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July 15, 2018

Even with the dramatic advances in computation speed, the demands of the petroleum exploration industry to find more oil faster has grown exponentially. Geosoft’s Gerry Connard explains the advantages of using Fast Fourier Transforms (FFT) for gravity and magnetic modelling.

**What research is the approach based on?**

Robert Parker’s seminal paper published in 1972, *The Rapid* *Calculation of Potential Anomalies*, has led to a revolution in using
FFT for gravity and magnetic modeling using ‘gridded’ data. Since
then, a number of additional papers, including some by Parker
himself, have extended and improved Parker’s original work.
Richard Blakely’s 1995 book summarizes most of this development
and provides some additional, related FFT algorithms for FFT-based
gravity and magnetic calculations (such as Blakely’s ‘Earth Filters’).

**What are the advantages of the FFT-based methods?**

Parker describes in the introduction of his 1972 paper that the computation time for a model grid containing N points is proportional to N ln(N). For equivalent space-domain calculations on the same type of model, the computation time is proportional to N2. This difference is not so significant for small models. For example, to calculate the response of a grid with 100 points, the space-domain approach would require approximately 20 times as many calculations as the FFT approach. However, as the number of grid point increase, the ratio of the number of calculations in the space-domain approach compared to the number of calculations in the FFT-based approach increases rapidly. For a grid with 1000 points, the ratio is 144. For a grid with one million points, the ratio is 72,382. So if the FFT-based approach took one minute of compute time, the space-domain approach would take 50 days.

**Are there disadvantages of the Parker method?**

There are pitfalls in the FFT-based calculation approach, including but not limited to the problems of edge effects, periodicity, and the fact that the original Parker algorithm is based on the convergence of a Taylor-series approximation. With two decades of practical experience using the FFT-based approach, most of these problems have been solved or at least minimised. For example the “Earth Filter” algorithm does not need the Taylor-series approximation.

**What are your future predictions?**

The FFT approach continues to evolve. Two papers by Parker in 1995 and 1996 extend his method to compute the results on an uneven surface. This allows more flexible models that more closely resemble a real earth model which are more appropriate in many exploration scenarios. In 2009, a new paper published by Caratori Tontini and others describes how to use 3D FFTs for gravity and magnetic calculations that will likely lead to significant improvements in FFT-based methods. Although raw computing power continues to grow according to Moore’s Law, our computing needs are growing even faster. Explorers today are taking advantage of a wealth of detailed exploration data to build larger and more complex models with grid sizes often exceeding one million points. FFT-based methods will play an important role in tools for the utilization of gravity and magnetic data in large, detailed models.

In spite of the disadvantages of the computational speed of space-domain techniques, they will also continue to be important tools in the interpretation tool kit. Space-domain techniques are inherently more flexible than FFT-based techniques and more easily utilised for inversion schemes. One powerful approach is to use a hybrid technique that combines both FFT-based and space-domain techniques in a modeling tool. Cloud computing (such as using large banks of parallel processors at a remote site) is also likely to be part of our exploration computing future. This approach is already being used by companies like Microsoft and Google to bring amazing computing power to desktops around the world.

*Gerry Connard is the Petroleum Industry Market* *Manager with Geosoft. Connard is a geophysicist* *with over 30 years’ experience in the exploration* *industry. He founded NGA, Inc. and developed* *gravity and magnetic profiling and modelling* *software – GM-SYS and GM-SYS 3D.*