Difference between revisions of "RMS amplitude"
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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. | 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 {x_1,x_2,…,x_n}, the RMS is | In a set of n values {x_1,x_2,…,x_n}, the RMS is | ||
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+ | <math>x_{RMS} = \sqrt{\tfrac{1}{n} \sum_{i=1}^n x_i^2 }</math> | ||
The RMS of the corresponding formula for a continuous waveform f(t) defined over the interval [T1, T2] is | The RMS of the corresponding formula for a continuous waveform f(t) defined over the interval [T1, T2] is | ||
− | <math> | + | |
+ | <math>f_{RMS} = \sqrt{\tfrac{1}{T_2 - T_1 \int_{T_1}^{T_2} [f(t)]^2} dt}</math> | ||
+ | |||
+ | and the RMS for a function over all time is | ||
+ | |||
+ | <math>f_{RMS} = \sqrt{\tfrac{1}{T \int_{0}^{T} [f(t)]^2} dt}</math> |
Revision as of 09:27, 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 {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