O błędzie usytuowania izolinii oraz wyinterpolowanej wartości Δg .
Abstract
ON ERRORS IN DRAWING ISOLINE AND INTERPRETED VALUE ΔG
Summary
Interpolation based on points with error-laden values results in delineation of an interpreted isoline in so-called "error zone". The magnitude of error in delineation of the isoline depends on:
1) errors connected with points used as the basis for interpolation;
2) distance between the above points; and
3) increase of gravity between the points.
The magnitude of error in delineation of isoline (Δg), mathematically treated, is as follows:
PK = 2mD/ ΔgAB
Error in value of anomaly Δg interpolated on the basis of points with error-laden values depends on:
1) errors of points used as the basis for interpolation;
2) location of the interpolated point in relation to those used as the basis for interpolation;
3) increase of gravity between points used as the basis for interpolation,
4) distance between the above points.
The magnitude of error of the interpolated point may be mathematically expressed by the equation [3]. The criterion of the maximum number of isolines which may be drawn between points A and B may be expressed by the following equation:
imax = [(ΔgAB)/2m] -1
In the above equations, A and B represent points used as the basis for interpolation, W - interpolated point, PK - magnitude of error in delineation of isoline, D - distance between points A and B, d - distance between points W and B, ΔgA - value of anomaly at the point A, ΔgB - as above, at the point B, Δgw - as above, at the point W, ΔgAB - increase of anomaly between points A and B, ΔgwB - as above, between points W and B, i - number of isolines, m - error of anomaly at points A and B, mΔgw - error of anomaly at interpolated point W, mΔgAB error in increase of anomaly between points A and B, mD - error in distance D, md - error in distance d.
Summary
Interpolation based on points with error-laden values results in delineation of an interpreted isoline in so-called "error zone". The magnitude of error in delineation of the isoline depends on:
1) errors connected with points used as the basis for interpolation;
2) distance between the above points; and
3) increase of gravity between the points.
The magnitude of error in delineation of isoline (Δg), mathematically treated, is as follows:
PK = 2mD/ ΔgAB
Error in value of anomaly Δg interpolated on the basis of points with error-laden values depends on:
1) errors of points used as the basis for interpolation;
2) location of the interpolated point in relation to those used as the basis for interpolation;
3) increase of gravity between points used as the basis for interpolation,
4) distance between the above points.
The magnitude of error of the interpolated point may be mathematically expressed by the equation [3]. The criterion of the maximum number of isolines which may be drawn between points A and B may be expressed by the following equation:
imax = [(ΔgAB)/2m] -1
In the above equations, A and B represent points used as the basis for interpolation, W - interpolated point, PK - magnitude of error in delineation of isoline, D - distance between points A and B, d - distance between points W and B, ΔgA - value of anomaly at the point A, ΔgB - as above, at the point B, Δgw - as above, at the point W, ΔgAB - increase of anomaly between points A and B, ΔgwB - as above, between points W and B, i - number of isolines, m - error of anomaly at points A and B, mΔgw - error of anomaly at interpolated point W, mΔgAB error in increase of anomaly between points A and B, mD - error in distance D, md - error in distance d.