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Evaluation of Procedures for Prediction of Unconventional Gas in the Presence of Geologic Trends

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Abstract

This study extends the application of local spatial nonparametric prediction models to the estimation of recoverable gas volumes in continuous-type gas plays to regimes where there is a single geologic trend. A transformation is presented, originally proposed by Tomczak, that offsets the distortions caused by the trend. This article reports on numerical experiments that compare predictive and classification performance of the local nonparametric prediction models based on the transformation with models based on Euclidean distance. The transformation offers improvement in average root mean square error when the trend is not severely misspecified. Because of the local nature of the models, even those based on Euclidean distance in the presence of trends are reasonably robust. The tests based on other model performance metrics such as prediction error associated with the high-grade tracts and the ability of the models to identify sites with the largest gas volumes also demonstrate the robustness of both local modeling approaches.

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Notes

  1. Wilcoxon–Mann–Whitney tests are most often used to determine whether the location parameters (i.e., the medians) of two distributions are equal (Hollander and Wolf, 1999).

References

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Correspondence to Emil D. Attanasi.

Appendix A

Appendix A

See Figures 712.

Figure 7
figure 7

Prediction performance: Distribution of root mean prediction errors over 101 samples based on (A) training samples size of 400 observations, 1200 prediction points and (B) training samples size of 640 observations, 960 prediction points; for 5 different states of nature where model set “a” used anisotropy transformation and “b” did not transform data. States of nature (anisotropy angle, anisotropy ratio): SN1 (45°, 2.67), SN2 (45°, 2.5), SN3 (11.3°, 2.5), SN4 (28.8°, 2.67), and SN5 (78.7°, 2.5)

Figure 8
figure 8

Prediction performance: Distribution of bias values over 101 samples based on (A) training samples size of 400 observations, 1200 prediction points and (B) training samples size of 640 observations, 960 prediction points; for 5 different states of nature where model set “a” used anisotropy transformation and “b” did not transform data. States of nature (anisotropy angle, anisotropy ratio): SN1 (45°, 2.67), SN2 (45°, 2.5), SN3 (11.3°, 2.5), SN4 (28.8°, 2.67), and SN5 (78.7°, 2.5)

Figure 9
figure 9

Box plots of the distributions of error sums of 100 sites (101 iterations) predicted to have largest volumes for various misspecifications of the transformed distance model given the true state of nature (SN1 where a = 45° and r = 2.67) and the median value of the error sums distribution at the high-volume sites predicted by the Euclidean model. (A) Training sample size is 160. (B) Training sample size is 400. The red marker indicates transform distance model median and blue marker indicates the Euclidean distance model marker

Figure 10
figure 10

Box plots of the distributions of error sums of 100 sites (101 iterations) predicted to have largest volumes for various misspecifications of the transformed distance model given the true state of nature (SN4 where a = 28.8° and r = 2.67) and the median value of the error sums distribution at the high-volume sites predicted by the Euclidean model. (A) Training sample size is 160. (B) Training sample size is 400. The red marker indicates transform distance model median and blue marker indicates the Euclidean distance model marker

Figure 11
figure 11

Box plots of the distribution of gas in 100 sites (101 iterations) predicted to have largest volumes for various misspecifications of the transformed distance model given the true state of nature (SN1 where a = 45° and r = 2.67) and the median value of the distribution of gas at the high-volume sites predicted by the Euclidean model. (A) Training sample size is 160. (B) Training sample size is 400. The red marker indicates the transform distance model median and the blue marker indicates the Euclidean distance model marker

Figure 12
figure 12

Box plots of the distribution of gas in 100 sites (101 iterations) predicted to have largest volumes for various misspecifications of the transformed distance model given the true state of nature (SN4 where a = 28.8° and r = 2.5) and the median value of the distribution of gas at the high-volume sites predicted by the Euclidean model. (A) Training sample size is 160. (B) Training sample size is 400. The red marker indicates the transform distance model median and the blue marker indicates the Euclidean distance model marker

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Attanasi, E.D., Coburn, T.C. Evaluation of Procedures for Prediction of Unconventional Gas in the Presence of Geologic Trends. Nat Resour Res 18, 153–171 (2009). https://doi.org/10.1007/s11053-009-9100-6

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