Termen Flashcards
Range
Distance where the semivariance approaches variance, in other words the x-axis until the semivariogram becomes flat
Still
The region where semi-variance no longer increases and semi-variogram becomes flat
Nugget
Bottom part of the Still which doesn’t have influence on the semi-variogram (y(x=0) or y_max-y(x=0)
A priori
Assumed probability distribution before evidence
A postiori
Assumed probability distribution after evidence
Variance
Average square deviation of a distribution
Covariance
Joint variation of a pair of variables
Correlation
Ratio of covariance over the product of their standard deviation. +1 is related and -1 negatively related
Autocovariance
Covariance of the same set with lag
Autocorrelation/cross-correlation
Ratio of autocovariance also called lagged correlation or serial correlation
Regionalized variable
Variables which lie between truly random and completely deterministic
Support of regionalized variable
Characteristics such as size, shape, orientation and spatial arrangement
Semivariance
Expressing the rate of change of a regionalized variable along a specific orientation. Measuring a degree of spatial dependence between observations along a specific support. i.e. if the spacing is delta, the semivariance can be estimated for multiple times of delta
Semivariogram
Plotted result of semivariance, either experimental of theoretical
Residual
Regionalized variable - Drift
Drift
Expected value of the regionalized variable at a point
Spectral analysis
Harmonic analysis of a time function
Spectral estimator
Smoothed approximation of the periodogram
Detrending
removing the trend and the mean of a series
Filtering
weighted move average that extends over a small span of adjacent harmonics
Spectral window/filter
The set of weights
Aliasing
Estimating the wrong frequency by measuring slower than the true frequency
Nyquist frequency
Highest frequency that can be estimated by the periodogram 1/2dt
Continuous spectrum or spectral density
variance of time is appropriated among a set of frequency bands
Frequency bands
Spectral resolution, multiples of 1/T
Ensemble
Complete set of time frequencies
Homogeneous
Spatial time series with the same characteristics
First-order stationary
When all segments tend to have the same mean, as well as the mean of the entire timeseries
Second-order stationary/weak stationarity
If autocovariance changes only with lag and not with the position along the time serie
Strongly stationary
If only dependent on lag and not the position
Ergodic ensemble
If not pm;y strongly stationary but all statistics are invariant
Self-stationary
If all segments of the timeseries are the same in variance and mean
Leveling or detrending
Subtracting a linear trend of observations resulting in stationary mean
Bin averaging
Smoothed periodogram by applying a filter
Segment averaging
Averaged periodogram of overlapped windowed segments of a timeserie, more reliable but losing resolution
Fundamental frequency
minimal frequency 1/(N*dt)
Spectral leakage
Results in leakage of energy to neighbouring frequencies
Tapering
Preventing spectral leakage by isolating a part of the frequency i.e. Hanning or
Contouring
Drawing line between points where certain values are located in. i.e. everything below this line is 10 above 20
Contouring by computer
Done by mathematical calculations and extrapolation between points
Contouring by triangulation
Drawing lines between controlpoints forming a triangular grid without lines crossing, drawing lines on interpolated points
Contouring by gridding
placing a grid over your data points and calculating the grid nodes by interpolating between control points. Weights can be applied to data points to make more accurate estimations. This can be done with quadrant/octant searches or by nearest neightbour
(problems in contouring)Edge effects
on the edge of the grid control points might be far away, therefore a wrongly chosen angle or unrealistic gradients may be projected
(problems in contouring)Zero isopach
Using (0,0) to avoid negative values, but those could be realistic
(problems in contouring) faulted surfaces
Cliff etc can be ignored when interpolating
Kriging
Estimation of the surface at any unsampled location, linear regression technique by neighbours. Requires prior knowledge in form of a model of the semivariogram or spatial variance. It varies from regular linear regression by not assuming independent variates
Simple kriging
3 assumptions:
1: observations are partial realizationg of random function Z(x)
2: Random function is second-order stationary, so mean spatial covariance and semivariance do not depend on x
3: mean is known
Kriging estimator
weighted average of values at control point Z(x)
Ordinary kriging
1: observations are partial realizationg of random function Z(x)
2: Random function is second-order stationary, so mean spatial covariance and semivariance do not depend on x
3: mean is estimated to be constant
Univsersal kriging
First order nonstationary treated with drift and resuduals
1: observations are partial realizationg of random function Z(x)
2: Random function is second-order stationary, so mean spatial covariance and semivariance do not depend on x
Factor analysis (R-Mode)
extracting eigenvectors from all possible pairs of objects
Factor analysis(Q-Mode)
samples regarded as being taken from a much larger population
Single value decomposition
Taking the mean of a column of the matrix then subtracting it from that column.
[X] = [V] [S] [U’]
[U] = Spatial
[S] = Spectrum/ relates to variance
[V] = Temporal
Principal vector
Vector full of loadings
Loadings
Represent the proportion or weighting that must be assigned to each variable in order to project the objects onto the principal vectors as scores
Principal Component Analysis
eigenvectors of a variance-covariance matrix or a correlation matrix
Principal axes
yield of the eigenvectors of the variance-covariance matrix/correlation matrix, eigenvalues half of the lengths of successive principal axis
Semi axes
Eigenvalue are the legnths
Prinicple component score
Projection of data point on the new axis
Principle component loading
Characterizes the spread in values in the direction of PC1
Emprical Orthogonal Function analysis
Extract coherent patterns in large spatio-temporal data sets temporal data sets.
PCA on repeated measurements of a single type of variable at multiple location
Spatial EOF
Looking at the space part
Temporal EOF
Looking at the time part
same still different range
Geometric anisotrop
Same range different sill
Zonal anisotropy
