Merge pull request #360 from mibillen/fix_slab_tip

taper slab age at tip

CHANGELOG.md

@@ -29,6 +29,7 @@ This project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.htm
 ### Fixed
 - Using slabs and faults beyond the -180 to 180 range gave issues. These are now fixed and it now works and is tested for the -380 to 380 range. \[Menno Fraters; 2021-10-22; [#338](https://github.com/GeodynamicWorldBuilder/WorldBuilder/issues/338), [#340](https://github.com/GeodynamicWorldBuilder/WorldBuilder/pull/340) and [#342](https://github.com/GeodynamicWorldBuilder/WorldBuilder/pull/342)\]
 - The ridge coordinates for the mass conservative slab temperature model where not convered to radians interally. \[Menno Fraters; 2021-10-27; [#352](https://github.com/GeodynamicWorldBuilder/WorldBuilder/issues/352)\]
+- Fixed the taper of temperature at the slab tip for the bottom part of the slab, and fixed issue with negative temperatures above slab when there is an existing overririding plate temperature. \[Magali Billen; 2021-11-02; [#353](https:https://github.com/GeodynamicWorldBuilder/WorldBuilder/issues/353)
 
 ## [0.4.0] - 2021-06-22
 ### Added

source/features/subducting_plate_models/temperature/mass_conserving.cc

@@ -315,7 +315,7 @@ namespace WorldBuilder
               // Taper the heat_content and min temperature to create a smooth slab tip
               const double start_taper_distance =  total_segment_length -  taper_distance;
 
-              if ((distance_along_plane >= start_taper_distance) )
+              if ((distance_along_plane > start_taper_distance) )
                 {
                   initial_heat_content = initial_heat_content * (total_segment_length - distance_along_plane)/taper_distance;
 
@@ -332,15 +332,20 @@ namespace WorldBuilder
                   // 3. Determine the heat content for side 1 (bottom) of the slab
                   // Comes from integrating the half-space cooling model temperature
 
-                  const double time_since_subducting = (distance_along_plane / plate_velocity) * seconds_in_year; // m/(m/y) = y(seconds_in_year)
+                  double effective_plate_age = plate_age_sec + (distance_along_plane / plate_velocity) * seconds_in_year; // m/(m/y) = y(seconds_in_year)
+                  if (distance_along_plane > start_taper_distance)
+                    {
+                      effective_plate_age = effective_plate_age * (total_segment_length - distance_along_plane)/ (taper_distance);
+                    }
+
                   const double bottom_heat_content = 2 * thermal_conductivity * (min_temperature - potential_mantle_temperature) *
-                                                     std::sqrt((plate_age_sec + time_since_subducting) / (thermal_diffusivity * const_pi));
+                                                     std::sqrt(effective_plate_age /(thermal_diffusivity * const_pi));
 
                   // 4. The difference in heat content goes into the temperature above where Tmin occurs.
                   double top_heat_content = initial_heat_content - bottom_heat_content;
 
                   // Also need to taper the top_heat_content otherwise slab top will continue to thicken to the tip.
-                  if (distance_along_plane >= start_taper_distance)
+                  if (distance_along_plane > start_taper_distance)
                     {
                       top_heat_content = top_heat_content * (total_segment_length - distance_along_plane)/ (taper_distance);
                     }
@@ -352,17 +357,25 @@ namespace WorldBuilder
                       double time_top_slab = (1/(const_pi*thermal_diffusivity))*pow(((2*top_heat_content)/
                                                                                      (2*density*specific_heat*(min_temperature - temperature_ + 1e-16))),2) + 1e-16;
 
-                      // temperature = temperature_;
-                      temperature  = temperature_ + (2*top_heat_content/(2*density*specific_heat*std::sqrt(const_pi*thermal_diffusivity*time_top_slab)))*
-                                     std::exp(-(adjusted_distance*adjusted_distance)/(4*thermal_diffusivity*time_top_slab));
+                      // for overriding plate region where plate temperature is less the minimum slab temperature
+                      // need to set temperature = temperature_ otherwise end up with temperature less than surface temperature ;
+                      if (temperature_ < min_temperature)
+                        {
+                          temperature = temperature_;
+                        }
+                      else
+                        {
+                          temperature  = temperature_ + (2*top_heat_content/(2*density*specific_heat*std::sqrt(const_pi*thermal_diffusivity*time_top_slab)))*
+                                         std::exp(-(adjusted_distance*adjusted_distance)/(4*thermal_diffusivity*time_top_slab));
+                        }
                       // temperature = temperature_ + (2 * top_heat_content / (2 * density * specific_heat * std::sqrt(const_pi * thermal_diffusivity * time_top_slab))) *
                       //              std::exp(-(adjusted_distance * adjusted_distance) / (4 * thermal_diffusivity * time_top_slab));
                     }
                   else
                     {
                       // use half-space cooling model for the bottom (side 1) of the slab
                       temperature = background_temperature + (min_temperature - background_temperature) *
-                                    std::erfc(adjusted_distance / (2 * std::sqrt(thermal_diffusivity * (plate_age_sec + time_since_subducting))));
+                                    std::erfc(adjusted_distance / (2 * std::sqrt(thermal_diffusivity * effective_plate_age)));
                     }
                 }
               else

