Dear Isaiah Adelere,

I understand that your question does not have a unique answer, and it is made in geographical units ("...I intend to use 4 half-degree aeromagnetic sheets for geothermal analysis with the intention of a 10' by 10' block size...."). I will try to help with the following explanation:

First of all, you must put in geological/structural/tectonic context, it means: if your scenario is related to a relatively high heat flow regime, the window size should be small enough to estimate the Curie point depth (CPD) because it is expected to be shallow. In contrast, if your geological scenario is considered a low heat flow, it should be large enough to estimate the deeper CPDs. It means several window sizes you must test, and the appropriate length must be selected based on the criteria of the minimal block size that does not cut off the spectral peak (Ravat et al., 2007).

On the other hand: if you have land, airborne, or satellite data, the filtering effect of anomalies could be critical, also the spectral answers. Therefore, the question is: Which is your data source for your research? Satellite magnetic data complement the existing local and regional data sets by providing a globally unified data set. It means: the local structures below the minimum wavelength content cannot be resolved in such a data set, therefore: you must choose the window size for FFT and CDPs estimation according to or in the function of your dataset.

The methodology that I recommend using to estimate Curie point depth is founded on the 2-D radial average power spectral (RAPS) analysis of magnetic anomaly data described basically by three foundational works:

• 1) Spector and Grant (1970), where estimated the depth to the top of magnetized rectangular prisms (Zt) from the slope of the log power spectrum.
• 2) Bhattacharyya and Leu (1975a, b, 1977) calculated the depth of the centroid of the magnetic source bodies (Z0).
• 3) Okubo et al. (1985) developed a method to estimate the bottom depth of the magnetic bodies (Zb) using the spectral analysis method of Spector and Grant (1970).

Mathematically, the Fourier transform of a space domain function f(x,y) is measured in radians per meter if x and y are in given meters. These are related to spatial "frequencies" fx and fy, in cycles per meter. All spectral analysis must be in distance units, such as meters, not in geographical coordinates such as latitude and longitude. FFT will take the 2-D forward Fast Fourier Transform and perform one or more mathematical operations in the frequency domain before transforming back to the space domain. An option is provided to scale the data before writing the new values to an output file. The horizontal dimensions of the grid are assumed to be in meters. For other grids geographical grids were you want to convert degrees into meters.

The input dataset of a magnetic anomaly - the emphasis for land research - must reduce the influence:

• 1) Boundary conditions and edge effects;
• 2) Avoid high-frequency noise caused by tiny structures near the ground after lowpass filtering.
• 3) The reduction to pole (RTP, Baranov, 1957) must be applied to the magnetic anomalies to obtain anomaly values induced by the inclination of 90º and the declination of 0º. In theory, appropriate only when all bodies/sources in your ZOI are magnetized parallel to the geomagnetic field and at the same time it has a vertical dip.

The depth estimation from your RAPS advises you that the optimal square window dimension is about 10 times the estimated depth (Chiozzi et al., 2005). Thus, you should divide your work area/zone of interest (in km/m units) into square subareas of such as for example 300 km x 300 km to say you an accurate value, each of them overlapping with respect to each other in a step increment, for example, 100 km, and then applying the 2-D FFT RAPS method individually to get Zo and Zt. The computation requires an extensive dataset for estimating Curie point depth.

Best regards, Mario E. Sigismondi

Mario Emilio Sigismondi

Dear Dr. Emilio Sigismondi I appreciate you for finding time out of your busy schedule to provide a comprehensive answer to the question I asked about analysing geothermal potential using Aeromagnetic data. It was an eye-opener and I have learned from the answer.

However, I have a few questions about the points you raised. Below are my questions

1. In the first paragraph, you spoke about "... It means several window sizes you must test, and the appropriate length must be selected based on the criteria of the minimal block size that does not cut off the spectral peak". How do I know the minimal block size does not cut off the spectral peak?

2. My dataset is Satellite magnetic data, do I need to perform regional and residual separation and apply the RAPS method on the residual? If yes, Which method of separation is advisable, is it upward continuation or polynomial?

Lastly, is there any lecture note or video tutorial that explains geothermal analysis from aeromagnetic data? If there is please recommend it. I will not mind you scheduling a meeting, so I can share files and the result I have gotten.

Thank you.

Isaiah Adelere