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  • <center><math>\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 </math> is the time shift or lag. For equally sampled (digital) data the autocorrelation is
    2 KB (257 words) - 01:06, 25 December 2017
  • <center><math>\int_{0}^{\infty}\frac{p(f)df}{p_{max}} ;</math></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> <math> \sum ln \left\{1+\left[ \frac{ d^\star_i - d_i } {\sigma}\right]^2\right\} </math> ,</center> where <math>d^\star_i</math> are observed and <math>d_i</math> 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><math>y=\sum \frac{\left(f_i - e_i\right)^2}{e_i} </math>.</center>
    869 bytes (139 words) - 09:37, 28 November 2017
  • <center> <math> \phi(z) = \arctan \left( \frac{\mbox{Im } F(z)}{\mbox{Re } F(z)} \right) </math>.</center> Now, we assert that our recorded data <math> f(t)</math> is the real part of this complex
    6 KB (1,026 words) - 08:43, 10 August 2017
  • <center><math>\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 }</math>,</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><math>\gamma (f) = \arctan \bigg(\frac{\text{imaginary part of } G(f)}{\text{real part of } G(f)}\bigg) </math></c ...a_n \cos(2\pi n ( \frac{t}{T}) ) + \sum_{n=1}^{\infty} b_n \sin(2\pi n ( \frac{t}{T}) )</math></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><math>\frac{1}{2} + \frac{\cos{\phi}}{2}, \quad -\pi<\phi<\pi</math>,</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)}</math></center> ...hase'']] calculation and <math>f(t)</math> is the real part of the seismic data and <math>g(t)</math> is the imaginary part of the complex trace i.e the [[
    3 KB (387 words) - 21:47, 14 August 2018
  • <center><math>\phi(t) = \arctan \left( \frac{\mbox{Im} \; F(t)}{\mbox{Re} \; F(t)} \right) </math></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> <math>\textbf{J} = \left\|J_{ik}\right\| = \left\| \frac{\partial y_i}{\partial x_k} \right\|</math>.</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><math> 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><math>MF=2\pi10^{3}\frac{(PFE)}{\rho_{\alpha}}</math></center>
    2 KB (302 words) - 12:12, 6 March 2017
  • <center> <math>\sum \text{ln} \left[ cosh \left[ \frac{ \left(d_i^\star - d_i\right)}{\sigma}\right]^2\right]</math>,</center> ...rors have the probability distribution <math>\frac{1}{\pi\sigma}sech\left[\frac{\left(d-d_0\right)}{\sigma}\right]</math>, where sech is the hyperbolic sec
    759 bytes (110 words) - 16:15, 3 November 2017
  • <center><math> \sigma=\sqrt{\frac{1}{n}\sum_{i=1}^n\left(X_i-\overline{X}\right)^2}</math></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><math> V_s=\sqrt{\frac{\mu}{\rho}} = \sqrt{\frac{E}{2\rho(1+\sigma)}}.</math></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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