1.1.3. Grid2Time - 3D model grid to travel-time and angles grids
Given a velocity model grid, Grid2Time calculates the travel-time from a source point in a 3D grid to all other points in the grid. Optionally, the program also estimates the take-off angles for rays from each point in the grid to the source.
`Overview <#_overview_>`__ - `Podvin and Lecomte Algorithm <#_pl_algorithm_>`__ - `Take-Off Angles Algorithm <#_angles_algorithm_>`__ - `Running the program-Input <#_running_>`__ - `Output <#_output_>`__ - `Processing and Display of results <#_processing_>`__ - [NonLinLoc Home]
1.1.3.1. Overview
The Grid2Time program calculates the travel-times between a station and all nodes of an x,y,z spatial grid using the Eikonal finite-difference scheme of Podvin and Lecomte (1991). The results are stored on disk in a travel-time `3D Grid <./formats.html#_grid_>`__ files.
Optionally, the Grid2Time program also estimates the take-off angles for rays from each point in the grid to the source by examining the gradients of the travel-time field. These results are stored in an angles grid.
The 3D travel-time computation and the size of the output time-grid files grow rapidly with grid dimension. However, for location in horizontally layered models the travel-times can be stored on compact 2D grids. A layered model / 2D grid can also be used for”regional” stations far from the local search volume in combination with 3D models and 3D grids for stations within the search volume. This option may introduce some error if strong heterogeneity in the local 3D velocity structure intersects the (usually downgoing) ray paths to the regional stations.
The Grid2Time program uses a “flat earth”, rectangular, left-handed, x,y,z,t coordinate system (positive X = East, positive Y = North, positive Z = down). Distance units are kilometers, and many input/output distance quantities can be expressed in rectangular or geographic (latitude and logitude) coordinates.
1.1.3.2. Podvin and Lecomte, Eikonal, Finite-difference Algorithm
The travel times between a station and all nodes of a 3D grid are calculated using the Eikonal finite-difference scheme of Podvin and Lecomte (1991). The algorithm is implemented in the Grid2Time program using a C function time_3d() due to P. Podvin (last revision 2 January 1992). The abstract of Podvin and Lecomte (1991) describes the algorithm as:
This method relies on a systematic application of Huygen’s principle in the finite difference approximation. Such approximation explicitly takes into account the existence of different propagation modes (transmitted and diffracted body waves, head waves). Local discontinuities of the time gradient in the first arrival time field (e.g. caustics) are built as intersections of locally independent wavefronts. As a consequence, the proposed method provides accurate first travel times in the presence of extremely severe, arbitrarily shaped velocity contrasts.
Associated to a simple procedure which accurately traces rays in the obtained time field, this method provides a very fast tool for a large spectrum of seismic and seismological problems.
1.1.3.3. Take-Off Angles Algorithm
The take-off angles at a node for the first-arrival ray to the source are estimated from the gradients of travel-time at the node. Two gradients are estimated for each axis direction x, y, z - one G:sub:`low` between the node and its preceeding neighbour along the axis, and a second G:sub:`high` between the following neighbor and the node. The total gradient G:sub:`axis` along an axis is the mean of these two gradients; the total gradient along the three axes determine the vector gradient of travel-time. The ray take-off angles R:sub:`dip` (dip, range of 0 (down) to 180 deg (up)) and R:sub:`az` (azimuth, range of 0 to 360 deg CW from North) specify the direction opposite to the vector gradient of travel-time.
A crude quality factor Q:sub:`axis` between 0 and 10 is determined from the ratio
Q:sub:`axis` = (20 G:sub:`low` G:sub:`high`) / (G:sub:`low`2 + G:sub:`high`2)
If Q:sub:`axis` < 0 (i.e. the two gradients have opposite sign), Q:sub:`axis` is set equal to 0. If Q:sub:`axis` = 10 then the two gradients have the same magnitude and sign. A final quality for the take-off angles is determined from the weighted average of the qualities along each axis, where the weighting is given by the magnitude of the mean gradient along each axis,
1.1.3.4. Running the program - Input
Synopsis: Grid2Time InputControlFile
The Grid2Time program takes a single argument InputControlFile which
specifies the complete path and filename for an Input Control
File with certain required and optional statements
specifying program parameters and input/output file names and locations.
See the `Grid2Time Statements section <./control.html#_Grid2Time_>`__ of
the Input Control File for more details. Note that to run Grid2Time the
`Generic Statements section <./control.html#_generic_>`__ of the Input
Control File must contain the CONTROL and TRANS (Geographic
Transformation) statements.
In addition, the Grid2Time program requires:
A 2D or a 3D velocity model `3D Grid <./formats.html#_grid_>`__ file created using Vel2Grid or other software. One velocity model grid is required for each wave type (i.e. P or S). Note that a 3D Grid file may specify a 2D model.
The names, locations and other information for these files is specified in the `Grid2Time Statements section <./control.html#_Grid2Time_>`__ of the Input Control File.
1.1.3.5. Output
The travel-times and take-off angles throughout a grid are written to a
separate `3D Grid File <formats.html#_grid_>`__ for each phase at each
station. For a descrition of the naming convention for these grid files,
see the `GTFILES <./control.html#_Grid2Time_gtfiles_>`__ statement
in the Grid2Time Statements section of the Input Control File.
1.1.3.6. Processing and Display of results
The travel-time and angles grid results for a single source can be post-processed with the program Grid2GMT to produce a GMT command script for plotting with the GMT plotting package.
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Anthony Lomax