Difference between revisions of "RMS amplitude"

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(Mathematical Expression)
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=== Mathematical Expression ===
 
=== 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. <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.
 
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.
 
In a set of n values {}, the RMS is
 
  
 
<math>f_{RMS} = \sqrt{\tfrac{1}{T_2 - T_1 \int_{T_1}^{T_2} [f(t)]^2} dt}</math><math>x_{RMS} = \sqrt{\tfrac{1}{n} \sum_{i=1}^n x_i^2 }</math>
 
<math>f_{RMS} = \sqrt{\tfrac{1}{T_2 - T_1 \int_{T_1}^{T_2} [f(t)]^2} dt}</math><math>x_{RMS} = \sqrt{\tfrac{1}{n} \sum_{i=1}^n x_i^2 }</math>

Revision as of 10:22, 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.