CVM-S4.26 Proposed Final Model

Description

The CVM-S4.26 proposed final model was first described by Tom Jordan as an effort to integrate Po's perturbations while still honoring the CVM-S4 GTL. The desired effect is that we recover the CVM-S GTL while smoothly adding in positive perturbations.

Definition of Terms

• Base Model - CVM-S4 material properties as delivered by CVM-S4
• Starting Model for Inversion - CVM-S4 material properties with min Vs=1000m/s
• Final Model with Inversion - CVM-S4 with Perturbations

Algorithm

The proposed final model incorporates Po's 26th iteration in the following manner:

BASE Vp, Vs, Rho = CVM-S4 material properties
STARTING Vp, Vs, Rho = Po and En-Jui's starting model from which all the iterations were derived
FINAL Vp, Vs, Rho = Returned material properties
PERTURBATION Vp, Vs, Rho = Po and En-Jui's 26th iteration of perturbations

IF BASE Vs < 1000m/s THEN
    IF BASE Vs + PERTURBATION Vs < BASE Vs THEN
        FINAL Vp = BASE Vp
        FINAL Vs = BASE Vs
        FINAL Rho = BASE Rho
    ELSE
        FINAL Vp = BASE Vp + PERTURBATION Vp
        FINAL Vs = BASE Vs + PERTURBATION Vs
        FINAL Rho = BASE Rho + PERTURBATION Rho
    END IF
ELSE
    FINAL Vp = STARTING Vp + PERTURBATION Vp
    FINAL Vs = STARTING Vs + PERTURBATION Vs
    FINAL Rho = STARTING Rho + PERTURBATION Rho
END IF

RETURN FINAL Vp, Vs, Rho

The starting model is the one that Po and En-Jui used to begin their inversions. It is as follows:

LET CORNER Vp = 3000
LET CORNER Vs = 1500
LET CORNER Rho = 2300

LET MINIMUM Vp = 2000
LET MINIMUM Vs = 1000
LET MINIMUM Rho = 2000

LET BASE_MINIMUM Vs = 100
LET BASE_MINIMUM Vp = 283.637
LET BASE_MINIMUM Rho = 1909.786

LET STARTING Vp = BASE Vp
LET STARTING Vs = BASE Vs
LET STARTING Rho = BASE Rho

IF STARTING Vs < BASE_MINIMUM Vs THEN
    STARTING Vs = BASE_MINIMUM Vs
END IF

IF STARTING Vp < BASE_MINIMUM Vp THEN
    STARTING Vp = BASE_MINIMUM Vp
END IF

IF STARTING Rho < BASE_MINIMUM Rho THEN
    STARTING Rho = BASE_MINIMUM Rho
END IF

IF STARTING Vp < CORNER Vp THEN
    STARTING Vp = (CORNER Vp * (MINIMUM Vp - BASE_MINIMUM Vp) + STARTING Vp * (CORNER Vp - MINIMUM Vp)) / (CORNER Vp - BASE_MINIMUM Vp)
END IF

IF STARTING Vs < CORNER Vs THEN
    STARTING Vs = (CORNER Vs * (MINIMUM Vs - BASE_MINIMUM Vs) + STARTING Vs * (CORNER Vs - MINIMUM Vs)) / (CORNER Vs - BASE_MINIMUM Vs)
END IF

IF STARTING Rho < CORNER Rho THEN
    STARTING Rho = (CORNER Rho * (MINIMUM Rho - BASE_MINIMUM Rho) + STARTING Rho * (CORNER Rho - MINIMUM Rho)) / (CORNER Rho - BASE_MINIMUM Rho)
END IF

IF STARTING Vp / STARTING Vs < 1.45 THEN
    STARTING Vs = STARTING Vp / 1.45
END IF

RETURN STARTING Vp, Vs, and Rho