tests/app/mass_conserving_slab_temperature.dat

@@ -1,35 +1,19 @@
-# Profiles across a vertical slab 
+# Profiles across a slab dipping at 30 degrees 
 # Now define parameters:
 # dim = 2
 # compositions = 0
 # x z d g T 
-2420e3 0 50e3 10
-2440e3 0 50e3 10
-2460e3 0 50e3 10
-2480e3 0 50e3 10
-2500e3 0 50e3 10
-2520e3 0 50e3 10
-2540e3 0 50e3 10
-2560e3 0 50e3 10
-2580e3 0 50e3 10
-2600e3 0 50e3 10
-2420e3 0 150e3 10
-2440e3 0 150e3 10
-2460e3 0 150e3 10
-2480e3 0 150e3 10
-2500e3 0 150e3 10
-2520e3 0 150e3 10
-2540e3 0 150e3 10
-2560e3 0 150e3 10
-2580e3 0 150e3 10
-2600e3 0 150e3 10
-2420e3 0 600e3 10
-2440e3 0 600e3 10
-2460e3 0 600e3 10
-2480e3 0 600e3 10
-2500e3 0 600e3 10
-2520e3 0 600e3 10
-2540e3 0 600e3 10
-2560e3 0 600e3 10
-2580e3 0 600e3 10
-2600e3 0 600e3 10
+2490e3 0 5e3 10
+2495e3 0 5e3 10
+2460e3 0 25e3 10
+2475e3 0 35e3 10
+2495e3 0 55e3 10
+2540e3 0 125e3 10
+2365e3 0 125e3 10
+2375e3 0 135e3 10
+2395e3 0 160e3 10
+2425e3 0 200e3 10
+2085e3 0 395e3 10
+2095e3 0 425e3 10
+2125e3 0 445e3 10
+2155e3 0 470e3 10

tests/app/mass_conserving_slab_temperature.wb

@@ -6,11 +6,17 @@
   "specific heat":1000, "thermal diffusivity":1.0e-6,
   "features":
   [
-    { "model":"subducting plate", "name":"Slab",   
+    { "model":"oceanic plate", "name":"Overriding", "max depth":300e3,"min depth":0,
+      "coordinates":[[0,-100e3],[0,100e3],[2500e3,100e3],[2500e3,-100e3]],
+      "temperature models":[
+        {"model":"half space model", "min depth":-10e3,  "max depth":300e3, "spreading velocity":0.0625,
+        "top temperature":273, "bottom temperature":-1,
+         "ridge coordinates": [[0,-100e3],[0,100e3]]}]},
+	{ "model":"subducting plate", "name":"Slab",   
      "coordinates":[[2500e3,-100e3],[2500e3,100e3]], 
      "dip point":[0,0],
-	  "segments":[{"length":200e3,"thickness":[300e3],"top truncation":[-100e3],"angle":[90]},
-	  {"length":460e3,"thickness":[300e3],"top truncation":[-300e3],"angle":[90]}],
+	  "segments":[{"length":200e3,"thickness":[300e3],"top truncation":[-100e3],"angle":[45]},
+	  {"length":460e3,"thickness":[300e3],"top truncation":[-300e3],"angle":[45]}],
 	 "temperature models":[{"model":"mass conserving", "density":3300, "thermal conductivity":3.3,
 	 	"adiabatic heating":true,"plate velocity":0.125,
 	 	"ridge coordinates":[[12500e3,-100e3],[12500e3,100e3]], 

tests/app/mass_conserving_slab_temperature/screen-output.log

@@ -1,31 +1,15 @@
 # x z d g T 
-2420e3 0 50e3 10 1699.13 
-2440e3 0 50e3 10 1699.13 
-2460e3 0 50e3 10 1699.13 
-2480e3 0 50e3 10 1699.13 
-2500e3 0 50e3 10 718.923 
-2520e3 0 50e3 10 608.515 
-2540e3 0 50e3 10 891.918 
-2560e3 0 50e3 10 1135.44 
-2580e3 0 50e3 10 1328.92 
-2600e3 0 50e3 10 1471.07 
-2420e3 0 150e3 10 1752.63 
-2440e3 0 150e3 10 1752.63 
-2460e3 0 150e3 10 1752.63 
-2480e3 0 150e3 10 1752.63 
-2500e3 0 150e3 10 844.342 
-2520e3 0 150e3 10 650.018 
-2540e3 0 150e3 10 929.275 
-2560e3 0 150e3 10 1171.94 
-2580e3 0 150e3 10 1367.07 
-2600e3 0 150e3 10 1512.28 
-2420e3 0 600e3 10 2015 
-2440e3 0 600e3 10 2015 
-2460e3 0 600e3 10 2014.86 
-2480e3 0 600e3 10 1991.33 
-2500e3 0 600e3 10 1602.21 
-2520e3 0 600e3 10 1271.86 
-2540e3 0 600e3 10 1439.21 
-2560e3 0 600e3 10 1591.74 
-2580e3 0 600e3 10 1720.8 
-2600e3 0 600e3 10 1822.18 
+2490e3 0 5e3 10 314.684 
+2495e3 0 5e3 10 280.275 
+2460e3 0 25e3 10 810.382 
+2475e3 0 35e3 10 407.808 
+2495e3 0 55e3 10 828.11 
+2540e3 0 125e3 10 1589.85 
+2365e3 0 125e3 10 1617.34 
+2375e3 0 135e3 10 469.316 
+2395e3 0 160e3 10 920.435 
+2425e3 0 200e3 10 1452.72 
+2085e3 0 395e3 10 1649.95 
+2095e3 0 425e3 10 1029.35 
+2125e3 0 445e3 10 1342.83 
+2155e3 0 470e3 10 1658.84 

