**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.