# Difference between revisions of "RMS amplitude"

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

${\displaystyle f_{RMS}={\sqrt {{\tfrac {1}{T_{2}-T_{1}\int _{T_{1}}^{T_{2}}[f(t)]^{2}}}dt}}}$${\displaystyle x_{RMS}={\sqrt {{\tfrac {1}{n}}\sum _{i=1}^{n}x_{i}^{2}}}}$