Moho Depth According to the Vening Meinesz' Theory


Program objectives

Vening Meinesz modified the Airy floating theory, introducing regional instead of local compensation, as consequence of this, the Moho depth can be calculated with the Vening Meinesz’ theory instead of the Airy theory (Corchete et al., 2010). The Vening Meinesz’ theory allows the computation of a more realistic Moho surface, than the Moho surface obtained by means of the Airy theory (Moritz, 1990). You can compute the Moho depth for any area of the earth by means of the present program, as it will be described below.

Program description

The VENING program and its files, which are needed to run this application, are enclosed into a ZIP file named "Vening.zip". When you have got the ZIP file and you have uncompressed this file, you have three files named Vening.exe, Vening.dat and ETOPO1.asc. The file Vening.exe contains a program (in FORTRAN code for PC) for the computation of the Moho depth. The file Vening.dat is an ASCII file in the free format and contains the parameters:

Y0, X0, MT, NT, DEPTH_MAX, DEPTH_MIN, T0, DR

The description of these parameters is as follows:

Y0, X0 = Geographical coordinates (latitude in north degrees and longitude in east degrees) for the origin point of the grid data, in which the digital terrain model (DTM) is given.
M = Number of points data in the grid for y-axis (latitude). The maximum value for this number is 1201.
N = Number of points data in the grid for x-axis (longitude). The maximum value for this number is 1201.
DEPTH_MAX = Maximum value for the Moho depth (in km) in the study area considered.
DEPTH_MIN = Minimum value for the Moho depth (in km) in the study area considered.
T0 = Media thickness of the crust in the study area considered.
DR = Value for the degree of regionality (in km). This parameter (called by Vening Meinesz as degree of regionality) has a length dimension and its values (in S.I. units) ranges from 10 to 60 km. Small values of this parameter causes Moho surface with minima more narrow and deeper, the opposite causes wide and shallow minima (Moritz, 1990).

Running the program

Firstly, we need obtain the DTM file ETOPO1.asc for the study area considered. This area must be less than or equal to 20x20 degrees, because the maximum value for the MT and NT parameters is 1201. Then, with a resolution of 1/60 degrees the maximum size is (1/60)*1200 = 20 degrees. This resolution corresponds to the grid spacing of the ETOPO1 global relief. Thus, we need to get the ETOPO1.asc for the study area considered, connecting with the GEODAS web page at http://www.ngdc.noaa.gov/mgg/gdas/gd_designagrid.html and then select the study area (less than or equal to 20x20 degrees), introducing the coordinates of the window that enclosed the study area considered. We must select the options "ASCII Raster Format" and "No Header", to generate an ASCII file valid for the VENING program, other formats cannot be read. After that, we can get a ZIP file containing the ASCII file ETOPO1.asc for the study area considered. Then, we can run the VENING program using this file and the file named Vening.dat. This program generates the files DTM.dat and Moho.dat. The data file DTM.dat contains the DTM written in the format (longitude, latitude, elevation) for plotting. The data file Moho.dat contains the Moho depth calculated according to the Vening Meinesz’ theory and written in the format (longitude, latitude, elevation) for plotting. The results of this program are shown in the Figures 1 and 2.


Fig. 1. Digital terrain model of the study area contained in the data file DTM.dat.


Fig. 2. Moho depth computed for the study area and contained in the data file Moho.dat.

References

Moritz H. (1990). The figure of the Earth. Wichmann, Berlin.

Corchete V., Chourak M. and Khattach D. (2010). A Methodology for Filtering and Inversion of Gravity Data: an Example of Application to the Determination of the Moho Undulation in Morocco. Engineering, 2, 149-159.