.. index:: ! gmtflexure .. include:: ../module_supplements_purpose.rst_ ********** gmtflexure ********** |gmtflexure_purpose| Synopsis -------- .. include:: ../../common_SYN_OPTs.rst_ **gmt flexure** |-D|\ *rm*/*rl*\ [/*ri*]\ /*rw* |-E|\ *Te*\ [**k**]\|\ *D*\|\ *file* |-Q|\ *args* [ |-A|\ [**l**\|\ **r**]\ *bc*\ [/*args*] ] [ |-C|\ **p**\|\ **y**\ *value* ] [ |-F|\ *force* ] [ |-L| ] [ |-M|\ [**h**][**v**] ] [ |-S| ] [ |-T|\ *wfile*] [ |SYN_OPT-V| ] [ |-W|\ *wd*\ [**k**]] [ |-Z|\ *zm*\ [**k**]] [ |SYN_OPT-bi| ] [ |SYN_OPT-bo| ] [ |SYN_OPT-d| ] [ |SYN_OPT-e| ] [ |SYN_OPT-h| ] [ |SYN_OPT-i| ] [ |SYN_OPT-o| ] [ |SYN_OPT--| ] |No-spaces| Description ----------- **flexure** computes the flexural response to 2-D loads using a range of user-selectable options, such as boundary conditions, pre-existing deformations, variable rigidity and restoring force, and more. The solutions are obtained using finite difference approximations to the differential equations [*Bodine*,\ 1980]. Required Arguments ------------------ .. _-D: **-D**\ *rm*/*rl*\ [/*ri*]\ /*rw* Sets density for mantle, load, infill (optionally, otherwise it is assumed to equal the load density), and water. If *ri* is not given then it defaults to *rl*. .. _-E: **-E**\ *Te*\ [**k**]\|\ *D*\|\ *file* Sets the elastic plate thickness (in meter); append **k** for km. If the elastic thickness exceeds 1e10 it will be interpreted as a flexural rigidity *D* instead (by default *D* is computed from *Te*, Young's modulus, and Poisson's ratio; see |-C| to change these values). Alternatively, supply a *file* with variable plate thicknesses or rigidities. The file must be co-registered with any file given via |-Q|. .. _-Q: **-Qn**\|\ **q**\|\ **t**\ [*args*] Sets the vertical load specification. Choose among these three options: **-Qn** means there is no input load file and that any deformation is simply driven by the boundary conditions set via |-A|. If no rigidity or elastic thickness file is given via |-E| then you must also append arguments to create the locations used for the calculations; for details on array creation, see `Generate 1-D Array`_. **-Qq**\ [*loadfile*] is a file (or standard input if not given) with (x,load in Pa) for all equidistant data locations. Finally, **-Qt**\ [*topofile*] is a file (or standard input if not given) with (x,load in m or km, positive up); see |-M| for topography unit used [m]. Optional Arguments ------------------ .. _-A: **-A**\ [**l**\|\ **r**]\ *bc*\ [/*args*] Sets the boundary conditions at the **l**\ eft and **r**\ ight boundary. The *bc* can be one of four codes: 0 selects the infinity condition, were both the deflection and its slope are set to zero. 1 selects the periodic condition where both the first and third derivatives of the deflection are set to zero. 2 selects the clamped condition where *args* (if given) sets the deflection value [0] (and its first derivative is set to zero), while 3 selects the free condition where *args* is given as *moment*/*force* which specify the end bending moment and vertical shear force [0/0]. Use SI units for any optional arguments. .. _-C: **-C**\ **p**\|\ **y**\ *value* Append **p** or **y** to change the current value of Poisson's ratio [0.25] or Young's modulus [7.0e10 N/m\ :sup:`2`], respectively. .. _-F: **-F**\ *force* Set a constant horizontal in-plane force, in Pa m [0]. .. _-L: **-L** Use a variable restoring force that depends on sign of the flexure [constant]. .. _-M: **-M**\ [**h**][**v**] Optionally append one or both of **h** and **v**: Use **h** to indicated that all horizontal distances are in km [meters] and **v** to indicate that all vertical deflections are in km [meters]. .. _-S: **-S** Compute the curvature along with the deflections and report them via the third output column [none]. .. _-T: **-T**\ *wfile* Supply a file with pre-existing deformations [undeformed surface]. .. |Add_-V| replace:: |Add_-V_links| .. include:: /explain_-V.rst_ :start-after: **Syntax** :end-before: **Description** .. _-W: **-W**\ *wd*\ [**k**] Specify water depth in m; append **k** for km. Must be positive [0]. Any subaerial topography (i.e., amplitudes in the input relief that exceeds this depth) will be scaled via the densities set in |-D| to compensate for the larger density contrast with air. .. _-Z: **-Z**\ *zm*\ [**k**] Undeformed plate flexure means *z = 0*. Specify the distance between the observation level [*z = 0*] and the undeformed flexed surface in m; append **k** for km. Must be positive [0]. We subtract this value from the flexed surface before output. Thus, if the observation level is at sealevel and you are looking a seafloor deformation in 5 km of water, use -Z5k and the undeformed surface will have *z = -5000* on output. .. |Add_-bi| unicode:: 0x20 .. just an invisible code .. include:: ../../explain_-bi.rst_ .. |Add_-bo| unicode:: 0x20 .. just an invisible code .. include:: ../../explain_-bo.rst_ .. |Add_-d| unicode:: 0x20 .. just an invisible code .. include:: ../../explain_-d.rst_ .. |Add_-e| unicode:: 0x20 .. just an invisible code .. include:: ../../explain_-e.rst_ .. |Add_-h| unicode:: 0x20 .. just an invisible code .. include:: ../../explain_-h.rst_ .. include:: ../../explain_-icols.rst_ .. include:: ../../explain_-ocols.rst_ .. include:: ../../explain_help.rst_ .. include:: ../../explain_array.rst_ .. include:: explain_geometry.rst_ Note on Units ------------- The |-M| option controls the units used in all input and output files. However, this option does *not* control values given on the command line to the |-E|, |-W|, and |-Z| options. These are assumed to be in meters unless an optional **k** for km is appended. Plate Flexure Notes ------------------- We solve for plate flexure using a finite difference approach. This method can accommodate situations such as variable rigidity, restoring force that depends on the deflection being positive or negative, pre-existing deformation, and different boundary conditions. Examples -------- To compute elastic plate flexure from the topography load in *topo.txt*, for a 10 km thick plate with typical densities, try :: gmt flexure -Qttopo.txt -E10k -D2700/3300/1035 > flex.txt References ---------- Bodine, J. H., 1980, *Numerical computation of plate flexure in marine geophysics*, Tech. Rep. CU-1-80, Columbia University. See Also -------- :doc:`gmt `, :doc:`gravfft `, :doc:`grdflexure `, :doc:`grdmath `