Difference between revisions of "RMS amplitude"

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The root mean square amplitude (RMS) is a commonly used technique to display amplitude values in a specified window of stack data. With RMS amplitude, hydrocarbon indicators can be mapped directly by measure reflectivity in a zone of interest.
  
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=== Definition ===
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In statistics, RMS is typical value of a number (n) of values of a quantity (x<sub>1</sub>, x<sub>2</sub>, x<sub>3</sub>…) equal to the square root of the sum of the squares of the values divided by n. <sup>[1]</sup>
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In geophysics, RMS amplitude is the square root of the average of the squares of a series of measurements. The auto correlation value (without normalizing) for zero lag is the mean square value. For a sine wave, the RMS value is () times the peak amplitude.<sup>[2]</sup>
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=== Mathematical Expression ===
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The RMS value of a set of values is the square root of the arithmetic mean of the squares of the values, or the square of the function that defines the continuous-time waveform. <sup>[3]</sup> It’s also known as the quadratic mean of amplitude and is a particular case of the generalized mean with exponent 2.
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In a set of n values {}, the RMS is
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<math>x_{RMS} = \sqrt{\tfrac{1}{n} \sum_{i=1}^n x_i^2 }</math>

Revision as of 10:17, 21 October 2019

The root mean square amplitude (RMS) is a commonly used technique to display amplitude values in a specified window of stack data. With RMS amplitude, hydrocarbon indicators can be mapped directly by measure reflectivity in a zone of interest.

Definition

In statistics, RMS is typical value of a number (n) of values of a quantity (x1, x2, x3…) equal to the square root of the sum of the squares of the values divided by n. [1]

In geophysics, RMS amplitude is the square root of the average of the squares of a series of measurements. The auto correlation value (without normalizing) for zero lag is the mean square value. For a sine wave, the RMS value is () times the peak amplitude.[2]

Mathematical Expression

The RMS value of a set of values is the square root of the arithmetic mean of the squares of the values, or the square of the function that defines the continuous-time waveform. [3] It’s also known as the quadratic mean of amplitude and is a particular case of the generalized mean with exponent 2.

In a set of n values {}, the RMS is