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• <center>$\phi_{ff}(\tau) = \lim_{t_1 \to \infty} \lim_{t_2 \to \infty } \frac {\displaystyle \int^{t_2}_{t_1} f(t) f(t+\tau) dt }{\displaystyle\int^{t_2} ...math> \tau$ is the time shift or lag. For equally sampled (digital) data the autocorrelation is
2 KB (257 words) - 01:06, 25 December 2017
• <center>$\int_{0}^{\infty}\frac{p(f)df}{p_{max}} ;$</center> <b>4</b>. The rate at which a computer resource can carry (accept or deliver) data. Usually expressed in bytes per second or bits per second.
939 bytes (153 words) - 22:09, 30 January 2017
• <center> $\sum ln \left\{1+\left[ \frac{ d^\star_i - d_i } {\sigma}\right]^2\right\}$ ,</center> where $d^\star_i$ are observed and $d_i$ are model data. Implies that errors have the probability distribution
741 bytes (107 words) - 17:46, 15 April 2017
• The issue of causality affects data both in the time domain and the frequency domain. This fact is apparent whe ...(t) e^{i \omega t } \; dt = \frac{1}{2 \pi} ( F \star \hat{H})(\omega) = \frac{1}{2 \pi} \int_{-\infty}^{\infty} \hat{H}(\omega -\Omega) F(\Omega) \; d \O
8 KB (1,347 words) - 15:34, 26 September 2019
• ...mean, and with unit variance. The chi-square test is a statistical test of data distribution. If ''f''<sub>''i''</sub> are observed, frequencies of occurre <center>$y=\sum \frac{\left(f_i - e_i\right)^2}{e_i}$.</center>
869 bytes (139 words) - 09:37, 28 November 2017
• <center> $\phi(z) = \arctan \left( \frac{\mbox{Im } F(z)}{\mbox{Re } F(z)} \right)$.</center> Now, we assert that our recorded data $f(t)$ is the real part of this complex
6 KB (1,026 words) - 08:43, 10 August 2017
• <center>$\phi_{GH}(\tau)=\frac{\displaystyle \int_{-\infty}^{+\infty}G(t)H(t+\tau)dt}{ \displaystyle \int_ For digital data this becomes 2 KB (278 words) - 08:18, 2 October 2017 • ...or the time delay on an offset trace assuming horizontality, DMO moves the data to the correct zero-offset trace for a dipping reflection, and migration fu ...rac{y}{2}}{V}\right)^2 }+ \sqrt{\left(\frac{h}{2V}\right)^2+\left(\frac{m-\frac{y}{2}}{V}\right)^2 }$,</center>
3 KB (432 words) - 15:07, 31 January 2017
• \text{erf} (t)=\frac{2}{\sqrt{\pi}} \int_0^x e^{-y^2} dy For data which have a Gaussian distribution, the probability that an error lies betw
645 bytes (100 words) - 23:03, 14 February 2017
• <center>$\gamma (f) = \arctan \bigg(\frac{\text{imaginary part of } G(f)}{\text{real part of } G(f)}\bigg)$</c ...a_n \cos(2\pi n ( \frac{t}{T}) ) + \sum_{n=1}^{\infty} b_n \sin(2\pi n ( \frac{t}{T}) )[/itex]</center>
11 KB (1,757 words) - 05:57, 15 June 2017
• A function used to shape the cutoff of a window in data processing to avoid undesirable effects of sharp truncation: <center>$\frac{1}{2} + \frac{\cos{\phi}}{2}, \quad -\pi<\phi<\pi$,</center>
924 bytes (141 words) - 16:10, 24 July 2016
• ...\frac{f(x,t) \cdot \displaystyle \frac{dg}{dt}-g(x,t) \cdot \displaystyle \frac{df}{dt}}{f^2(x,t)+g^2(x,t)}[/itex]</center> ...hase'']] calculation and $f(t)$ is the real part of the seismic data and $g(t)$ is the imaginary part of the complex trace i.e the [[
3 KB (387 words) - 21:47, 14 August 2018
• <center>$\phi(t) = \arctan \left( \frac{\mbox{Im} \; F(t)}{\mbox{Re} \; F(t)} \right)$</center> ...(t)'' is the seismic trace and ''Re F(t)'' is the real part of the seismic data ''Im F(t)'' is the imaginary part of the complex trace.Since, most of the t
2 KB (250 words) - 17:20, 24 April 2019
• <center> $\textbf{J} = \left\|J_{ik}\right\| = \left\| \frac{\partial y_i}{\partial x_k} \right\|$.</center> ...led the <b>data influence matrix</b> as it shows how a small change in the data would influence the inversion result. Vanishing of the determinant of the J
1 KB (205 words) - 12:53, 26 November 2017
• ...''Geophys. Prosp.'', '''16''', 159–162.</ref>) for Wenner-configuration data. The derivation of resistivity stratification from the kernel is shown by P <center>$V = \frac{C}{r} + 2 C \int \!\! K(\lambda) J_o (\lambda r) \, \mathrm{d}\lambda </mat 2 KB (289 words) - 20:16, 28 March 2017 • ...conductivity or capacitivity of a rock, used in the interpretatation of IP data. Metal factor is the [[Special:MyLanguage/Dictionary:percent_frequency_effe <center>[itex]MF=2\pi10^{3}\frac{(PFE)}{\rho_{\alpha}}$</center>
2 KB (302 words) - 12:12, 6 March 2017
• <center> $\sum \text{ln} \left[ cosh \left[ \frac{ \left(d_i^\star - d_i\right)}{\sigma}\right]^2\right]$,</center> ...rors have the probability distribution $\frac{1}{\pi\sigma}sech\left[\frac{\left(d-d_0\right)}{\sigma}\right]$, where sech is the hyperbolic sec
759 bytes (110 words) - 16:15, 3 November 2017
• <center>$\sigma=\sqrt{\frac{1}{n}\sum_{i=1}^n\left(X_i-\overline{X}\right)^2}$</center> With a normal or Gaussian distribution of data, 68.3&#x0025; of the data fall within a standard deviation about the mean. The square of the standard
1 KB (188 words) - 14:40, 2 October 2017
• <center>$V_s=\sqrt{\frac{\mu}{\rho}} = \sqrt{\frac{E}{2\rho(1+\sigma)}}.$</center> ...ta are often displayed at half the vertical scale of the comparable P-wave data to compensate roughly for the differences between S-wave and P-wave velocit
3 KB (364 words) - 19:45, 19 September 2020
• ...combined into the Thomsen parameters that relate more directly to seismic data: \alpha_0 = \sqrt{\frac{c_{33}}{\rho}}
5 KB (615 words) - 22:16, 18 September 2020

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