A mathematical twist to model gravity
We have learned a lot about gravity on Earth since its discovery in the 17th century, including how it varies depending on the density of different rock types, and how modelling it allows geoscientists to sense the geological makeup of the Earth. Now, thanks to new NCRIS enabled research and a good dose of mathematical wizardry, geoscientists can look forward to modelling gravity data with far greater efficiency.
Gathering gravity data
Gravity works on the Earth as the attraction between the entire mass of the Earth and its constituent parts. The moon also hefts its gravitational weight around, causing the rise and fall of tides. The strength of the gravitational force at the Earth’s surface depends on the size and density of the rocks beneath. For example, a basin full of limestone will have a different gravitational force than the more dense rock of a volcanic island chain.
Gravity data is gathered by geophysicists walking across the landscape taking measurements using a gravitometer. To cover larger distances they are strapped on to aeroplanes, boats, or drones. As a result, geoscientists have been generating a lot of gravity data and consequently building a picture of Earth’s subsurface! The next challenge is to enable researchers to access this data and work with it effectively to generate geological insights.
A short explanation of how gravity surveys work. Source: OresomeResources
Stepping off the grid
Geophysicists often make gravity data workable by converting randomly spaced raw data into gridded data using interpolation. This method reduces the number of data points that need to be processed and results in more efficient computer modelling. Without this, large data sets can take days or weeks to compute. However, gridding data inevitably requires that some data is thrown away, reducing the effective resolution of the data that is available.
In response to this challenge of speed and data density, and to use all the available data without having to wait days for an answer, Dr Andrea Codd and Associate Professor Lutz Gross have used NCRIS supported esys-escript and gambit computer codes to create a new way to work with gravity data. Their results have been published in the Geophysical Journal International.
Their method uses mathematics and gambit codes to generate detailed mesh models in record time. Simply put, that means every data point is used in the modelling process! Dr Andrea Codd explains how this new method makes data analysis more efficient:
“The numerical techniques used mean that we can solve big problems in terms of data as well as the extent of the data. This is possible because every algorithm design decision takes advantage of methods that work together optimally to improve computation speed.”
Data Access
Ease of access to gravity data has been an exciting aspect of this study. The data used by the team is freely available from the Department of Natural Resources, Queensland. Similar data (measurements and locations) are available throughout Australia. Dr Andrea Codd reflects on what this access meant for her project and future geoscientists,
“It is really exciting to log onto the GeoResGlobe website, pick a region that looks interesting and download the gravity data. It means I can test my algorithm easily with real data.
Geophysicists can also use the software and invert their own data to produce subsurface density profiles. It could also help to inform where they take measurements, as regions of particular variability could have greater concentration of observations. All the data is used so they won’t lose resolution by having to transform the observations to a grid.”
Map showing gravity data observation points across the study region of Mt Isa. Data was obtained from GeoResGlobe and mapped by Andrea Codd. This image was generated using matplotlib. Image: Codd & Gross, 2021
The study generated three-dimensional inversion models of gravity anomalies in Western Queensland using 6,519 observations from twenty-three different gravity surveys. Inversion is like going backwards from the answer to the question. We have the answer (the gravity data), now we just need to work out the density that would generate the same gravity field as the data.
The study benefited from the ability to combine surveys efficiently. Dr Andrea Codd reflects on the gains that have been made when dealing with multiple surveys:
“Inversion is all about taking ground-level observations and converting them into information about what is going on in the subsurface. The goal is to take more and more observations at their exact locations to get a clearer picture. Thus, we invert multiple surveys with irregularly spaced observations in one go.”
The resulting flexible mesh model and mathematical adjustments allowed the team to capture slight differences in gravity measurements across a large area to determine density profiles in the subsurface.
A density inversion result for the Mt Isa - Cloncurry region of North Queensland. The red represents higher density areas, and the blue represents lower density areas. The horizontal plane is 5km below the ground surface. This image was generated using VisIt software. Image: Codd & Gross, 2021
The team is excited to share their new methods and to encourage geoscientists to dive into the freely available data that is just waiting to be explored. If you are curious to try out your own inversion, you can find the relevant links in the KEY RESOURCES section of this story (in the sidebar).
AUTHORS
Philomena Manifold
and Dr Andrea Codd
Edited by Jo Condon
KEY CONTACT
Dr Andrea Codd
KEY RESOURCES
Github: esys-escript
gambit GeoResGlobe
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