tests/app/mass_conserving_slab_temperature_proto.dat

@@ -0,0 +1,8 @@
+# Profiles across a slab dipping 30 degrees 
+# Now define parameters:
+# dim = 2
+# compositions = 0
+# x z d g T 
+2435e3 0 5e3 10
+2430e3 0 5e3 10
+2425e3 0 5e3 10

tests/app/mass_conserving_slab_temperature_proto.wb

@@ -0,0 +1,35 @@
+{
+  "version":"0.5",
+  "coordinate system":{"model":"cartesian"},
+  "cross section":[[0,0],[1000e3,0]],"surface temperature":273, "force surface temperature":true,
+  "potential mantle temperature":1673, "thermal expansion coefficient":3.1e-5, 
+  "specific heat":1000, "thermal diffusivity":1.0e-6,
+  "features":
+  [
+    { "model":"oceanic plate", "name":"Overriding", "max depth":300e3,"min depth":0,
+      "coordinates":[[0,-100e3],[0,100e3],[2500e3,100e3],[2500e3,-100e3]],
+      "temperature models":[
+        {"model":"half space model", "min depth":-10e3,  "max depth":300e3, "spreading velocity":0.0625,
+        "top temperature":273, "bottom temperature":-1,
+         "ridge coordinates": [[0,-100e3],[0,100e3]]}]},
+    { "model":"oceanic plate", "name":"Subducting", "max depth":300e3,"min depth":0,
+      "coordinates" :[[2500e3,100e3],[2500e3,-100e3],[4500e3,-100e3],[4500e3,100e3]],
+      "temperature models":[
+        {"model":"half space model", "min depth":0,  "max depth":300e3, "spreading velocity":0.05,
+        "top temperature":273, "bottom temperature":-1,
+         "ridge coordinates": [[4500e3,-100e3],[4500e3,100e3]]}],
+      "composition models":[
+        {"model":"uniform", "compositions":[0], "min depth":0, "max depth":100e3}]}, 
+    { "model":"subducting plate", "name":"Slab",   
+     "coordinates":[[2500e3,-100e3],[2500e3,100e3]], 
+     "dip point":[0,0],"max depth":1000e3,
+	  "segments":[{"length":350e3,"thickness":[300e3],"top truncation":[-200e3],"angle":[0, 90]}],
+	 "temperature models":[{"model":"mass conserving", "density":3300, "thermal conductivity":3.3,
+	 	"adiabatic heating":true,"plate velocity":0.05,"ridge coordinates":[[4500e3,-100e3],[4500e3,100e3]],
+	 	"coupling depth":80e3, "shallow dip":30.0, "taper distance":50e3, 
+	 	"min distance slab top":-50e3, "max distance slab top":300e3}],
+	 "composition models":[
+	 {"model":"uniform", "compositions":[0], "max distance slab top":100e3}]
+	 }      
+  ]
+}

tests/app/mass_conserving_slab_temperature_proto/screen-output.log

@@ -0,0 +1,4 @@
+# x z d g T 
+2435e3 0 5e3 10 385.65 
+2430e3 0 5e3 10 385.765 
+2425e3 0 5e3 10 385.881 

tests/app/spherical_slab_mass_conserving_slab_temperature/screen-output.log

@@ -27,7 +27,7 @@
 5930600 -388800 533000 200000 10 1780.01 
 5930600 -388800 533000 300000 10 1836.05 
 5930600 -388800 533000 350000 10 2834 
-5930600 -388800 533000 400000 10 1815.6 
-5930600 -388800 533000 403817 10 1838.65 
-5930600 -388800 533000 405000 10 1844.76 
+5930600 -388800 533000 400000 10 1847.39 
+5930600 -388800 533000 403817 10 1867.04 
+5930600 -388800 533000 405000 10 1871.92 
 5930600 -388800 533000 500000 10 1953.49