Abstract
As we saw in chapter 6:
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the average vertical velocity is the time average of the instantaneous velocities v:
$${V_M} = \frac{1}{T}\int_o^T {v(t)dt} $$or
$${V_M} = \frac{1}{T}\sum\limits_{k = 1}^n {{v_k}{t_k}} $$ -
the root mean square velocity VRMS is the square root of the time average of the squares of the instantaneous velocities:
$$V_{RMS}^2 = \frac{1}{T}\int_o^T {{v^2}(t)dt} $$or
$$V_{RMS}^2 = \frac{1}{T}\sum\limits_{k = 1}^n {v_k^2(t){t_k}} $$
It is important to note that for a given depth, the values of VM and VRMS are independent by definition of the distribution function of the velocities vk.
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© 1985 Springer Science+Business Media Dordrecht
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Cordier, JP. (1985). Relationships between Root Mean Square Velocities, Average Velocities, and Coefficients of Heterogeneity. In: Velocities in Reflection Seismology. Seismology and Exploration Geophysics, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3641-1_8
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DOI: https://doi.org/10.1007/978-94-017-3641-1_8
Publisher Name: Springer, Dordrecht
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