Moving topography displacement files¶
For tsunami generation a dtopo file is often used to specify the displacement of the topography relative to that specified in the topo files, which are described in Topography data. The dtopo file specifies the change in topography over some region (by specifying the displacement on a grid of points) either at a single time or at a sequence of times. Various file formats are allowed, see dtopo file formats below.
This displacement might arise from various sources, including:
An earthquake creating motion of the seafloor, specified as either a time history of the displacement might be available, or simply as the final static displacement at the end of the shaking (for an “instantaneous” event).
A submarine landslide, slump, or mass flow, or a subareal landslide along the coast that strikes and enters the water.
In the latter case it is generally challenging to model the landslide motion accurately and it is often necessary to use a fully coupled model that includes the effect of the fluid motion on the landslide during its evolution. Such cases cannot be modeled simply by providing a dtopo file as described here. But in some cases it may be possible to run a separate landslide model first and use the evolution of the surface to generate a dtopo file that can then be used to generate a tsunami. See Landslides for more details and an example.
The D-Claw code is an extension of GeoClaw that can model dense debris flows and some kinds of landslides, including subareal landslides striking water and generating a tsunami. See D-Claw for debris flows and landslides for more details.
dtopo files for earthquakes¶
Genearating a tsunami in GeoClaw often proceeds by specifying the vertical motion of the seafloor at one or more times. The entire water column in each grid cell is then moved vertically by the same amount (or some filtering may be applied, see below). This creates a disturbance of the sea surface, which in turn results in tsunami waves that propagate away from the source region.
Calculating the seafloor deformation due to an earthquake usually starts by specifying some amount of slip on a fault plane interior to the earth, or more likely on a finite set of subfaults, each of which is a planar rectangle or triangle, and which together better approximate the fault surface for a complex fault.
There are three distinct ways of approximating seafloor deformation resulting from an earthquake that are commonly used in GeoClaw:
The Okada model is a simple approach in which the earth is assumed to be a homogeneous halfspace, with the earth’s surface (and seafloor) at the top free surface. The slip on a single subfault then results in a static deformation of the surface at some time after all the seismic waves have propagated away. The Okada model can be applied to either a single rectangle or triangle, and then for a more complex fault the deformation due to each subfault is simply summed up, assuming linearity. This approach does not model the shaking of the earthquake but the final static deformation is often sufficient to model the resulting tsunami. This is often called a “static displacement” or “instantaneous displacement” model, since the earthquake is assumed to act at the same time on all subfaults and the final static deformation from each subfault is used immediately at the earthquake time (usually either at the time t0 where the GeoClaw simulation starts or perhaps 1 second later so that the initial flat ocean surface is also captured in the output).
A “kinematic” earthquake model assigns slips to each subfault and also assigns a “rupture time” and a “rise time” for each subfault, with the latter determining how long it takes the slip to build up on the subfault. A quasi-static approach can then be used in which the Okada model is used at each time from t0 to the final time of any subfault motion, with the cumulative slip up to that time used as the seafloor deformation at that time. Alternatively, a full 3D seismic simulation could be performed to model the generation and propagation of seismic waves spreading out from the fault. The motion of the free surface in the seismic simulation is then used as the seafloor deformation, and is evolving in time from the initial time t0 of the earthquake to a later time when all the seismic waves have decayed. At this time, the final seafloor deformation may be similar to what the Okada model would predict, particularly if the seismic simulation is done in a homogeneous half-space. However, the seismic simulation can instead be done using a model of the structure of the earth in which the elastic parameters (and seismic wave speeds) vary in space. Some seismic codes also allow the free surface to model the topography and bathymetry of the sea floor as well, and may even model the ocean as a separate acoustic layer on top of the earth.
A “dynamic” rupture model is even more complex, in that the initial fault geometry and stresses are prescribed but the slip on each subfault is then determined dynamically by using a rupture model for the rock mechanics, coupled with the 3D elastic wave equations.
Regardless of how complex the model is that determines the seafloor motion, in GeoClaw we simply read in the resulting vertical seafloor displacement on a uniform grid at a sequence of one or more times.
dtopo file formats¶
Currently two formats are supported for this file:
dtopotype=1:
Similar to topo files with topotype=1 as described above, except that each line starts with a t value for the time, so each line contains t,x,y,dz
The x,y,dz values give the displacement dz at x,y at time t. It is assumed that the grid is uniform and that the file contains mx*my*mt lines if mt different times are specified for an mx*my grid.
dtopotype=3:
This is the recommended dtopo_type. Similar to topo files with topotype=3 as described above, but the header is different, and contains lines specifying mx, my, mt, xlower, ylower, t0, dx, dy, and dt. These are followed by mt sets of my lines, each line containing mx values of dz.
Here is an example header for a dtopofile:
721 mx
1201 my
56 mt
-1.28500000000000e+02 xlower
4.00000000000000e+01 ylower
0.00000000000000e+00 t0
8.33333333332575e-03 dx
8.33333333333286e-03 dy
1.00000000000000e+01 dt
The time increment is dt=10 seconds and mt=56 snapshots of the vertical deformation are stored in this file; this header is followed by 1201 x 56 lines, each having 721 values giving the vertical displacement on one line of constant latitude.
Note that while the topography is moving, it is important to insure that the time step is small enough to capture the motion. The setrun.py parameter rundata.dtopo_data.dt_max_dtopo can be set to the maximum timestep to be used between time t0 = 0 and t0 + (mt-1)*dt = 550 seconds, in the example above. See Topography data file parameters.
GeoClaw does not include any capabilities for 3D seismic modeling, but the Okada model on both rectangles and triangles is implemented, along with tools for reading the fault parameters in various formats, applying the Okada model, and generating a dtopo file with the resulting displacements. See Earthquake sources: Fault slip and the Okada model and dtopotools module for moving topography for more details.
qinit data file¶
Instead of (or in addition to) specifying a displacement of the topography it is possible to specify a perturbation to the depth, momentum, or surface elevation of the initial data. This is generally useful only for tsunami modeling where the initial data specified in the default qinit.f90 function is the stationary water with surface elevation equal to sea_level as set in setrun.py (see Specifying GeoClaw parameters in setrun.py).
Of course it is possible to copy the qinit.f90 function to your directory and modify it, but for some applications the initial elevation may be given on grid of the same type as described above. In this case file can be provided as described at qinit data file parameters containing this perturbation.
The file format is similar to what is described above for topotype=1, but now each line contains x,y,dq where dq is a perturbation to one of the components of q as specified by the value of qinit_type specified (see qinit data file parameters). If qinit_type = 4, the value dq is instead the surface elevation desired for the initial data and the depth h (first component of q) is set accordingly.
