1. Advanced uses of the Mathematics attribute OpendTect Master Class June 15, 2014

2. Mathematics attribute The mathematics attribute allows to combine datasets and to compute new output using mathematical expressions. The input(s) can be 2D/3D volumes, horizon data and 2D/3D attributes. The same functionality is available in the well log manager to create math logs from other logs. In OpendTect 5.0, formulas can be saved and retrieved.

3. Mathematics attribute The mathematics attribute supports : –Usual operators Arithmetic : + – * / ^ Comparison: > = == != Logical: && (and) || (or) –Functions sqrt() exp() ln() log() sin() cos() tan() asin() acos() atan() abs() idiv() mod() –Statistical rand() randg() min() max() sum() avg() med() var()

4. Mathematics attribute Constants: –Undef/undef corresponds to undefined values. –Pi and euler –c0, c1, cX are constants. The advantage is that a constant value can be tested using the evaluate option. example: evaluating the cut-off value in the ridge enhancement filter Other quantities: –z step : DZ –Depth : Z –Inline and crossline : Inl and Crl –X/Y coordinates : XCoord and YCoord 4

5. Mathematics attribute – Undef In OpendTect: undef = 1e30 A volume can have undefined values and/or null traces. A trace where all values are undefined is still part of the dataset (on disk and in memory). When using mathematics, one volume might cover a different area than another. An output trace will only be created where all datasets have an input trace. Thus you may want to “add” null traces such the input volumes have similar sizes. 5 Manage Seismic dataCopy cube

6. Mathematics attribute - Uses Different types of syntaxes can be used in the Mathematics attribute: 1.Logical : used to combine volumes/attributes/logs CONDITION ? OUTPUT IF TRUE : OUTPUT IF FALSE Example : Create a litholog -Sand : Porosity >= 15%, Vclay < 40% - code = 1 -Shale : Vclay >= 60% - code = 2 -Other - code = 3 → Vclay >= 0.6 ? 2 : (Porosity >= 0.15 && Vclay < 0.40 ? 1 : 3) 6

7. Mathematics attribute - Uses Different types of syntaxes can be used in the Mathematics attribute: 2.Vertical shift: Any volume/attribute written attribute[c0], the number in the [ ] corresponds to a shift in number of samples (here c0 samples), i.e a vertical shift. Example : Centered differentiation : (seis[+1]-seis[-1])/(2*DZ) where seis=seismic 7

8. Mathematics attribute - Uses Different types of syntaxes can be used in the Mathematics attribute: 3.Recursive : A recursive filter uses past output values x[n-i] for the calculation of the current output x[n]. OUT[-i] allows to create recursive filters. OUT[-i] corresponds to x[n-i]. n is the current sample index and does not need to be specified. The start value and a starting time/depth of the function need to be specified. Example : Single pole low-pass recursive filter Filter(n)= (1-c0) seis(n)+c0*Filter(n-1)  (1-c0)*seis+c0*OUT[-1] where c0 is a variable 8

9. Conclusions With basic arithmetic, the mathematics tool can calculate new output with one or more input. Logic syntax allows to combine attribute/volumes in a more complex way to create for example a lithocube. Advanced user-defined filters can be computed using shift and recursive functionalities. 9