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Tau-P Processing of Seismic Refraction Data

Documentation and Related Programs

seiswiggle

Written by:
Andrew R. Gorman
Department of Earth and Ocean Sciences
University of British Columbia
2219 Main Mall
Vancouver, British Columbia V6T 1Z4
Canada
e-mail: gorman@eos.ubc.ca


This document summarises the procedures that are currently being developed at UBC to use Tau-P techniques to evaluate the seismic refraction data acquired during the SAREX and Deep Probe experiments of 1995. The aim is to make this process a simple and easy to run procedure that can be applied to any refraction data set. It preferably should be used as a first attempt to define two-dimensional velocity structure and could be used as a preliminary model for use in such schemes as RAYINVR. The routines outlined here are freely available for non-profit use by others; please contact the author for more information.

A paper detailing this procedure has recently (12 January 1999) been accepted for publication in Geophysical Research Letters. A web-browsable version of this paper: "Wave-field tau-p analysis for 2-D velocity models: Application to western North American lithosphere" is available.

Cautionary Note

This site and the programs described here were under construction from the autumn of 1997 to the summer of 1998. Although the programs discussed here have been extensively tested by the author and several other users at UBC, it is still conceivable that errors will be found. Any corrections or suggestions that others find would be greatly welcomed and appreciated!


Table of Contents

Overview

Tau-P Stack (Slant Stack) Program: plotsec_taup
- Overview
- Program Details

Tau-P Space to Z-P Space Downward Continuation: plotsec_tpau
- Overview
- Program Details

WKBJ Forward Modelling

References


Overview

Tau-P processing of seismic refraction data is a quick way to obtain a one-dimensional interpretation of a seismic refraction data set without having to pick arrivals on a seismic section. This involves two major steps.

  • First, the uninterpreted data are transformed from the t-x domain into the tau-p domain through a tau-p transform.
  • Second, the data are downward continued into z-p space using an arbitrary input velocity function. This velocity function can be modified as needed to produce a good fit to the data.

The accuracy of the velocity analysis can be checked by calculating the time-distance curves resulting from the velocity function. This can be done using Chris Chapman's WKBJ algorithm. By overlaying the input refraction data set with the calculated time-distance curves, the accuracy of the model can be checked. If desired, the velocity model can then be refined further. The WKBJ routine can also be used to calculate synthetic seismograms which can also be compared to the input data.

A suggested processing flow for using the programs available would look like this.

Tau-P Processing Flow Diagram

Most seismic refraction surveys involve several combinations of shots and receivers. Each refraction profile in a particular experiment can be analysed using the method detailed here and these results can be combined to obtain a quasi-two-dimensional interpretation that can be used for input to a more rigorous interpretation scheme (like RAYINVR).

In combining several one-dimensional models, it is useful to keep in mind that the horizontal region of the subsurface sampled increases with depth. If sufficient data are available, it is preferable to plot the one-dimensional v(z) function as a v(z,x) function where the x corresponds to the offset of the bottoming location (z) of the rays.


Tau-P Stack (Slant Stack) Program: plotsec_taup

Purpose: A program to convert an ordinary refraction data set from x-t space to tau-p space. The input and output data are in plotsec format.

seiswiggle

Overview

This is a simple, well-known linear wave field transformation that takes an input data set in the time-offset domain and transforms it into a new data set in the intercept time - slowness domain. In this case, the input data set, P, is the observed seismogram wavefield. In S, the transformed wavefield, p is the horizontal slowness and tau is the time intercept.

(1)

A simple way to look at the transform is to think of each point in the tau-p plane being the sum of all the points in the t-x plane lying along a straight line with a slope of p and a time-axis intercept of tau. The seismogram is decomposed into plane wave elements (McMechan, et al., 1982.)

A significant strength of this tau-p transform routine is that the trace spacing of the input data set does not have to be uniform. This lends itself well to crustal scale refraction surveys.

Program Details

INPUT:
The input for this program can be any plotsec refraction data set which should be composed of ps_data.out and head.dmp files. A plotsec_taup.com file is also required to control the program. The program, plotsec_taup, and all necessary files currently reside on wrang at /data6/deepprobe/plotsec/src/plotsec_taup/.

The format of the plotsec_taup.com command file is as follows.

#----------------------plotsec_taup.com-----------------------
# This routine calculates the tau-p transform of an input x-t 
# data set.  
#
# Set the level of output to the screen. (0=none, 1=some, 2=lots)
DEBUG 1
#
INPUT-HEAD  ../head.dmp
INPUT-DATA  ../ps_data.out
INPUT-MUTE  ../mute.out
#
OUTPUT-HEAD  head.dmp
OUTPUT-DATA  ps_data.out
#--------------------------------------------------------------
#    select the tau range for output (from, to, ievery)
TAU-RANGE 0 150 0.032
#--------------------------------------------------------------
#    select the slowness range (in s/km) for output (from, to, ievery)
SLOWNESS-RANGE 0.07 0.50 0.005
#--------------------------------------------------------------
#    select the trace sequential window to process (from, to, ievery)
#TRACE-RANGE 1 678 1
#--------------------------------------------------------------
#    apply the mute values storied in the INPUT-MUTE file
#APPLY-MUTE
#    remove the traces marked as killed in the INPUT-MUTE file
#REMOVE-KILLED
#--------------------------------------------------------------
#    Trace normalisation (1=MAXamp, 2=RMSamp, 3=no normalisation)
#TRACE-NORMALISATION  3
#--------------------------------------------------------------
OUTPUT:
The output for the program is in the form of standard plotsec head.dmp and ps_data.out files. Instead of offset distance, the traces are saved by slowness (in ms/km). The units have been chosen to facilitate plotting. When plotting the data, be sure to use the options available in plotsec_plot to override the labelling of the x and y axes.


