Hello Steemit community, today I will tell you a little about a very interesting topic in the area of ​​geophysics as is the Seismic Spectral Decomposition.

Spectral decomposition is a method of analyzing seismic data that is based on Fourier concepts that a repeated function can be constructed through the sum of an infinite number of mono-frequency wavelets, each with its own amplitude values and phase. For a seismic interpreter, this method is a data filter with a series of mono-frequency wavelets which cover the usable usable spectrum of the seismic data. The results are presented as sections of horizons, time and strata through seismic surfaces in 3 dimensions.

The base functions of sine and cosine are the most common to apply spectral decomposition, although there are other methods, all of them are based on using a set of base functions to obtain the transformative coefficients through the cross-correlation of each base function with a time window of the seismic data.

To properly understand what spectral decomposition is about, we will first develop a little about the foundations that support the development of this.

The spectral decomposition is mainly supported by Fourier analysis, which is used to decompose a function, signal or periodic wave as infinite or finite sum of functions, signals or harmonic or sinusoidal waves. Fourier analysis allows to decompose the signal into sinusoidal components of different frequencies, it can also be defined as a mathematical technique that can transform the point of view of a signal from the time domain to the frequency domain, as can be seen in the following image:

The spectral decomposition offers patented methods of spectral calculation, among them is the method of the discrete Fourier transform (DFT), which is based on a transformation of the seismic time data, g (t), in the frequency space , G (f):

The geophysical properties of DTF are well known, and it has a well deserved reputation for being safe and reliable. Specifically, the DTF calculates an amplitude value in each Hertz from the frequency of the start to the final frequency. The mathematics of the DTF algorithm is shown below.

The resulting output is a complex spectrum which can also be expressed as:

The amplitude spectrum is calculated by:

The phase spectrum is calculated by:

That's all for today's Steemit community, I hope it's to your liking and interest.

See you another time.