Geoelectrical parameter-based multivariate regression borehole yield model for predicting aquifer yield in managing groundwater resource sustainability

Peer review under responsibility of Taibah University.

Figures & data

Fig. 1 The study area map both the VES location, the geologic rock types map with inset map of Nigeria.

Fig. 2 The flowchart of the adopted methodology for the study.

Fig. 3 The borehole distribution inventory map of the area.

Table 1 Borehole yield rating inventory records of the area.

BH location	Easting	Northing	Borehole yield records (l/s)
1	812,450	733,340	1.20
2	796,868	744,129	1.12
3	800,301	741,145	1.14
4	814,326	740,086	0.20
5	807,079	747,427	1.20
6	793,129	739,270	0.20
7	806,085	737,591	0.90
8	803,218	739,455	0.80
9	819,920	726,332	0.80
10	806,377	737,676	1.20
11	793,126	739,258	1.10
12	795,941	785,935	1.24
13	809,576	807,360	1.10
14	827,590	802,671	0.59
15	826,342	802,678	0.70
16	801,783	743,350	1.14
17	801,798	743,271	0.80
18	803,232	761,824	1.21
19	799,246	758,367	0.80
20	850,119	820,582	1.23
21	819,602	822,630	1.23
22	802,716	741,710	5.90
23	738,805	664,528	2.64
24	748,867	678,543	1.39
25	748,148	683,394	1.80
26	749,226	686,809	1.24
27	754,617	683,934	1.39
28	744,555	709,448	3.89
29	767,913	718,432	1.08
30	774,022	716,635	3.89
31	774,740	720,588	2.28
32	780,850	717,713	2.90
33	785,521	716,276	1.29
34	790,912	720,589	1.40
35	788,755	710,885	2.40
36	790,912	713,042	0.80
37	796,302	711,604	1.26
38	773,662	741,790	11.8
39	773,303	746,102	1.80
40	775,819	747,180	3.00
41	790,436	746,927	5.10
42	791,573	751,746	7.60
43	794,188	749,472	3.30
44	791,118	747,312	1.07
45	793,392	743,446	1.80
46	794,643	741,512	1.72
47	796,917	745,834	1.47
48	797,030	741,058	1.72
49	796,979	745,692	1.53
50	801,620	743,066	0.70
51	801,728	743,318	1.23
52	802,628	741,735	0.90
53	803,203	739,504	2.70
54	804,067	736,482	0.20
55	807,017	747,455	2.10
56	807,269	744,433	7.10
57	810,111	740,547	1.26
58	812,240	730,798	1.20
59	812,456	733,352	0.80
60	812,996	734,719	1.14
61	814,327	739,972	1.10
62	816,054	735,619	1.00
63	816,522	740,332	6.40
64	779,817	777,386	6.50
65	786,336	782,389	3.50
66	794,386	785,755	1.10
67	795,921	785,840	19.4
68	795,566	774,839	6.60
69	800,185	776,886	1.44
70	804,960	783,111	2.70
71	840,095	801,862	1.25
72	833,727	800,195	2.36
73	827,815	803,985	7.60
74	823,721	810,807	1.67
75	767,652	803,568	2.30
76	771,486	803,568	3.50
77	828,421	817,174	0.83

Fig. 4 Typical resistivity model curves obtained in the area.

Fig. 5 Borehole yield conditioning factors used in developing the multi-variate regression yield model where (a) aquifer resistivity map, (b) aquifer thickness map and (c) coefficient of anisotropy map.

Table 2 Summary of the interpreted geoelectric parameters.

