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Data analysis in water > Termen > Flashcards

Termen Flashcards

1
Q

Range

A

Distance where the semivariance approaches variance, in other words the x-axis until the semivariogram becomes flat

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2
Q

Still

A

The region where semi-variance no longer increases and semi-variogram becomes flat

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3
Q

Nugget

A

Bottom part of the Still which doesnā€™t have influence on the semi-variogram (y(x=0) or y_max-y(x=0)

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4
Q

A priori

A

Assumed probability distribution before evidence

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5
Q

A postiori

A

Assumed probability distribution after evidence

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6
Q

Variance

A

Average square deviation of a distribution

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7
Q

Covariance

A

Joint variation of a pair of variables

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8
Q

Correlation

A

Ratio of covariance over the product of their standard deviation. +1 is related and -1 negatively related

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9
Q

Autocovariance

A

Covariance of the same set with lag

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10
Q

Autocorrelation/cross-correlation

A

Ratio of autocovariance also called lagged correlation or serial correlation

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11
Q

Regionalized variable

A

Variables which lie between truly random and completely deterministic

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12
Q

Support of regionalized variable

A

Characteristics such as size, shape, orientation and spatial arrangement

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13
Q

Semivariance

A

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

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14
Q

Semivariogram

A

Plotted result of semivariance, either experimental of theoretical

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15
Q

Residual

A

Regionalized variable - Drift

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16
Q

Drift

A

Expected value of the regionalized variable at a point

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17
Q

Spectral analysis

A

Harmonic analysis of a time function

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18
Q

Spectral estimator

A

Smoothed approximation of the periodogram

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19
Q

Detrending

A

removing the trend and the mean of a series

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20
Q

Filtering

A

weighted move average that extends over a small span of adjacent harmonics

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21
Q

Spectral window/filter

A

The set of weights

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22
Q

Aliasing

A

Estimating the wrong frequency by measuring slower than the true frequency

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23
Q

Nyquist frequency

A

Highest frequency that can be estimated by the periodogram 1/2dt

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24
Q

Continuous spectrum or spectral density

A

variance of time is appropriated among a set of frequency bands

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25
Q

Frequency bands

A

Spectral resolution, multiples of 1/T

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26
Q

Ensemble

A

Complete set of time frequencies

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27
Q

Homogeneous

A

Spatial time series with the same characteristics

28
Q

First-order stationary

A

When all segments tend to have the same mean, as well as the mean of the entire timeseries

29
Q

Second-order stationary/weak stationarity

A

If autocovariance changes only with lag and not with the position along the time serie

30
Q

Strongly stationary

A

If only dependent on lag and not the position

31
Q

Ergodic ensemble

A

If not pm;y strongly stationary but all statistics are invariant

32
Q

Self-stationary

A

If all segments of the timeseries are the same in variance and mean

33
Q

Leveling or detrending

A

Subtracting a linear trend of observations resulting in stationary mean

34
Q

Bin averaging

A

Smoothed periodogram by applying a filter

35
Q

Segment averaging

A

Averaged periodogram of overlapped windowed segments of a timeserie, more reliable but losing resolution

36
Q

Fundamental frequency

A

minimal frequency 1/(N*dt)

37
Q

Spectral leakage

A

Results in leakage of energy to neighbouring frequencies

38
Q

Tapering

A

Preventing spectral leakage by isolating a part of the frequency i.e. Hanning or

39
Q

Contouring

A

Drawing line between points where certain values are located in. i.e. everything below this line is 10 above 20

40
Q

Contouring by computer

A

Done by mathematical calculations and extrapolation between points

41
Q

Contouring by triangulation

A

Drawing lines between controlpoints forming a triangular grid without lines crossing, drawing lines on interpolated points

42
Q

Contouring by gridding

A

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

43
Q

(problems in contouring)Edge effects

A

on the edge of the grid control points might be far away, therefore a wrongly chosen angle or unrealistic gradients may be projected

44
Q

(problems in contouring)Zero isopach

A

Using (0,0) to avoid negative values, but those could be realistic

45
Q

(problems in contouring) faulted surfaces

A

Cliff etc can be ignored when interpolating

46
Q

Kriging

A

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

47
Q

Simple kriging

A

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

48
Q

Kriging estimator

A

weighted average of values at control point Z(x)

49
Q

Ordinary kriging

A

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

50
Q

Univsersal kriging

A

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

51
Q

Factor analysis (R-Mode)

A

extracting eigenvectors from all possible pairs of objects

52
Q

Factor analysis(Q-Mode)

A

samples regarded as being taken from a much larger population

53
Q

Single value decomposition

A

Taking the mean of a column of the matrix then subtracting it from that column.
[X] = [V] [S] [Uā€™]
[U] = Spatial
[S] = Spectrum/ relates to variance
[V] = Temporal

54
Q

Principal vector

A

Vector full of loadings

55
Q

Loadings

A

Represent the proportion or weighting that must be assigned to each variable in order to project the objects onto the principal vectors as scores

56
Q

Principal Component Analysis

A

eigenvectors of a variance-covariance matrix or a correlation matrix

57
Q

Principal axes

A

yield of the eigenvectors of the variance-covariance matrix/correlation matrix, eigenvalues half of the lengths of successive principal axis

58
Q

Semi axes

A

Eigenvalue are the legnths

59
Q

Prinicple component score

A

Projection of data point on the new axis

60
Q

Principle component loading

A

Characterizes the spread in values in the direction of PC1

61
Q

Emprical Orthogonal Function analysis

A

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

62
Q

Spatial EOF

A

Looking at the space part

63
Q

Temporal EOF

A

Looking at the time part

64
Q

same still different range

A

Geometric anisotrop

65
Q

Same range different sill

A

Zonal anisotropy

Data analysis in water (2 decks)

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