–isostatic model i.e. the Vening Meinesz–Moritz model. Inverse problems in isostasy consist in making the isostatic anomalies to be zero under a certain isostatic hypothesis. The Vening Meinesz–Moritz problem is to determine the Moho depth such that the compensating attraction totally compensates the Bouguer gravity anomaly on the Earthʹs surface, implying that the isostatic anomaly vanishes on the Earthʹs surface. The main idea is easy but the theoretical analysis is somewhat difficult. Here a practical method to recover the Moho depth from the gravity data is used in the MATLAB code (MohoIso.m) based on the Vening Meinesz–Moritz method. The code has been designed based on different sub-codes. The body of the main code works according to the vectorization technique, because this technique causes that the speed of code increases. One of the important possible limitations for the code is over-flow and under-flow for higher degrees in the fully normalized associated Legendre function. This problem occurs in the subroutine applied in this study, it limits the numerical study up to degrees 1800–2000.