VES NO	Northing	Easting	Ar	At	λ	CT
1	815,896.8	807,147.3	200	4.30	0.09	H
2	815,872.5	807,196.6	561	12.6	0.29	HA
3	801,509.2	746,343.9	296	4.10	0.06	H
4	801,527.6	746,334.6	179	3.90	0.04	H
5	797,873.3	740,475.3	136	6.00	0.04	H
6	823,907.7	800,671.3	147	8.80	0.03	H
7	823,895.6	800,702	239	14.9	0.07	H
8	823,892.6	800,711.2	111	5.40	0.02	H
9	803,404.7	743,741.5	245	2.40	0.02	H
10	803,401.6	743,741.5	958	7.10	0.74	KH
11	803,312.6	743,769.6	347	2.00	0.02	HA
12	803,525.7	739,530.7	63	13.70	0.04	H
13	803,516.5	739,543.1	150	13.90	0.04	HA
14	802,386.9	743,611.4	947	32.40	1.57	H
15	803,176.6	743,607.6	121	3.80	0.02	HA
16	803,136.5	743,571	128	5.60	0.02	H
17	803,146.4	743,712.1	311	8.30	0.09	H
18	803,167.3	743,589.2	157	5.00	0.03	H
19	803,177	743,687.4	326	7.60	0.03	HK
20	803,177	743,684.3	148	3.00	0.03	H
21	816,233.7	801,973.6	312	5.00	0.01	HA
22	816,187.6	801,983.1	194	4.20	0.03	H
23	800,485.3	777,998.8	373	3.70	0.08	H
24	800,516.4	778,063.1	299	11.10	0.05	H
25	800,444	742,147.8	362	23.60	0.12	H
26	796,914.4	743,634.9	51	4.80	0.02	H
27	807,934.3	743,808.3	584	14.10	0.15	HKHK
28	798,722.3	743,859.4	23	12.20	0.05	QH
29	819,450	727,582.5	31	0.90	0.02	H
30	796,715.4	784,288.2	13	1.70	0.02	H
31	796,718.5	784,294.4	80	7.90	0.03	QH
32	796,854.3	786,565.4	50	12.00	0.04	KH
33	793,601.7	746,753.9	72	12.00	0.07	KH
34	793,493.6	746,644	63	7.00	0.14	H
35	799,085.2	743,289.9	65	9.30	0.02	QH
36	799,050.8	743,167.3	105	15.60	0.05	H
37	797,093.6	741,927.6	832	11.10	4.20	A
38	799,003	740,239.8	160	5.00	0.09	KH
39	799,000	740,255.1	22	4.70	0.05	KH
40	798,214	742,944.2	89	14.20	0.04	HKH
?.	–	–	–	–	–	–
?	–	–	–	–	–	–
450			79	10.40	0.04	H

A_r = aquifer layer resistivity, A_t = aquifer layer thickness, λ = coefficient of anisotropy and C_T = curve types.

Fig. 6 Linear relationship between the borehole yield rate records and the geoelectrical derived parameters where graphs (a)–(c) are resistivity, thickness and coefficient of anisotropy parameters models, respectively.

Table 3 Results of the geoelectric parameters and the corresponding actual borehole yield values.

