# 3.3.8. Octree Mesh File¶

Octree meshes define the global domain for which the inverse problem is solved and the local domains for which the set of forward problems are solved in parallel. The format of Octree mesh files is as follows:

nx $$\;$$ ny $$\;$$ nz $$\;$$ xpL $$\;$$ xpU $$\;$$ ypL $$\;$$ ypU $$\;$$ zpL $$\;$$ zpU
x0 $$\;$$ y0 $$\;$$ z0
dx $$\;$$ dy $$\;$$ dz
Lx_1 $$\;$$ Ly_1 $$\;$$ Lz_1 $$\;$$ M_1
Lx_2 $$\;$$ Ly_2 $$\;$$ Lz_2 $$\;$$ M_2
$$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\vdots$$
Lx_N $$\;$$ Ly_N $$\;$$ Lz_N $$\;$$ M_N

An example of an octree mesh file is shown below

Note

The set of local meshes for which the

## 3.3.8.1. Parameter Descriptions¶

• nx ny nz: Dimensions of the mesh in x, y and z respectively, in terms of the number of base mesh cells (cells of smallest size). Thus the mesh has dimensions $$[nx \times dx, ny \times dy, nz \times dz]$$.

• xpL xpU ypL ypU zpL zpU: These parameters set the padding distance, relative to the core region, in terms of the number of base mesh cells. For example, the region of padding cells in the southern direction (defined by xpL) has a width of $$xpL \times dy$$.

• x0 y0 z0: The x, y and z location denoting the top southwest corner of the mesh

• dx dy dz: Sets the x, y and z widths of the base mesh cells (smallest cells)

• N: Total number of cells in the mesh. Note that $$nx \times ny \times nz \neq N$$

• Lx_i Ly_i Lz_i M_i: The location and dimensions of each cell i=1,…,N is defined by 4 parameters. Lx_i defines how many base cell widths in the x direction (i.e. dx) the top southwest corner of this cell is from the top southwest corner of the mesh plus one; i.e. the cell is $$dx \times (Lx-1)$$ metres from the top southwest corner in the x direction. This is likewise for Ly_i and Lz_i. M_i defines the width of the cell in x,y and z in terms of the number of base mesh cells. Thus, the volume of each cell is $$V = dx \times dy \times dz \times M^3$$

Note

• Cell locations are defined by their distances from the top southwest corner.

• See the first cell defined in the Octree mesh file (line 5). The top southwest corner if this cell corresponds with that of the mesh. However, its location is defined as 1 1 1 instead of 0 0 0 due to convention.