Sedimentological Control Parameters and Compaction ...
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Figure 6 shows the resulting map. This illustration clearly indicates that in most
cases the measured data are exactly equal to the respective areas in the isoline
map. This encouraging result justified establishing a combined data set, enclosing the modeled data as well as the porosity measurements.
7
Regional Modeling of Initial Porosity by Means ofTrend Surface Analysis
Systematic decrease of porosity from high values in the center to low values at
the margin of the basin (see Fig. 6) led to the hypothesis of a second-order trend
in the data. We ran trend-surface analysis to confirm this hypothesis.
7.1
Trend-Surface Analysis
In the case of this study, the trend surface takes the form of an elliptic paraboloid
given by
CPo { x,y) = -10301.4-2.7x + 375.5 y + 2.7xy-0.4x 2 _3.4y2,
(4)
where x and yare the geographical longitude and latitude. The ellipsoid, shown
in Fig. 7,is elongated in east-west direction, with the center situated in the middle
of the Arkona Basin. The axes run nearly parallel to the longitude and latitude.
7.2
Analysis of Residuals
According to the F-test, the trend surface is a significant descriptor of the data.
Nevertheless, the R2 of 0.5 indicates important differences between modeled and
measured data. Are these differences distributed randomly or do they show a
systematic behaviour? In order to answer this question, we analyzed the distribution of the residuals:
• low differences between model and measurement (gray),
• measurement is at least 6% lower than model (white),
• measurement is at least 6% higher than model (black).
The distribution of the residual is given in Fig. 7. Most of the locations, covering especially the center of the basin, show differences less than 6%. Higher
differences appear mainly at the margins. The residuals alternate between positive values in the deeper parts (SE, SW, NE) and negative values near-shore and
around submarine hills (S, W, E), precisely tracing the even center and the morphologically differentiated margin of the basin. They clearly show the expected
dependence of initial porosity from morphological features of the basin.
Thus, the surface modeling the variation in porosity forms a convex ellipsoidal surface with a slight continuous transition from higher to intermediate val-
383
Figure 6 shows the resulting map. This illustration clearly indicates that in most
cases the measured data are exactly equal to the respective areas in the isoline
map. This encouraging result justified establishing a combined data set, enclosing the modeled data as well as the porosity measurements.
7
Regional Modeling of Initial Porosity by Means ofTrend Surface Analysis
Systematic decrease of porosity from high values in the center to low values at
the margin of the basin (see Fig. 6) led to the hypothesis of a second-order trend
in the data. We ran trend-surface analysis to confirm this hypothesis.
7.1
Trend-Surface Analysis
In the case of this study, the trend surface takes the form of an elliptic paraboloid
given by
CPo { x,y) = -10301.4-2.7x + 375.5 y + 2.7xy-0.4x 2 _3.4y2,
(4)
where x and yare the geographical longitude and latitude. The ellipsoid, shown
in Fig. 7,is elongated in east-west direction, with the center situated in the middle
of the Arkona Basin. The axes run nearly parallel to the longitude and latitude.
7.2
Analysis of Residuals
According to the F-test, the trend surface is a significant descriptor of the data.
Nevertheless, the R2 of 0.5 indicates important differences between modeled and
measured data. Are these differences distributed randomly or do they show a
systematic behaviour? In order to answer this question, we analyzed the distribution of the residuals:
• low differences between model and measurement (gray),
• measurement is at least 6% lower than model (white),
• measurement is at least 6% higher than model (black).
The distribution of the residual is given in Fig. 7. Most of the locations, covering especially the center of the basin, show differences less than 6%. Higher
differences appear mainly at the margins. The residuals alternate between positive values in the deeper parts (SE, SW, NE) and negative values near-shore and
around submarine hills (S, W, E), precisely tracing the even center and the morphologically differentiated margin of the basin. They clearly show the expected
dependence of initial porosity from morphological features of the basin.
Thus, the surface modeling the variation in porosity forms a convex ellipsoidal surface with a slight continuous transition from higher to intermediate val-