BH Location	Easting	Northing	Geoelectrical parameters			Borehole pumping test analysis
			Aquifer resistivity (Ωm) [ρ]	Aquifer thickness (m)[T]	Coefficient of anisotrophy (λ)	The actual borehole yield results (l/s)
1	812,450	733,340	105	10.49	0.25	1.20
2	796,868	744,129	130	8.80	0.10	1.12
3	800,301	741,145	115	12.42	0.11	1.14
4	814,326	740,086	115	4.58	0.01	0.20
5	807,079	747,427	145	6.85	0.08	1.20
6	793,129	739,270	120	4.58	0.01	0.20
7	806,085	737,591	128	5.00	0.12	0.90
8	803,218	739,455	140	4.75	0.06	0.80
9	819,920	726,332	125	4.75	0.04	0.80
10	806,377	737,676	105	12.25	0.13	1.20
11	793,126	739,258	85	9.50	0.37	1.10
12	795,941	785,935	140	13.54	0.22	1.24
13	809,576	807,360	115	10.42	0.10	1.10
14	827,590	802,671	100	4.65	0.14	0.59
15	826,342	802,678	110	9.88	0.08	0.70
16	801,783	743,350	75	6.21	0.51	1.14
17	801,798	743,271	125	8.60	0.06	0.80
18	803,232	761,824	128	7.06	0.20	1.21
19	799,246	758,367	122	7.96	0.07	0.80
20	850,119	820,582	135	7.89	0.13	1.23
21	819,602	822,630	136	9.70	0.11	1.23
22	802,716	741,710	225	13.90	0.78	5.90
23	738,805	664,528	135	12.65	0.44	2.64
24	748,867	678,543	65	10.00	0.84	1.39
25	748,148	683,394	125	12.65	0.31	1.80
26	749,226	686,809	65	12.07	0.49	1.24
27	754,617	683,934	95	9.80	0.38	1.39
28	744,555	709,448	170	13.54	0.59	3.89
29	767,913	718,432	105	9.82	0.22	1.08
30	774,022	716,635	168	13.54	0.60	3.89
31	774,740	720,588	125	12.42	0.42	2.28
32	780,850	717,713	156	12.73	0.39	2.90
33	785,521	716,276	132	12.22	0.11	1.29
34	790,912	720,589	75	12.25	0.42	1.40
35	788,755	710,885	148	12.32	0.42	2.40
36	790,912	713,042	122	8.75	0.06	0.80
37	796,302	711,604	106	12.00	0.32	1.26
38	773,662	741,790	380	17.50	1.43	11.8
39	773,303	746,102	118	11.88	0.30	1.80
40	775,819	747,180	148	13.13	0.45	3.00
41	790,436	746,927	240	13.56	0.65	5.10
42	791,573	751,746	320	15.44	1.23	7.60
43	794,188	749,472	152	13.22	0.49	3.30
44	791,118	747,312	131	7.28	0.13	1.07
45	793,392	743,446	115	11.70	0.31	1.80
46	794,643	741,512	120	11.70	0.28	1.72
47	796,917	745,834	112	11.60	0.25	1.47
48	797,030	741,058	121	10.90	0.28	1.72
49	796,979	745,692	110	11.84	0.27	1.53
50	801,620	743,066	109	8.00	0.10	0.70
51	801,728	743,318	116	10.20	0.18	1.23
52	802,628	741,735	105	5.77	0.18	0.90
53	803,203	739,504	135	13.90	0.46	2.70
54	804,067	736,482	100	4.58	0.08	0.20
55	807,017	747,455	127	12.07	0.37	2.10
56	807,269	744,433	342	15.44	1.20	7.10
57	810,111	740,547	230	10.20	0.11	1.26
58	812,240	730,798	165	11.00	0.18	1.20
59	812,456	733,352	185	8.50	0.24	0.80
60	812,996	734,719	259	10.99	0.14	1.14
61	814,327	739,972	127	10.39	0.14	1.10
62	816,054	735,619	247	9.90	0.12	1.00
63	816,522	740,332	340	13.94	0.84	6.40
64	779,817	777,386	380	15.21	1.18	6.50
65	786,336	782,389	161	13.56	0.51	3.50
66	794,386	785,755	143	9.00	0.01	1.10
67	795,921	785,840	456	20.47	1.70	19.40
68	795,566	774,839	390	15.22	1.90	6.60
69	800,185	776,886	198	11.50	0.24	1.44
70	804,960	783,111	225	13.90	0.5	2.70
71	840,095	801,862	106	13.22	0.16	1.25
72	833,727	800,195	207	10.48	0.43	2.36
73	827,815	803,985	320	15.48	1.22	7.60
74	823,721	810,807	134	9.80	0.26	1.67
75	767,652	803,568	245	12.21	0.40	2.30
76	771,486	803,568	270	13.56	0.52	3.50
77	828,421	817,174	125	7.04	0.04	0.83

Table 4 Parameters estimations analysis of the developed multiple variate regression (MVR) yield model developed in the area.

