CVM-S4.26 Proposed Final Model

Description

The CVM-S4.26 proposed final model corresponds to version 2.2.3 of our available model options. It is 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 and negative perturbations.

Presently, we have three possible options for incorporating the GTL:

1. Apply positive perturbations to the base model within the basin. Apply both positive and negative perturbations to the starting model outside of the basin.
2. Applying negative perturbations only if outside the basin and always applying positive perturbations even if inside the basin - to the starting model.
3. Same as 2. but disregard positive perturbations inside the basin - to the starting model.

Option 1 is currently the proposed final idea for the final CVM-S4.26 model, although we are evaluating each idea using 3D wave propagation simulations.

Algorithms and Plots

- 1st option (preferred)	2nd option	3rd option

Plots of option 2.2.3

Plots of option 2.2.2

Plots of option 2.2.1

Plots of base model

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

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

Algorithm for 2.2.3

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

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
        IF FINAL Vp / FINAL Vs < 1.45 THEN
            FINAL Vp = FINAL Vs * 1.45
        END IF     END IF
ELSE
    FINAL Vp = STARTING Vp + PERTURBATION Vp
    FINAL Vs = STARTING Vs + PERTURBATION Vs
    FINAL Rho = STARTING Rho
END IF

RETURN FINAL Vp, Vs, Rho

Algorithm for 2.2.2

IF BASE Vs < STARTING Vs THEN
    // Quick comment: As per the algorithm, for regions outside of the basin, STARTING Vs = BASE Vs, so this doesn't trigger.
    FINAL Vs = BASE Vs
ELSE
    FINAL Vs = STARTING Vs + PERTURBATION Vs
END IF

IF BASE Vp < STARTING Vp THEN
    // Quick comment: As per the algorithm, for regions outside of the basin, STARTING Vp = BASE Vp, so this doesn't trigger.
    FINAL Vp = BASE Vp
ELSE
    FINAL Vp = STARTING Vp + PERTURBATION Vp
END IF

FINAL Rho = STARTING Rho

IF FINAL Vp / FINAL Vs < 1.45 THEN
    FINAL Vp = FINAL Vs * 1.45
END IF

Algorithm for 2.2.1

IF (BASE Vs < STARTING Vs AND PERTURBATION Vs < 0) OR (BASE Vs > STARTING Vs AND PERTURBATION Vs > 0) THEN
    // Quick comment: As per the algorithm, for regions outside of the basin, STARTING Vs = BASE Vs, so this doesn't trigger.
    FINAL Vs = BASE Vs
ELSE
    FINAL Vs = STARTING Vs + PERTURBATION Vs
END IF

IF (BASE Vp < STARTING Vp AND PERTURBATION Vp < 0) OR (BASE Vp > STARTING Vp AND PERTURBATION Vp > 0) THEN
    // Quick comment: As per the algorithm, for regions outside of the basin, STARTING Vp = BASE Vp, so this doesn't trigger.
    FINAL Vp = BASE Vp
ELSE
    FINAL Vp = STARTING Vp + PERTURBATION Vp
END IF

FINAL Rho = STARTING Rho

IF FINAL Vp / FINAL Vs < 1.45 THEN
    FINAL Vp = FINAL Vs * 1.45
END IF

Starting Model Algorithm

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