## Analytic Signal Solutions

Use the **Pdepth > Analytic Signal Solutions** option (ANASIG GX) to compute analytic signal depth solutions from magnetic (or gravity) profiles.

### Anasig - Generate Hilbert 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). |

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

Max. 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". |

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. |

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

### Application Notes

#### Gravity Applications

To use analytic signal 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. The calculated Analytic Signal of the input total-field magnetics is saved in the database as "AS_Mag" and the calculated Analytic Signal of the input horizontal-gradient magnetics is saved in the database as "AS_HGrad".

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), which is based on the method published by Nabighian (1972, 1974). The input profiles are interpolated to an even sample interval using the standard OASIS spline calls before processing by Anasig. 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. Anasig uses an FFT technique to calculate the horizontal derivative if the user does not specify an input gradient channel.

### References

- [1] Phillips, J. D., 1997, "Potential-Field Geophysical Software for the PC, version 2.2",
*USGS*, Open-File Report 97-725, desc. 39 p. - [2] Nabighian, M. N., 1972, "The Analytic Signal of Two-Dimensional Magnetic Bodies with Polygonal Cross-Section: Its Properties and Use for Automated Anomaly Interpretation",
*Geophysics*, vol. 37 (3), pp. 507-517. - [3] Nabighian, M. N., 1974, "Additional Comments on the Analytic Signal of Two-Dimensional Magnetic Bodies with Polygonal Cross-Section",
*Geophysics*, vol. 39 (1), pp. 85-92.

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