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taylor expansion

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What does "truncation of a taylor expansion" mean? 

 

 

 

 

 

Are someone here familiar with what an aperture is defined as in geophysics? 

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15 minutes ago, helpplease said:

What does "truncation of a taylor expansion" mean? 

 

 

 

 

 

Are someone here familiar with what an aperture is defined as in geophysics? 

1) A taylor series, like any converging series (do you understand converging) may be used to estimate in numeric calculation or stand in for algebraically in formula an expression that is difficult to handle.
If the series convderges quickly enough (it often does) we can ignore all terms after the first n, for some small n.
There are criteria for deciding how many terms to use. The process of discarding the rest is called truncation.

Wolfram has a good explanation

https://mathworld.wolfram.com/TaylorSeries.html

 

2) An aperture is an opening, which is used to describe the 'size' of something or the size of something being measured or that can pass through.

So this term is widely used in geosciences.

Polyzoa (Fenestrilina) colonies form a basket like weave with apertures in the basket to filter and trap particles washing through.

Acidic groundwater percolating through susceptible rocks (eg limestone) solution weather apertures in the solid rock.

In photogeology the aperture is the camera opening that controls the amount of light entering.

Similary magnetic sensor arrays and seismic arrays have an aperture sensitivity.

These control the amplitude and frequency that can be accepted by the arrays.

Other wave phenomena (eg ultrasonic) have similar use of the term.

https://en.wikipedia.org/wiki/Seismic_array

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Quote

A taylor series, like any converging series (do you understand converging) may be used to estimate in numeric calculation or stand in for algebraically in formula an expression that is difficult to handle.
If the series convderges quickly enough (it often does) we can ignore all terms after the first n, for some small n.
There are criteria for deciding how many terms to use. The process of discarding the rest is called truncation.

Hello, thank you for your reply.

Could you explan this image to simply understand this? What does this mean? 

Its also a sentence where it says: The truncation of this Taylor expansion leads to inaccuracies considering large apertures in the midpoint and offset domain.

This is what i asked earlier. 

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Edited by helpplease

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