Difference between revisions of "RMS amplitude"

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where y is displacement, t is time, f is frequency, and A is amplitude (the peak deviation of the function from zero)
 
where y is displacement, t is time, f is frequency, and A is amplitude (the peak deviation of the function from zero)
  
<math>y_{RMS} = \sqrt{\tfrac{1}{T} \int_{0}^{T} [Asin(\omegat)]^2 dt}</math>
+
<math>Y_{RMS} = \sqrt{\tfrac{1}{T \int_{0}^{T} [Asin(\omegat)]^2 dt}</math>
  
 
Thus, the RMS=√2/2 A, it’s 0.707 times the maximum amplitude.
 
Thus, the RMS=√2/2 A, it’s 0.707 times the maximum amplitude.

Revision as of 10:39, 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

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)

Failed to parse (unknown function "\omegat"): {\displaystyle Y_{RMS} = \sqrt{\tfrac{1}{T \int_{0}^{T} [Asin(\omegat)]^2 dt}}

Thus, the RMS=√2/2 A, it’s 0.707 times the maximum amplitude.