# Bishop Model

## Overview of the Bishop5x test dataset

Topographic data for a portion of the volcanic tablelands area north of Bishop, CA has been upscaled by a factor of 30 in x,y, and z dimensions and then shifted in the depth direction such that the structures are all now subsurface (approx 100 to 9300 meters subsea) to use as a test data set for gravity and magnetic calculations (see image below).

Forward calculations of the gravity and magnetic fields were done using GM-SYS-3D from Northwest Geophysical using default extrapolation parameters for a series of models using the depth model with some arbitrary additional susceptibility boundaries added to represent basement lithologic changes/intrusives (image below). The magnetic field was calculated for each model using inclinations of 0, 30, 45, 60 and 90 degrees and a total field of 50,000 nT. Additionally the fields were calculated using varying depths to the base of the magnetic layer (15000 m, 20000 m, 30000 m and a Moho varying from approximately 33000 to 22000 m generated to approximate a passive margin setting).

All files are available as Geosoft binary grids (filename.grd) or GXF grids (filename.gxf) defined as follows:

*x*,*y*grid spacing 200 m*x*,*y*nodes 1901 × 2011*x*extent 2000 m to 382,000 m*y*extent 141000 m to 543000 m

bishop5_basement depth to basement in meters – negative down

bishop5_mag_base_*_i** calculated magnetic field

where * indicates depth to basement of model

and ** indicates inclination

bishop5_susceptibility basement susceptibility

bishop5_gravity calculated gravity (see details below)

bishop5_moho depth to moho in meters - negative down (see details below)

The approximated Moho was calculated as follows:

1. A forward gravity calculation was generated using a sediment depth density function of:

- 0 to 1000 m 2.1 g/cc
- 1000 to 3000 m 2.2 g/cc
- 3000 to 5000 m 2.3 g/cc
- 5000 to 7000 m 2.4 g/cc
- 7000 to 9000 m 2.5 g/cc
- 9000 m to basement 2.6 g/cc
- basement to flat lower crustal layer at 20000m 2.70 g/cc
- flat lower crustal layer to flat base crust at 32800 m 2.90 g/cc
- mantle 3.30 g/cc

2. An inversion was done on the top of the mantle surface to generate an approximated Moho (base crust) that would bring the observed gravity field to 0

3. The inverted base crust was then filtered at 300 km to remove local features and generate a reasonable looking base crust (Moho) surface.

The calculated gravity file was generated by using the depth/density parameters above with the approximated Moho as base crust. A constant of 4000 mGal was subtracted from the calculated gravity to make the numbers more reasonable.

## How to obtain a copy of the data

Left clicking (button 1) on the link http://docs.google.com/open?id=0B_notXWcvuh8dGZWbHlGODRMWEE will download the Geosoft binary grids data to the Download directory on a Linux computer. You can also right click mouse (button 3) and select another location, or use the Linux command:

`wget http://docs.google.com/open?id=0B_notXWcvuh8dGZWbHlGODRMWEE`

from the command line to download the data. The wget command is useful, to build a script to download, unpack, and process the grids.

Now, open a terminal window and type the following dialog:

cd find . -name bishop_Geosoft_grids.tar.gz

On my computer it finds the file as `Downloads/bishop_Geosoft_grids.tar.gz`

or `/tmp/bishop_Geosoft_grids.tar.gz`

. Continue the dialog with:

mkdir open_data mkdir open_data/bishop cd open_data/bishop mv ../../Downloads/bishop_Geosoft_grids.tar.gz . tar -xvf bishop_Geosoft_grids.tar.gz

This will untar the directory. When it completes, type:

cd Geosoft_grids ls

This will list the Geosoft grid files.

GXF grids can be download in a similar way. Use the link http://docs.google.com/open?id=0B_notXWcvuh8dGZWbHlGODRMWEE to download the bishop_GXF_grids.tar.gz file. Proceed in the way described in for the Geosoft grids to tar -xvf, cd and ls the GXF grid files.

The old location for the Geosoft grids was at the link http://docs.google.com/open?id=0B_notXWcvuh8dGZWbHlGODRMWEE. I will maintain this location for a transition period, then I plan to delete it.

