3
The variogram measures the spatial dependence of a
variable. It shows how the values of a variable change with
distance, and at what distance the variable becomes spa-
tially independent.
The variogram is a key tool used in geostatistics to
study how a variable changes in space. It is used to measure
the spatial variability and continuity of the variable of the
study. (Cantú-González et al., 2024)
The variograms are also called semi- variograms, the
formula used for the calculation is as follows:
Z x Z hh@2 2N^hh
1
i i i
N c =-+^hh ^^x ^hh h 6 /(1)
Inverse Distance (ID) or Inverse Distance Weighting
(IDW)
IDW is a popular method for estimating the value of a
variable at a point based on the values of that variable at
nearby points. IDW assumes that the values of the variable
are more similar at closer points than at further points. The
weight given to each nearby point is inversely proportional
to the distance from the point to be estimated. This means
that points closer to the point to be estimated are given
more weight. IDW calculates the estimated value by tak-
ing a weighted average of the values at the nearby points.
(Boumpoulis et al., 2023)
The formula used for the calculation is as follows:
Z x
d
d
x
1
ij
r i
ij
r i
n
0
1
1
1
=
=
=
^h /n
/
(2)
Grade- Tonnage Curve
Grade tonnage curves act as a visual tool for assessing the
exploitation potential of a deposit under various cut-off
grade scenarios. The curve illustrates the average grade and
quantity of ore above a specified cut-off.
Grade tonnage curves show how the amount of min-
eralized material in a deposit change as the cut-off grade is
changed. If the deposit contains multiple metals of economic
value, then the grade tonnage curve should be calculated
Table 1. Coding, name, and specific weight of mineralized
structures
Id Code Name
Specific
Weight
1 01_AÑA No participation —
2 02_BRI Brigith 2.67
3 03_CHA Charapita 2.49
4 04_CHO Cholita 2.55
5 05_COL Colonial 2.55
6 06_ESC Escondida 2.55
7 07_ESP B Española B 2.58
8 08_ESP BN Española B Norte 2.57
9 09_ESP C Española C 2.61
10 10_ESP C1 Española C1 2.57
11 11_ESP S1 Española Sur 1 2.57
12 12_ESP S2 Española Sur 2 2.57
13 13_ESP S3 Española Sur 3 2.57
14 14_ESP S4 No participation —
15 15_ESP S5 No participation —
16 16_ESP_A Española A 2.6
17 17_GLA Gladys 2.55
18 18_MEZT Mestiza 2.55
19 19_ORS Órsola 2.55
20 20_SORP Sorpresa 2.55
21 21_PER Peruanita 2.55
22 Veta 22 — 2.55
23 Veta 23 — 2.55
24 Veta 24 — 2.55
25 Veta 25 — 2.55
26 Veta 26 — 2.55
27 Veta 27 — 2.55
28 Veta 28 — 2.55
29 Veta 29 — 2.55
30 Veta 30 — 2.55
31 Veta 31 — 2.55
32 Veta 32 — 2.55
33 Veta 33 — 2.55
Table 2. Coding, name and specific weight of the most
profitable family of polymetallic veins
Id Code Name
Specific
Weight
A Fam. Española Veta Española 2.57
B General Average General Average of Vein 2.55
Figure 4. Example of Graphical of grade- tonnage curve
The variogram measures the spatial dependence of a
variable. It shows how the values of a variable change with
distance, and at what distance the variable becomes spa-
tially independent.
The variogram is a key tool used in geostatistics to
study how a variable changes in space. It is used to measure
the spatial variability and continuity of the variable of the
study. (Cantú-González et al., 2024)
The variograms are also called semi- variograms, the
formula used for the calculation is as follows:
Z x Z hh@2 2N^hh
1
i i i
N c =-+^hh ^^x ^hh h 6 /(1)
Inverse Distance (ID) or Inverse Distance Weighting
(IDW)
IDW is a popular method for estimating the value of a
variable at a point based on the values of that variable at
nearby points. IDW assumes that the values of the variable
are more similar at closer points than at further points. The
weight given to each nearby point is inversely proportional
to the distance from the point to be estimated. This means
that points closer to the point to be estimated are given
more weight. IDW calculates the estimated value by tak-
ing a weighted average of the values at the nearby points.
(Boumpoulis et al., 2023)
The formula used for the calculation is as follows:
Z x
d
d
x
1
ij
r i
ij
r i
n
0
1
1
1
=
=
=
^h /n
/
(2)
Grade- Tonnage Curve
Grade tonnage curves act as a visual tool for assessing the
exploitation potential of a deposit under various cut-off
grade scenarios. The curve illustrates the average grade and
quantity of ore above a specified cut-off.
Grade tonnage curves show how the amount of min-
eralized material in a deposit change as the cut-off grade is
changed. If the deposit contains multiple metals of economic
value, then the grade tonnage curve should be calculated
Table 1. Coding, name, and specific weight of mineralized
structures
Id Code Name
Specific
Weight
1 01_AÑA No participation —
2 02_BRI Brigith 2.67
3 03_CHA Charapita 2.49
4 04_CHO Cholita 2.55
5 05_COL Colonial 2.55
6 06_ESC Escondida 2.55
7 07_ESP B Española B 2.58
8 08_ESP BN Española B Norte 2.57
9 09_ESP C Española C 2.61
10 10_ESP C1 Española C1 2.57
11 11_ESP S1 Española Sur 1 2.57
12 12_ESP S2 Española Sur 2 2.57
13 13_ESP S3 Española Sur 3 2.57
14 14_ESP S4 No participation —
15 15_ESP S5 No participation —
16 16_ESP_A Española A 2.6
17 17_GLA Gladys 2.55
18 18_MEZT Mestiza 2.55
19 19_ORS Órsola 2.55
20 20_SORP Sorpresa 2.55
21 21_PER Peruanita 2.55
22 Veta 22 — 2.55
23 Veta 23 — 2.55
24 Veta 24 — 2.55
25 Veta 25 — 2.55
26 Veta 26 — 2.55
27 Veta 27 — 2.55
28 Veta 28 — 2.55
29 Veta 29 — 2.55
30 Veta 30 — 2.55
31 Veta 31 — 2.55
32 Veta 32 — 2.55
33 Veta 33 — 2.55
Table 2. Coding, name and specific weight of the most
profitable family of polymetallic veins
Id Code Name
Specific
Weight
A Fam. Española Veta Española 2.57
B General Average General Average of Vein 2.55
Figure 4. Example of Graphical of grade- tonnage curve