## Werner Solutions

Use the **Pdepth > Werner Solutions** menu option (WERNER GX) to compute the Werner deconvolution solutions from magnetic (or gravity) profiles.

### Werner Solutions dialog options

X channel |
Input x coordinate. (Assumes units are the same for X, Y, Elev, and Topo channels). |

Y channel |
Input y coordinate. (Assumes units are the same for X, Y, Elev, and Topo channels). |

Elev. channel |
Flight elevation (+up) relative to sea level. (Assumes units are the same for X, Y, Elev, and Topo channels). |

Mag. channel |
Magnetic (or gravity) anomaly channel. |

Horizontal derivative |
Input horizontal derivative channel. The key word "Calculate" forces the Werner to calculate derivative from the Mag Channel values. |

Topography |
Topographic elevation (+up) relative to sea level. (Assumes units are the same for X, Y, Elev, and Topo channels. Can be all dummies). |

Minimum depth |
Solutions shallower than minimum depth are discarded. (Relative to flight elevation, + down). |

Maximum depth |
Solutions deeper than maximum depth are discarded. (Relative to flight elevation, + down). |

Minimum window length |
Length (in horizontal distance units) of shortest Werner operator window used to detect peaks and calculate depths. |

Maximum window length |
Length (in horizontal distance units) of longest Werner operator window used to detect peaks and calculate depths. |

Window expansion increment |
Increment (in horizontal distance units) used to expand the operator window length for successive passes from "Min" to "Max". |

Window shift increment |
At each operator window size, the window will be advanced along the profiles by this distance (in horizontal distance units) for successive calculations. |

Detrend order |
Degree of polynomial used to calculate the regional removed from the data window. The allowable range is 0-2. (Default 1, i.e., linear regional). |

Relative strike |
Angle between profile direction and anomaly strike in degrees, positive counterclockwise. (Default 90 degrees). |

Field strength |
Earth's magnetic field strength. Used to calculate susceptibility which will be in same units. |

Inclination |
Earth's magnetic field inclination in degrees. |

Declination |
Earth's magnetic field declination in degrees. |

Residual cut-off |
Data windows with RMS residual (after regional removed) less than this value are discarded. Larger values generate fewer solutions. (Default 0, i.e., keep all solutions). |

X cut-off |
Solutions outside this distance (in % of window length) from the center of the window are discarded. Larger values generate more solutions. The allowable range is 5%-100%. (Default 20%). |

Output database name |
If a database with this name exists, Werner replaces existing lines with the new results but maintains the existing format and structure. |

### Application Notes

#### Gravity Applications

To use Werner Deconvolution on gravity profiles, use the vertical derivative of gravity as the input profile rather than total-field magnetics.

If the "Field Strength" is set to "1", "Inclination" set to "90", and the "Declination" set to zero, the "Susc" output channel will be the calculated density contrast. Note that the "Contact" solutions are computed from the 2nd horizontal derivative in the gravity case, so some low-pass filtering is often required.

#### Output

The solutions are sorted by distance-along-the-line, referenced to the first point in the input profile. The channel "Z_Dikes" contains the dike solution depths relative to the flight elevation. The channel "Z_Contacts" contains the contact solution depths relative to the flight elevation. All of the solutions are also in a 3rd channel named "Z_Both". The channel "Depth_sl" contains the depth relative to sea level calculated using the input "Elev" channel if it was non- dummy. The sign of the Z-axis is negative down for all of these channels (Z_Dikes, Z_contacts, Z_Both, Flt_Elev, and Depth_sl) to facilitate convenient profile plots. "Dike0_Cont1" contains a flag identifying the solution as a dike (0) or a contact (1) solution.

Four of the input channels, re-sampled to an even sample interval are copied to the output database: "Elev.", "Mag", "Horizontal Gradient", and "Topography". The "Elev" and "Topography" profiles are automatically plotted in the top pane, the "Mag" and "Horizontal Derivative" profiles are automatically plotted in the middle pane, and symbols for the "Z_dikes" and "Z_Contacts" are automatically plotted in the bottom pane.

Length and depth units in the output channels (e.g., meters or Kilometers) match the units of the X, Y, Elev, and Topography channels in the input database. All distance/depth units must be the same.

This GX is based on the USGS program PDEPTH (Phillips, 1997) and includes the iterative improvement scheme described by Ku and Sharp (1983). The input profiles are interpolated to an even sample interval using the standard OASIS spline calls before processing by Werner. The sample interval is the total profile length divided by the number of points in the profile. So profiles with large gaps should be split into multiple lines.

For noisy input profiles, the results can be improved significantly by filtering the input anomaly and gradient data. Werner uses a cubic spline technique to calculate the horizontal derivative if the user does not specify an input gradient channel.

The "Detrend Order" affects the number of data points used in the operator window. Order = 0 results in a four-point window, order = 1 results in a six-point window, and order = 2 results in a seven-point window. Ku and Sharp (1983) suggest the optimum data window length should be at least one half the width of the anomalies being analyzed. Werner will not find many valid solutions at depths shallower than the input data spacing or deeper than the window length.

Several parameters in the dialog control the number of solutions generated by Werner. "Min. Window Length" and "Max. Window Length" set the minimum and maximum lengths of the Werner operator, respectively. "Window Expansion Increment" determines the number and size of steps between the minimum and maximum. "Window Shift Increment" sets the distance the Werner operator is moved along the profile between calculations. These four parameters are specified in distance units. The distance units in the input parameters are always the same as those for the X and Y input channels. (If the X, Y channels are in meters, all the distance, depth inputs and outputs will be in meters; if X, Y are in kilometers, then all of the distance, depth inputs and outputs are in kilometers.) Smaller values of Window Expansion Increment and Window Shift Increment generate more calculations and hence more solutions.

Each Werner calculation potentially generates one solution. The last two input parameters determine if the solution will be saved in the output database. "Residual cut-off" sets an amplitude threshold for anomalies (in nT) and enables you to eliminate solutions caused by noise in the input profile. Larger values of Residual cut-off eliminate more solutions. "X cut-off" sets a horizontal distance threshold (in % of window length) for solutions relative to the center of the Werner operator. When X cut-off is decreased, more solutions are eliminated. Values of X cut-off greater than 2, combined with small values of Window Shift Increment, generate the "spray" patterns seen in some examples in the literature.

### References

- [1] Jeffrey D. Phillips, 1997, "Potential-Field Geophysical Software for the PC, Version 2.2",
*USGS*, Open-File Report 97-725, desc. 39 p. - [2] Chao C. Ku, John A. Sharp, 1983, "Werner Deconvolution for Automated Magnetic Interpretation and its Refinement Using Marquardt’s Inverse Modeling",
*Geophysics*, vol. 48 (6), pp. 754-774.

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