## Terms of use

The Bishop data set was created for an SEG workshop in 2006. In 2012, the data was installed in the SEG open data library. No restrictions on use of the data are known.

## References

To view the overview information above, click here To download information on the Bishop model on a linux computer click here. The download should begin automatically. Now, open a terminal window and type the following dialog:

cd find . -name bishop_Bishop_Workshop.tar.gz

On my computer it finds the file as `Downloads/bishop_Bishop_Workshop.tar.gz`

or `/tmp/bishop_Bishop_Workshop.tar.gz`

. Continue the dialog with:

mkdir open_data mkdir open_data/bishop cd open_data/bishop mv ../../Downloads/bishop_Bishop_Workshop.tar.gz . tar -xvf bishop_Bishop_Workshop.tar.gz

This will untar the directory. When it completes, type:

cd Bishop_Workshop ls acroread PhillipsWorkshop.pdf

Other PDF and Microsoft Word documents are available here.

## Useful Publications

Much has been written about the Bishop Model; the following information is intended to be a starting point for further exploration of the topic.

Williams, S., Fairhead, J.D., and Flanagan, G., 2002. Realistic models of basement topography for depth to magnetic basement testing, SEG, Expanded Abstracts, 814-817.

Fairhead, J. D., Williams, S.E. and Flanagan, G., 2004, Testing magnetic local wavenumber depth estimation methods using a complex 3D test model, SEG, Expanded Abstracts, 742–745.

Reid, A., FitzGerald, D., and Flanagan, G., 2005, Hybrid Euler magnetic basement depth estimation: Bishop 3D tests, SEG, Expanded Abstracts, 671–673.

Williams. S.E., 2005, Comparison of grid Euler deconvolution with and without 2D constraints using a realistic 3D magnetic basement model: Geophysics, 70, L13–L21.

Fitzgerald, D., Reid, A., Milligan, P. and Reed, G., 2006, Hybrid Euler magnetic basement depth estimation: integration into 3D Geological Models: AESC2006, Melbourne Australia.

Salem, A., Smith, R., Williams, S., Ravat, D., and Fairhead, D., 2007, Generalized magnetic tilt‐Euler deconvolution: SEG Technical Program Expanded Abstracts 2007, 790-794.

Salem, A., Williams, S., Fairhead, D., Smith, R., and Ravat, D., 2008, Interpretation of magnetic data using tilt-angle derivatives: Geophysics, 73, L1–L10.

Li, X., 2008, Seismic attributes and gravity and magnetic transformations: The same mathematics under different names for different geophysical data sets. SEG Technical Program Expanded Abstracts 2008: pp. 839-843.

Li, X., 2009, Spatial‐domain transformations: Something old and something new. SEG Technical Program Expanded Abstracts 2009: pp. 928-932.

Fedi, M., Florio, G. and Quarta, T.A., 2009, Multiridge analysis of potential fields: geometric method and reduced Euler deconvolution: Geophysics, 74, L53-L65.

Davis, K. and Li, Y., 2009, Enhancement of depth estimation techniques with amplitude analysis: 79th Annual International Meeting, SEG, Expanded Abstracts, 908-912.

Gerovska, D., Araúzo-Bravo, M., Whaler, K., Stavrev, P., and Reid, A., 2010, Three-dimensional interpretation of magnetic and gravity anomalies using the finite-difference similarity transform: Geophysics 75, L79–L90.

Barnes, G. and Lumley, J., 2011, Processing gravity gradient data: Geophysics, 76, I33–I47.

Salem, A., Green, C., Campbell, S., and Fairhead, J.D., 2012, A practical approach to 3D inversion of pseudo-gravity for depth to basement mapping – a test using the Bishop model: 74th EAGE Conference & Exhibition, Expanded Abstracts.

Flanagan, G. and Bain, J.E, 2012, Depth Extent – A practical example in magnetic depth estimation: 74th EAGE Conference & Exhibition, Expanded Abstracts.

## Contact information

Questions can be directed to: [email protected]