Documentation for the Geosoft gravity isostatic regional calculation method in marine areas

RichardLane

I am looking for documentation for the Geosoft gravity Isostatic Residual tool and for assistance with some questions that I have about the way that the calculations are performed.

The only documentation that I can find is an online eLearning tutorial and a short description on the product webpage.

https://www.geosoft.com/products/oasis-montaj/extensions/gravity-magnetic-interpretation

After going through these sources, I have the following inter-related questions:

- What does the "Bouguer density at sea" mean? What role does it play in the calculations? The tutorial shows an entry of "2.67 g/cm^3" for this box.

- Is the "Bouguer density at sea" the deficit between the bedrock and the ocean (e.g., (1.03 - 2.67 = -1.64 g/cm^3))?

- In offshore areas, do you include sea floor bathymetry in the "topographic grid"?

- Is the loading of the ocean included in the calculations?

- The tutorial indicates the "The gravity effect at sea level for the root is calculated." Does this mean that variable height continuation is required to obtain the gravity effect on the ground surface when there is significant topographic relief in the region of interest?

Many thanks for your time,

Richard Lane
Geoscience Australia

GerryConnard1

I checked our code to make sure that rhoW is being subtracted and it is.

GerryConnard1

The loading of the ocean is included. 1.027 gm/cc is subtracted from the value you input for Bouguer density at sea. You should include seafloor bathymetry in the topo grid. Yes a variable height continuation is required to obtain the gravity effect on the ground surface where there is significant topo relief.

The method is described in detail in the following 2 papers:
Simpson, Robert W., Jachens, Robert C., and Blakely, Richard J., 1983, Airyroot: A Fortran Program for Calculating the Gravitational Attraction of an Airy Isostatic Root Out to 166.7 KM:U.S.G.S. Open-File Report 83-883, 66 p.

Simpson, Robert W., Jachens, Robert C., Blakely, Richard J., and Saltus, Richard W., 1986, A New Isostatic Residual Gravity Map of the Conterminous United States With a Discussion on the Significance of Isostatic Residual Anomalies, JGR, 91, p8348-8372.

GerryConnard1

Richard, you may also be interested in a new feature added to GM-SYS 3D in 9.6 that we call IGI for "Isotatic Gravity Inversion". I can send you a pre-print of a paper describing it if you are interested.

RichardLane

Hello Gerry.

Thanks for responding to my request. A copy of your pre-print would be much appreciated ( rjllane@gmail.com ).

Thanks for the references. I am reasonably familiar with AIRYROOT. It doesn't explicitly deal with marine situations as far as I am aware, and definitely doesn't cater to a situation such as the one that I have at present that spans onshore and offshore areas.

Just to be absolutely clear with Geosoft, if I enter 2.67 g/cm^3 for the Bouguer density at sea, the program will subtract 1.027 g/cm^3 from my value? I shouldn't enter 1.643 g/cm^3?

... Richard Lane

GerryConnard1

AIRYROOT does explicitly does deal with marine situations. On page 5 of the JGR paper it states
"In the Airy-Heiskanen scheme, oceanic crustal columns with water depth dw (taken to be positive here) have a negative load (weight deficiency) at the top caused by the presence of water of density pw rather than rock [Heiskanen and Moritz, 1967]. Negative compensation is provided by an anti-root of denser material that has its top at a depth
d = ds - dw (rhoT - rhoW)/delta-rho"

We modified that slightly to allow for different oceanic mantle densities. So you can see that it does subtract the sea water density from the terrain density.

RichardLane

Hello again Gerry.

My comment with respect to AIRYROOT was based on inspection of the FORTRAN code itself. I agree that the JGR paper explains the situation.

Perhaps the paper is based on a modified version of the program, not the one that was published in the USGS OFR?

In any case, in Geosoft, I gather that rhoW is built-in and the user is entering rhoT_land, rho_T_ocean, delta_rho_land, and rho_T_ocean?

... Richard

RichardLane

Hello Gerry.

Thanks so much for taking the time to inspect the code. It is very reassuring to know that you did so, and confirmed the nature of the sea water loading calculations.

I am in the process of a final check: - confirming the Root Depth calculations done by Geosoft based on the information that you have given me, knowing the equations that are given in Simpson et al. (1986), and knowing the input grid and settings that I am using.

Have a great day.

... Richard Lane