View source for 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:

2.2.1. Applying negative perturbations only if outside the basin and always applying positive perturbations even if inside the basin - to the starting model.<br />
2.2.2. Same as 2.2.1. but disregard positive perturbations inside the basin - to the starting model.<br />
<b>2.2.3. Apply positive perturbations to the base model within the basin. Apply both positive and negative perturbations to the starting model outside of the basin.</b><br />

Option 2.2.3 is currently the proposed idea for the final CVM-S4.26 model.

Definitions for the other two options are available on the [http://scec.usc.edu/scecpedia/GTL GTL page].

== Plots ==

Plots of [http://hypocenter.usc.edu/research/plots/new/cvms426_223/ option 2.2.3]

Plots of [http://hypocenter.usc.edu/research/plots/new/cvms426_222/ option 2.2.2]

Plots of [http://hypocenter.usc.edu/research/plots/new/cvms426_221/ option 2.2.1]

Plots of [http://hypocenter.usc.edu/research/plots/new/cvms426_100/ 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<br />
STARTING Vp, Vs, Rho = Po and En-Jui's starting model from which all the iterations were derived<br />
FINAL Vp, Vs, Rho = Returned material properties<br />
PERTURBATION Vp, Vs, Rho = Po and En-Jui's 26th iteration of perturbations<br />

== Algorithm for 2.2.3 ==

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

IF BASE Vs < 1000m/s THEN<br />
&nbsp;&nbsp;&nbsp;&nbsp;IF BASE Vs + PERTURBATION Vs < BASE Vs THEN<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;FINAL Vp = BASE Vp<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;FINAL Vs = BASE Vs<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;FINAL Rho = BASE Rho<br />
&nbsp;&nbsp;&nbsp;&nbsp;ELSE<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;FINAL Vp = BASE Vp + PERTURBATION Vp<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;FINAL Vs = BASE Vs + PERTURBATION Vs<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;FINAL Rho = BASE Rho <br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;IF FINAL Vp / FINAL Vs < 1.45 THEN<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;FINAL Vp = FINAL Vs * 1.45<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;END IF
&nbsp;&nbsp;&nbsp;&nbsp;END IF<br />
ELSE<br />
&nbsp;&nbsp;&nbsp;&nbsp;FINAL Vp = STARTING Vp + PERTURBATION Vp<br />
&nbsp;&nbsp;&nbsp;&nbsp;FINAL Vs = STARTING Vs + PERTURBATION Vs<br />
&nbsp;&nbsp;&nbsp;&nbsp;FINAL Rho = STARTING Rho<br />
END IF<br />

RETURN FINAL Vp, Vs, Rho

== Algorithm for 2.2.2 ==

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

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

FINAL Rho = STARTING Rho

IF FINAL Vp / FINAL Vs < 1.45 THEN<br />
&nbsp;&nbsp;&nbsp;&nbsp;FINAL Vp = FINAL Vs * 1.45<br />
END IF<br />

== 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<br />
LET CORNER Vs = 1500<br />
LET CORNER Rho = 2300<br />

LET MINIMUM Vp = 2000<br />
LET MINIMUM Vs = 1000<br />
LET MINIMUM Rho = 2000<br />

LET BASE_MINIMUM Vs = 100<br />
LET BASE_MINIMUM Vp = 283.637<br />
LET BASE_MINIMUM Rho = 1909.786<br />

LET STARTING Vp = BASE Vp<br />
LET STARTING Vs = BASE Vs<br />
LET STARTING Rho = BASE Rho<br />

IF STARTING Vs < BASE_MINIMUM Vs THEN<br />
&nbsp;&nbsp;&nbsp;&nbsp;STARTING Vs = BASE_MINIMUM Vs<br />
END IF<br />

IF STARTING Vp < BASE_MINIMUM Vp THEN<br />
&nbsp;&nbsp;&nbsp;&nbsp;STARTING Vp = BASE_MINIMUM Vp<br />
END IF<br />

IF STARTING Rho < BASE_MINIMUM Rho THEN<br />
&nbsp;&nbsp;&nbsp;&nbsp;STARTING Rho = BASE_MINIMUM Rho<br />
END IF<br />

IF STARTING Vp < CORNER Vp THEN<br />
&nbsp;&nbsp;&nbsp;&nbsp;STARTING Vp = (CORNER Vp * (MINIMUM Vp - BASE_MINIMUM Vp) + STARTING Vp * (CORNER Vp - MINIMUM Vp)) / (CORNER Vp - BASE_MINIMUM Vp)<br />
END IF <br />

IF STARTING Vs < CORNER Vs THEN<br />
&nbsp;&nbsp;&nbsp;&nbsp;STARTING Vs = (CORNER Vs * (MINIMUM Vs - BASE_MINIMUM Vs) + STARTING Vs * (CORNER Vs - MINIMUM Vs)) / (CORNER Vs - BASE_MINIMUM Vs)<br />
END IF <br />

IF STARTING Rho < CORNER Rho THEN<br />
&nbsp;&nbsp;&nbsp;&nbsp;STARTING Rho = (CORNER Rho * (MINIMUM Rho - BASE_MINIMUM Rho) + STARTING Rho * (CORNER Rho - MINIMUM Rho)) / (CORNER Rho - BASE_MINIMUM Rho)<br />
END IF <br />

IF STARTING Vp / STARTING Vs < 1.45 THEN<br />
&nbsp;&nbsp;&nbsp;&nbsp;STARTING Vs = STARTING Vp / 1.45<br />
END IF<br />

RETURN STARTING Vp, Vs, and Rho