Tau-P Space to Z-P Space Downward Continuation Program: plotsec_tpau

Purpose: A program to downward continue a tau-p section (created using plotsec_taup) into a z-p section. The input and output data are in plotsec format. A one-dimensional input velocity function is also required.

This program is suitably named in honour of the Vulcan high official, T'Pau, who presided at Spock's 'failed' marriage to T'Pring in 2267. At that time, she was the only person ever to have turned down a seat on the Federation High Council. Her respect for the Federation was enhanced by the way in which Captain Kirk, a human, handled the Vulcan challenge issued to him by T'Pring to fight Spock to the death. T'Pau's judgement resulted in an elegant solution to a situation that seemed untenable. It is this same goal that the program plotsec_tpau has. (For more on T'Pau watch the episode named "Amok Time" from the original Star Trek series.)

seiswiggle

Overview

This procedure makes use of the idea that each trace in the input tau-p section represents plane waves with a common velocity (since velocity is the inverse of slowness.) Using an input velocity function, v(z), a new trace, s, is created for each input tau-p trace, S. This procedure is very similar to migration in that all points on the input trace are mapped to points on the output trace by the criteria imposed by the transform. In effect, the input trace is stretched and squeezed to form the output trace. Maximum `stretching' occurs in the vicinity of where the particular slowness of the input trace, p, is equal to the inverse of the input velocity function, v(z). No energy is transfered between traces; this is a simple trace by trace operation.

The formula used is:

(2)
where

Program Details

INPUT:
The input for this program should be a plotsec formatted tau-p data set (the output from plotsec_taup) made up of ps_data.out and head.dmp files. In addition, an input velocity function is required containing two columns: the first being depth (in km) and the second being velocity (in km/s). A plotsec_tpau.com file is required to control the program. The file names of the input data set and velocity function are entered here. The program, plotsec_tpau, and all necessary files currently reside on wrang at /data6/deepprobe/plotsec/src/plotsec_tpau/.

The format of the plotsec_tpau.com command file is as follows.

#-----------------------plotsec_tpau.com-----------------------
# This routine calculates the downward continuation of an input
# tau-p data set into z-p space using a specified input velocity.
#
# Set the level of output to the screen. (0=none, 1=some, 2=lots)
DEBUG 1
#
INPUT-HEAD  ../taup/head.dmp
INPUT-DATA  ../taup/ps_data.out
INPUT-VELOCITY  velocity.in
#
OUTPUT-HEAD  head.dmp
OUTPUT-DATA  ps_data.out
OUTPUT-SLOWNESS  slowness.out
#--------------------------------------------------------------
# select the z (depth in km) range for output (from, to, increment)
Z-RANGE 0 150 0.032
#--------------------------------------------------------------
OUTPUT:
The output for the program is in the form of standard plotsec head.dmp and ps_data.out files. Instead of offset distance, the traces are saved by slowness (in ms/km) - the same as was in the input tau-p data.

Plotsec_tpau also outputs a slowness data set (with a name specified in plotsec_tpau.com) with two columns: depth (km) and slowness (ms/km) which can be used by plotsec_plot to plot the velocity function used for the downward continuation on top of the data. Use the line: INPUT-REF 1 filename.ext for this purpose.

When plotting the data, be sure to use the options available in plotsec_plot to override the labelling of the x and y axes.


WKBJ Forward Modelling

Purpose: A powerful one-dimensional ray-theoretical forward modelling routine which can be used to confirm the velocity model being developed through the tau-p to z-p downward continuation.

seiswiggle

Overview

The procedure which is followed here is to use the velocity function developed through the tau-p analysis as input to the WKBJ routine.

The WKBJ routine is a powerful way of quickly producing ray theoretical seismograms, but it can also be used for the simpler purposes of producing travel time curves and ray diagrams. Three input files are required:

  • plotsec_wkbj.com, a file containing all the commands specific to controlling the routine.
  • A velocity function file (the name of which is specified in the .com file) which will be the same as the velocity function file used for the last downward continuation.
  • A ray specification file which establishes such things as where refractions and reflections will be calculated.

The WKBJ routine allows for various output files to be created. These are specified in the .com file. If the time-distance curves have been calculated, they can be plotted directly on the input refraction data set to see how well the derived velocity model ties the data.

Program Details

Please refer to the documentation for WKBJ.


References

The following references contain practical examples as well as the theory that is required for this method. Especially good examples are shown in Clayton and McMechan (1981) and McMehan et al. (1982).

Au. D. and R.M. Clowes 1982. Crustal structure from an OBS survey of the Nootka fault zone off western Canada. Geophys. J. R. astr. Soc

Clayton, R.W. and G.A. McMechan 1981. Inversion of refraction data by wave field continuation. Geophysics 46 (6): 860-868.

McMechan, G.A., R.W. Clayton and W.D. Mooney 1982. Application of wave field continuation to the inversion of refraction data. Journ. Geophys. Res. 87 (B2): 927-935.

Reiter, E.C., G.M. Purdy and M.N. Toksöz 1993. 2-D velocity inversion/imaging of large offset seismic data via the tau-p domain. Geophysics 58 (7): 1002-1016.

Walck, M.C. and R.W. Clayton 1984. Analysis of upper mantle structures using wave field continuation of P waves. Bull. Seis. Soc. Am. 74 (5): 1703-1719.


Last updated: 10 July 1998

A. R. Gorman (gorman@eos.ubc.ca)