Difference between revisions of "UCVM Density Formula"

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We have reviewed how the density values are calculated in our tomography improved velocity models. We have determined that CVM-S4.26 calculated density from model Vs, and CCA06 provides density values in a data file. We reviewed algorithms to confirm that the same algorith is used to calculated density for both CVM-S4.6 and CCA06.
 
We have reviewed how the density values are calculated in our tomography improved velocity models. We have determined that CVM-S4.26 calculated density from model Vs, and CCA06 provides density values in a data file. We reviewed algorithms to confirm that the same algorith is used to calculated density for both CVM-S4.6 and CCA06.
  
== Compare Model Density to Formula Density ==
+
== Compare CCA06, CVM-S4.26 and CenCal Density to Nafe Drake Vs Density Relationship ==
 
If model uses the formula, we'd expect values to fall on a diagonal line in these plots.
 
If model uses the formula, we'd expect values to fall on a diagonal line in these plots.
  
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| [[File:cvms5_rho_versus_density_1000km.png|thumb|400px|CVM-S4.26 Density (rho) at Depth 1000m (Density in g/cm^3)]]
 
| [[File:cvms5_rho_versus_density_1000km.png|thumb|400px|CVM-S4.26 Density (rho) at Depth 1000m (Density in g/cm^3)]]
 
| [[File:cencal_rho_versus_density_1000km.png|thumb|400px|Cencal Density (rho) at Depth 1000m]]
 
| [[File:cencal_rho_versus_density_1000km.png|thumb|400px|Cencal Density (rho) at Depth 1000m]]
 +
| [[File:cvmh_rho_versus_vs_density_1000km.png|thumb|400px|CVM-H Density (rho) at Depth 1000m]]
 
|}
 
|}
  
From these plots, we conclude that CCA and CVM-S4.26 use the same density formula, scaled from Vs.
+
Looks like CCA06 and CVM-S4.26 use this Vs-based density scaling relationship, but CenCal and CVM-H do not.
  
We were told CVM-H uses a Vp-based scaling relationship to give a density value based on nafe_drake. We plot density values for selected points extracted from cvm-s4.26, cca06, and cencal.
+
== Compare CCA06, CVM-S4.26 and CenCal Density to Nafe Drake Vp Density Relationship ==
 +
UCVM also provides an algorithm that defines a scaling relationship between Vp values and density values on a nafe drake density relationship. These plots show density values for selected points extracted from cvm-s4.26, cca06, and cencal, and cvm-h.
 
{|
 
{|
| [[File:cca_rho_versus_density_1000km.png|thumb|400px| CCA Density (rho) at Depth 1000m (Density in g/cm^3)]]
+
| [[File:cca_rho_versus_vp_density_1000km.png|thumb|400px| CCA Density (rho) at Depth 1000m (Density in g/cm^3)]]
| [[File:cvms5_rho_versus_density_1000km.png|thumb|400px|CVM-S4.26 Density (rho) at Depth 1000m (Density in g/cm^3)]]
+
| [[File:cvms5_rho_versus_vp_density_1000km.png|thumb|400px|CVM-S4.26 Density (rho) at Depth 1000m (Density in g/cm^3)]]
| [[File:cencal_rho_versus_density_1000km.png|thumb|400px|Cencal Density (rho) at Depth 1000m]]
+
| [[File:cencal_rho_versus_vp_density_1000km.png|thumb|400px|Cencal Density (rho) at Depth 1000m]]
 +
| [[File:cvmh_rho_versus_vp_density_1000km.png|thumb|400px|CVM-H Density (rho) at Depth 1000m]]
 
|}
 
|}
  
 
+
== Vs-based Density Formula used in CVM-S4.26 and CCA06 ==
== Density Formula used in CVM-S4.26 and CCA06 ==
 
 
<pre>
 
<pre>
  
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   retVal = retVal * 1000
 
   retVal = retVal * 1000
 
   return retVal
 
   return retVal
 +
</pre>
 +
 +
== Vp-based Density Formula in UCVM ==
 +
<pre>
 +
# Density derived from Vp via Nafe-Drake curve, Brocher (2005) eqn 1. */
 +
def vp_2_density(vp):
 +
  # Convert m to km
 +
  vp = vp * 0.001
 +
  rho = vp * (1.6612 - vp * (0.4721 - vp * (0.0671 - vp * (0.0043 - vp * 0.000106))))
 +
  if (rho < 1.0):
 +
    rho = 1.0
 +
  rho = rho * 1000.0;
 +
  return
 
</pre>
 
</pre>
  
 
== Related Entries ==
 
== Related Entries ==
 
*[[UCVM]]
 
*[[UCVM]]

Latest revision as of 22:18, 27 May 2018

We have reviewed how the density values are calculated in our tomography improved velocity models. We have determined that CVM-S4.26 calculated density from model Vs, and CCA06 provides density values in a data file. We reviewed algorithms to confirm that the same algorith is used to calculated density for both CVM-S4.6 and CCA06.

Compare CCA06, CVM-S4.26 and CenCal Density to Nafe Drake Vs Density Relationship

If model uses the formula, we'd expect values to fall on a diagonal line in these plots.

CCA Density (rho) at Depth 1000m (Density in g/cm^3)
CVM-S4.26 Density (rho) at Depth 1000m (Density in g/cm^3)
Cencal Density (rho) at Depth 1000m
CVM-H Density (rho) at Depth 1000m

Looks like CCA06 and CVM-S4.26 use this Vs-based density scaling relationship, but CenCal and CVM-H do not.

Compare CCA06, CVM-S4.26 and CenCal Density to Nafe Drake Vp Density Relationship

UCVM also provides an algorithm that defines a scaling relationship between Vp values and density values on a nafe drake density relationship. These plots show density values for selected points extracted from cvm-s4.26, cca06, and cencal, and cvm-h.

CCA Density (rho) at Depth 1000m (Density in g/cm^3)
CVM-S4.26 Density (rho) at Depth 1000m (Density in g/cm^3)
Cencal Density (rho) at Depth 1000m
CVM-H Density (rho) at Depth 1000m

Vs-based Density Formula used in CVM-S4.26 and CCA06


#
# * Calculates the density based off of Vs. Based on Nafe-Drake scaling relationship.
# *
# * @param vs The Vs value off which to scale.
# * @return Density, in g/m^3.
# */
def vs_2_density(vs):
  # Density scaling parameters
  p5 = -0.0024189659303912917
  p4 = 0.015600987888334450
  p3 = 0.051962399479341816
  p2 = -0.51231936640441489
  p1 = 1.2550758337054457
  p0 = 1.2948318548300342

  retVal = 0.0
  vs = vs / 1000.0
  retVal = p0 + p1 * vs + p2 * pow(vs, 2) + p3 * pow(vs, 3) + p4 * pow(vs, 4) + p5 * pow(vs, 5)
  retVal = retVal * 1000
  return retVal

Vp-based Density Formula in UCVM

# Density derived from Vp via Nafe-Drake curve, Brocher (2005) eqn 1. */
def vp_2_density(vp):
  # Convert m to km
  vp = vp * 0.001
  rho = vp * (1.6612 - vp * (0.4721 - vp * (0.0671 - vp * (0.0043 - vp * 0.000106))))
  if (rho < 1.0):
    rho = 1.0
  rho = rho * 1000.0;
  return 

Related Entries