Developed yield model	Parameters	Standard error and parameters significance testing using standard value of α at 5% significance level		Remark: parameters significance OK at Pr-value <5%
		t-Value	Pr (>〉|t|)-value
Y = 0.02(ρ) + 0.15(D) + 3.52(λ) − 2.6	ρ	4.49	2.68 × 10^−05	OK
	D	2.38	0.02	OK
	λ	5.15	2.09 × 10^−06	OK

(ρ): aquifer layer resistivity (Ωm); (D): aquifer layer thickness (m) and λ: coefficient of anisotropy.

Fig. 7 Linear relation between the actual borehole yield rate and the estimated borehole yield rate based on the MVR prediction yield model.

Table 5 The records of the actual borehole yield determined and the predicted borehole yield in the area.

BH location nos	Actual borehole yield determined in the area (yi)	Estimated borehole yield rate from the MVR prediction yield model $(\hat{y})$
1	1.20	1.23
2	1.12	1.06
3	1.14	1.08
4	0.20	0.10
5	1.20	1.13
6	0.20	0.20
7	0.90	0.78
8	0.80	0.79
9	0.80	0.80
10	1.20	0.94
11	1.10	1.16
12	1.24	1.25
13	1.10	0.89
14	0.59	0.26
15	0.70	0.67
16	1.14	1.19
17	0.80	0.80
18	1.21	1.21
19	0.80	0.72
20	1.23	1.19
21	1.23	1.23
22	5.90	5.76
23	2.64	2.64
24	1.39	1.40
25	1.80	2.00
26	1.24	1.25
27	1.39	1.42
28	3.89	3.90
29	1.08	1.06
30	3.89	3.96
31	2.28	2.37
32	2.90	2.91
33	1.29	1.30
34	1.40	1.36
35	2.40	2.82
36	0.80	0.75
37	1.26	1.61
38	11.8	11.43
39	1.80	1.77
40	3.00	2.99
41	5.10	5.10
42	7.60	7.40
43	3.30	3.22
44	1.07	1.06
45	1.80	1.73
46	1.72	1.65
47	1.47	1.45
48	1.72	1.68
49	1.53	1.50
50	0.70	0.57
51	1.23	1.17
52	0.90	0.60
53	2.70	2.83
54	0.20	0.05
55	2.10	2.21
56	7.10	9.70
57	1.26	3.20
58	1.20	2.21
59	0.80	2.62
60	1.14	3.95
61	1.10	1.26
62	1.00	3.55
63	6.40	8.27
64	6.50	10.37
65	3.50	3.50
66	1.10	1.02
67	19.40	19.40
68	6.60	13.11
69	1.44	3.12
70	2.70	4.77
71	1.25	1.14
72	2.36	3.89
73	7.60	9.33
74	1.67	1.78
75	2.30	4.68
76	3.50	5.72
77	0.83	0.60

Table 6 MVR yield model prediction accuracy analysis.

S/N	Proposed MVR yield model	Nos of borehole locations	${\chi }_p^2,\alpha =5\%$	K-value
1	Y = 0.02(ρ) + 0.15(D) + 3.52(λ) − 2.6	77	57.79	0.15

(ρ): aquifer layer resistivity (Ωm); (D): aquifer layer thickness (m) and λ: coefficient of anisotropy.

Fig. 8 The borehole yield rate prediction model map based on the MVR borehole yield model developed.

Table 7 The GIS based cross-tabulation analysis results for the model map validation.

Borehole yield zones predicted	Drains/rivers density		Lineament intersection density
	Range	Mean (km^−1)	Range	Mean
Low	0–0.1595	0.0503	0–0.0298	0.0040
Low medium	0–0.1329	0.0481	0–0119	0.0053
Medium	0–0.1064	0.0287	0–0.0179	0.0055
Medium high	0	0	0	0
High	0–0.774	0.0387	0.006–0.0119	0.0090