# UCVM Density Formula

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.

## Contents

## 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.

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.

## 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