# 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 (x_{1}, x_{2}, x_{3}…) 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 {x_1,x_2,…,x_n}, the RMS is

The RMS of the corresponding formula for a continuous waveform f(t) defined over the interval [T1, T2] is

and the RMS for a function over all time is

For a sine wave

where y is displacement, t is time, f is frequency, and A is amplitude (the peak deviation of the function from zero)