smumod

Process Help

SMUMOD - shortcut method for grade and tonnes above cut-off

Process Name	Menu Path	Link to Command Table
SMUMOD	Estimate ribbon \| SMU Analysis \| 'Shortcut' Reserves	Click here

Introduction
Files, Fields and Parameters
Notes
Example
Errors

Introduction

'Shortcut' method for grade and tonnes above cut-off.

How to use

The process uses the 'Shortcut' method to estimate the recovered tonnage and recovered grade above a single user specified cut-off. The input file must be a standard model file containing a kriged grade estimate and a kriged variance. The ouput model file contains all the fields from the input file plus two additional fields:

the proportion of the block above the cut-off;

the grade of the proportion above cut-off.

A Selective Mining Unit (SMU) is the smallest block size that can be mined selectively. The dimensions of an SMU can be defined using parameters SMUXINC , SMUYINC and SMUZINC. The recovered values in the output model file are a function of the specified size of SMU.

The process takes account of the distribution of SMUs within each model cell or subcell. This distribution may be either normal (1) or lognormal (2); it is specified by parameter SMUDIST. If a normal variogram model is fitted (i.e. LOG =0) but the distribution of the SMUs is lognormal (i.e. SMUDIST=2) then the mean of the data values (ie DATAMEAN) must be specified.

Care should be taken when using a normal distribution for SMUs (ie SMUDIST=1). Under certain conditions the method can give an overestimation of grade when the block grade is low. This is due to the fact that the theoretical normal distribution can have values below zero, which is not possible in practice. This can lead to the situation where the metal above a cut-off is estimated to be greater than the total metal for the whole block. In such a case a warning message is displayed.

INFOEFF is the information effect variance. It is a constant representing the final production data variance correction and is added to the kriging variance. For further information refer to Journel and Huibrechts.

A similar situation of overestimation can also arise using a lognormal distribution for SMUs when the grade is low compared to the additive constant (ADDCON). In such a case a reduction in the additive constant should be considered.

The dispersion variance of an SMU within a model cell or subcell can be defined using one of three methods as controlled by parameter DVMETHOD.

The user defines a single dispersion variance using parameter DISVAR. This variance will then be used as the variance of an SMU within every cell and subcell in the model. This option is therefore most appropriate if all cells in the model are the same size. If this is used there is no need to specify the dimensions of the SMU.
The user defines the variogram model and the dimensions of the SMU by parameter. A single dispersion variance is then calculated for the SMU within a parent cell, and this value is used for all cells and subcells. This is similar to 1 above, except that the dispersion variance is calculated by the process rather than being supplied by the user through parameter DISVAR.
The user defines the variogram model and the dimensions of the SMU by parameter. An individual dispersion variance is then calculated for the SMU within each cell and subcell. This is therefore more appropriate than options 1 or 2 if the model contains different cell sizes.

The calculation of the dispersion variance is one of the more time consuming parts of the process if DVMETHOD=3. This can be speeded up by making certain approximations as described below. This option is controlled by parameter VARTYPE.

The exact dimensions of the subcell are used, and so the dispersion variance is calculated for every subcell in the model.
Each subcell is approximated to one of a discrete number of subcells. As each subcell is processed reference is made to a look up table to see whether the dispersion variance for that size subcell has already been calculated. If it exists then the value is used; if not then it is calculated and stored in the table. This gives a large speed improvement

Whichever option is used the dispersion variance of an SMU in a parent cell is calculated once and stored. Therefore the increase in speed under option 2 will be most apparent when the model includes a large number of subcells.

If DVMETHOD=3 and VARTYPE=2 then each subcell is approximated by one of a discrete number of sizes. This is controlled by parameters XSTEP , YSTEP and ZSTEP. Dispersion variances are stored for subcells whose dimensions are an integer multiple of the step sizes. The maximum possible number of increments in each dimension is 20, making a total of 8000 (20**3) discrete sizes.

The user should ensure that the step size in each dimension is greater than or equal to one twentieth of the dimension of the parent cell for the model.
i.e. XSTEP >= XINC / 20

If this is not the case then the step value will be reset as one twentieth of the parent cell dimension.

Files, Fields and Parameters

Input Files

Name	Description	I/O Status	Required	Type
IN	Input model file containing the kriged grade estimate and the kriging variance.	Input	Yes	Block Model
VMODPARM	Variogram model parameter file. A variogram model is only required if DVMETHOD = 2 or 3.	Input	No	Variogram - Model

Output Files

Name	I/O Status	Required	Type	Description
OUT	Output	Yes	Block Model	Output model file.

Fields

Name	Description	Source	Required	Type	Default
VALUE	A field in the model file which contains the kriged grade estimate.	IN	Yes	Numeric	Undefined
VARIANCE	A field in the model file which contains the kriging variance (eg as created by ESTIMA).	IN	Yes	Numeric	Undefined
FRREC	The field to be created in the output model to store the recovered fraction.	OUT	Yes	Numeric	Undefined
VALREC	The field to be created in the output model to store the grade of the recovered fraction.	OUT	Yes	Numeric	Undefined

Parameters

Name

Description

Required

Default

Range

Values

CUTOFF

Cut-off grade for calculation of recovered fraction and grade.

1.0

0.000001,+

Undefined

DVMETHOD

Method for calculating dispersion variance (3)

Option	Description
1	by parameter DISVAR
2	user defines variogram model and the dimensions of the SMU by parameter. A single dispersion variance is calculated for the SMU within a parent cell, and this value is used for all cells and subcells.
3	user defines variogram model and the dimensions of the SMU by parameter. A dispersion variance is calculated for the SMU within each cell and subcell in the model.

1,3

1,2,3

VARTYPE

Method for calculating the variance of a sample in a cell (1). This only applies if DVMETHOD = 3.

Option	Description
1	the exact dimensions of the cell are used
2	the cell is approximated to one of a discrete number of cells. The values for these cells are stored to avoid the need for recalculation for the cell of the same size. This gives a large speed improvement

1,2

SMUDIST

Distribution of SMUs: (1) =1 normal =2 lognormal =3 truncated normal

1, 3

1, 2,3

DISVAR

Dispersion variance value. (0) This is only required if DVMETHOD =1.

Undefined

ADDCON

Additive constant for three parameter lognormal distribution of SMUs. (0). This only applies if SMUDIST =2.

Undefined

VMODNUM

Variogram model reference number as defined by the VREFNUM field in the VMODPARM file. This only applies if DVMETHOD = 2 or 3.

Undefined

LOG

Log/Normal variogram flag. Default(0). The variogram model, as defined by VMODNUM is, Normal if LOG =0 Lognormal if LOG =1.

0,1

SMUXINC

X dimension of the Selective Mining Unit (1). This only applies if DVMETHOD = 2 or 3.

Undefined

SMUYINC

Y dimension of the Selective Mining Unit (1) This only applies if DVMETHOD

Undefined

SMUZINC

Z dimension of the Selective Mining Unit (1) This only applies if DVMETHOD

Undefined

XSTEP

X step size for subcell approximation in variance calculations. This is only used if DVMETHOD =3 and VARTYPE =2. This must be less than the parent cell dimension in X. (1)

Undefined

YSTEP

Y step size for subcell approximation in variance calculations. This is only used if DVMETHOD =3 and VARTYPE =2. This must be less than the parent cell dimension in Y. (1)

Undefined

ZSTEP

Z step size for subcell approximation in variance calculations. This is only used if DVMETHOD =3 and VARTYPE =2. This must be less than the parent cell dimension in Z. (1)

Undefined

IPOINTS

Number of discretisation points in X to simulate model cell (6)

Undefined

JPOINTS

Number of discretisation points in Y to simulate model cell (6)

Undefined

KPOINTS

Number of discretisation points in Z to simulate model cell (6)

Undefined

DATAMEAN

Mean grade of the input data (*VALUE). This is compulsory if both a normal variogram model is selected (@LOG=0) and a lognormal distribution of SMUs is selected (@SMUDIST=3). The value is used in the calculation of the variance.

Undefined

INFOEFF

The information effect variance. (0) This is subtracted from the variance. Refer to Journel and Huijbregts, Mining Geostatistics, pp 449-454 for details.

Undefined

Notes

No additional notes.

Example

!smumod	&IN(model),&VMODPARM(vmodel),&OUT(smumod),*VALUE(Fe1),
	VARIANCE(KV1),FRREC(RECFRAC),*VALREC(RECGRADE),@CUTOFF=2.5,
	@DVMETHOD=3,@VARTYPE=1,@SMUDIST=2,@DISVAR=0,@ADDCON=0,@VMODNUM=1,
	@LOG=0,@SMUXINC=1,@SMUYINC=1,@SMUZINC=1,@XSTEP=1,@YSTEP=1,
	@ZSTEP=1,@IPOINTS=3,@JPOINTS=3,@KPOINTS=3

Variogram model file VMODEL includes fields for up to 9 structures.
The file contains 2 records.

Model 1.00 has been retrieved from file.
Number of fully defined structures = 1
N Nugget Variance = 15.0000
All rotation angles are zero.
Structure Model Type Range X Range Y Range Z Spatial Var
T AX AY AZ C
1 1 50.0 50.0 50.0 35.0000
A normal variogram model has been selected.
The variances for a parent cell and SMU are calculated exactly as:
Parent cell ( 50.00 50.00 50.00) has variance 42.72099
SMU ( 1.00 1.00 1.00) has variance 15.67861
Dispersion variance = 27.04237
The variance of each model cell will be calculated as a function of its size.
The variance of each model cell will be calculated using its exact dimensions.

>>> 50 RECORDS IN FILE SMUMOD <<<
>>> SMUMOD Completed <<<

Error and Warning Messages

Message	Description	Solution