View source for CVM-SI

== Overview ==

CVM-SCEC Improved (CVM-SI), is a 3D seismic velocity model based upon original [[CVM-S]] with changes made based on full 3D tomography inversion results.

In the current implementation of CVM-SI, the CVM-SI software combines material properties from the starting CVM-S model, with CVM-S perturbations that are a result of iterations of inversion simulations by Chen et al (2011) and Lee et al (2010). 

The CVMSI query program combines the CVM-S starting model with perturbations. The goal of our cvmsi_query model is to generate high resolution velocity meshes (<100m mesh spacing) using low resolution perturbation model (500m).

The development is being done with CVM-S iteration 20 and higher. Previous CVM-SI implementations were done by combining the perturbations with the starting model directly and serving the low-resolution model. Our new approach serves the starting model at the desired resolution and modifying it based on interpolated values from the perturbation model.

'''Please note''': While the perturbations span the entire CVM-S region horizontally, they are only 50km deep. As such, querying CVM-SI 20 below 50km will simply return CVM-S material properties.

== Interpolation Methods ==

The broad idea behind CVM-SI21 is that we can take the low resolution perturbation mesh and interpolate it onto the CVM-S model, which is rule-based and therefore arbitrary precision. However, since the perturbations were calculated using a Vs minimum of 1000m/s, in certain areas of CVM-S (like boreholes), doing a straight trilinear interpolation of the perturbations with the CVM-S material properties can result in negative Vs and/or Vp values. 

In order to solve this problem, three interpolation methods have been proposed:

'''Cosine Taper Where Vs < 1000m/s'''

Since the inversions were done with a Vs minimum of 1000m/s, one proposed method is to do a cosine taper in sections of the CVM-S model that have Vs < 1000m/s. More precisely, we define this method as:

If CVMS_VS < 1000:<br />
&nbsp;&nbsp;&nbsp;&nbsp;CVMS_COS_RATIO = 0.5 * (1 + cos(PI - (CVMS_VS / 1000) * PI))<br />
&nbsp;&nbsp;&nbsp;&nbsp;CVMSI21_VS = (CVMS_COS_RATIO * CVMSI21_DVS) + CVMS_VS<br />
&nbsp;&nbsp;&nbsp;&nbsp;CVMSI21_VP = (CVMS_COS_RATIO * CVMSI21_DVP) + CVMS_VP<br />
Else:<br />
&nbsp;&nbsp;&nbsp;&nbsp;CVMSI21_VS = CVMSI21_DVS + CVMS_VS<br />
&nbsp;&nbsp;&nbsp;&nbsp;CVMSI21_VP = CVMSI21_DVP + CVMS_VP<br />
End If<br />

Where CVMSI21_DVS and CVMSI21_DVP are &#916;Vs and &#916;Vp (i.e. the perturbation).

Below are 5 plots that show the Vs 1D velocity profiles using this interpolation method.

*[http://northridge.usc.edu/cybershake/datarequest/plots/plot_USC.pdf USC cosine taper]
*[http://northridge.usc.edu/cybershake/datarequest/plots/plot_DLA.pdf DLA cosine taper]
*[http://northridge.usc.edu/cybershake/datarequest/plots/plot_PASC.pdf PASC cosine taper]
*[http://northridge.usc.edu/cybershake/datarequest/plots/plot_SVD.pdf SVD cosine taper]
*[http://northridge.usc.edu/cybershake/datarequest/plots/plot_Perris-2.pdf Perris-2 cosine taper]

'''Linear Scaling Between Vs > 800m/s and Vs < 1200m/s in the GTL'''

Another proposed method is to discard the perturbations in the GTL entirely when the CVM-S Vs is less than 800m/s and apply the perturbations fully when CVM-S Vs > 1200m/s. In between those values, we linearly scale the perturbation value so that 0% of the CVM-SI21 &#916;Vs value is applied at 800m/s and 100% of the CVM-SI21 &#916;Vs value is applied at 1200m/s. When we go deeper than the GTL (i.e. past 350m) we always apply the perturbations fully. The pseudo-code for this method is as follows:

If depth < 350:<br />
&nbsp;&nbsp;&nbsp;&nbsp;If original CVM-S Vs <= 800 m/s:<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Vs = CVM-S Vs<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Vp = CVM-S Vp<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Rho = CVM-S Rho<br />
&nbsp;&nbsp;&nbsp;&nbsp;Else if original CVM-S Vs > 800 m/s and original CVM-S Vs < 1200 m/s:<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Scaling factor = (CVM-S Vs - 800) / 400<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Comment: Note the above line calculates how far we are between 800 and 1200. If the Vs is 1100 m/s for example, then (1100-800) / 400 = 300/400 = 75%<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Vs = CVM-S Vs + (Scaling factor x Perturbation Vs)<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Comment: For our example above, this would mean if the original CVM-S Vs was 1100 m/s we would add 75% of the perturbation Vs to CVM-S Vs.<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Vp = CVM-S Vp + (Scaling factor x Perturbation Vp)<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Rho = CVM-S Rho<br />
&nbsp;&nbsp;&nbsp;&nbsp;Else if original CVM-S Vs >= 1200 m/s:<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Vs = CVM-S Vs + Perturbation Vs<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Vp = CVM-S Vp + Perturbation Vp<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Rho = CVM-S Rho<br />
&nbsp;&nbsp;&nbsp;&nbsp;End If<br />
End If<br />

Below are plots for the same 5 sites for this method:

*[http://hypocenter.usc.edu/research/plots/proposed_scheme_USC.pdf USC linear taper GTL]
*[http://hypocenter.usc.edu/research/plots/proposed_scheme_DLA.pdf DLA linear taper GTL]
*[http://hypocenter.usc.edu/research/plots/proposed_scheme_PASC.pdf PASC linear taper GTL]
*[http://hypocenter.usc.edu/research/plots/proposed_scheme_SVD.pdf SVD linear taper GTL]
*[http://hypocenter.usc.edu/research/plots/proposed_scheme_Perris-2.pdf Perris-2 linear taper GTL]

'''Cosine Scaling Between Vs > 800m/s and Vs < 1200m/s in the GTL'''

This interpolation method works similarly to the Linear Scaling method with the exception that our scaling factor is not linear but rather a cosine method. That is:

Scaling factor = 0.5 * (1 + cos(PI - ((CVMS_VS - 800) / 400) * PI))

This helps smooth out some discontinuities that might be seen in the linearly scaled version.

*[http://hypocenter.usc.edu/research/plots/plot_cos_USC.pdf USC cosine taper GTL]
*[http://hypocenter.usc.edu/research/plots/plot_cos_DLA.pdf DLA cosine taper GTL]
*[http://hypocenter.usc.edu/research/plots/plot_cos_PASC.pdf PASC cosine taper GTL]
*[http://hypocenter.usc.edu/research/plots/plot_cos_SVD.pdf SVD cosine taper GTL]
*[http://hypocenter.usc.edu/research/plots/plot_cos_Perris-2.pdf Perris-2 cosine taper GTL]

<!--

The following plots compare Vs profiles from 0 - 60km for the starting model and the CVM-SI20 final model for five sites in California.

The following plots compare Vs profiles from 0 - 1000m (1 km) at a query interval of 10m for the starting model, CVM-S, and the CVM-SI20 final model for the same five sites. The proposed GTL scheme dampens the perturbations in the GTL using the following algorithm:

If depth < 350:<br />
&nbsp;&nbsp;&nbsp;&nbsp;If original CVM-S Vs <= 800 m/s:<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Vs = CVM-S Vs<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Vp = CVM-S Vp<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Rho = CVM-S Rho<br />
&nbsp;&nbsp;&nbsp;&nbsp;Else if original CVM-S Vs > 800 m/s and original CVM-S Vs < 1200 m/s:<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Scaling factor = (CVM-S Vs - 800) / 400<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Comment: Note the above line calculates how far we are between 800 and 1200. If the Vs is 1100 m/s for example, then (1100-800) / 400 = 300/400 = 75%<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Vs = CVM-S Vs + (Scaling factor x Perturbation Vs)<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Comment: For our example above, this would mean if the original CVM-S Vs was 1100 m/s we would add 75% of the perturbation Vs to CVM-S Vs.<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Vp = CVM-S Vp + (Scaling factor x Perturbation Vp)<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Rho = CVM-S Rho<br />
&nbsp;&nbsp;&nbsp;&nbsp;Else if original CVM-S Vs >= 1200 m/s:<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Vs = CVM-S Vs + Perturbation Vs<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Vp = CVM-S Vp + Perturbation Vp<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;CVM-S4.20 Rho = CVM-S Rho<br />
&nbsp;&nbsp;&nbsp;&nbsp;End If<br />
End If<br />

*USC ([http://hypocenter.usc.edu/research/plots/plot_cos_USC.pdf cosine taper GTL]) ([http://hypocenter.usc.edu/research/plots/proposed_scheme_USC.pdf linear taper GTL])

*DLA ([http://hypocenter.usc.edu/research/plots/plot_cos_DLA.pdf cosine taper GTL]) ([http://hypocenter.usc.edu/research/plots/proposed_scheme_DLA.pdf linear taper GTL])

*PASC ([http://hypocenter.usc.edu/research/plots/plot_cos_PASC.pdf cosine taper GTL]) ([http://hypocenter.usc.edu/research/plots/proposed_scheme_PASC.pdf linear taper GTL])

*SVD ([http://hypocenter.usc.edu/research/plots/plot_cos_SVD.pdf cosine taper GTL]) ([http://hypocenter.usc.edu/research/plots/proposed_scheme_SVD.pdf linear taper GTL])

*PERRIS ([http://hypocenter.usc.edu/research/plots/plot_cos_Perris-2.pdf cosine taper GTL]) ([http://hypocenter.usc.edu/research/plots/proposed_scheme_Perris-2.pdf linear taper GTL])

-->

To see more about these sites and where they're located, we have provided the KML file:

*[http://hypocenter.usc.edu/research/UCVM/Profile_Sites.kml Profile Sites in KML format]

<!--

Horizontal and vertical slices for CVM-SI are available [http://www.compudav.com/cvmeval/chino_uf/plots/cvmsi_linear/ here]. For comparison, there are also [http://www.compudav.com/cvmeval/chino_uf/plots/cvms/ CVM-S slices] which have the same map dimensions and scales.

-->

== Perturbation Models ==

The model is expressed as a 3D grid of 1536 x 992 x 100 cells with a grid spacing of 500 m. Query points are smoothed by interpolating the surrounding eight grid points. The four corners of the model region are:

<pre>
  -116.00000000000000        30.449999999999999     
  -122.30000000000000        34.783499999999997     
  -118.94748257396012        38.303452459152524     
  -112.51822905852465        33.781862621842393     
  -116.00000000000000        30.449999999999999
</pre>

The map projection is a UTM zone 11 projection. The velocity model is C/Fortran code and associated files that are downloaded, compiled, and run locally. The user queries the models by creating an input file of latitude, longitude, and depth values, and the model returns Vp, Vs, and density at each of those points. 
This improved model has been imported into UCVM and is referenced with the model label "cvmsi".

== Iteration 20 Perturbations ==

The VP and VP perturbation results are posted the USC computer under: ~pochen/SC_F3DT_dV_SI20/

The perturbations are separated into few files:

CVM4SI20_dV_#  :  # from 001~100 for perturbations at different depths

The file format is:
<pre>
column 1: X
column 2: Y
column 3: Z
column 4: longitude
column 5: latitude
column 6: depth (m)  ; 0 is surface
column 7: dVP  (m/sec) ; VP of CVM4SI20 - VP of CVM4
column 8: dVS  (m/sec) ; VS of CVM4SI20 - VS of CVM4
</pre>

Attached a figure of waveform comparisons for Chino Hills event. In the figure, the black lines are data waveforms and the red lines are synthetic waveforms generated based on our current model.
We have applied a six-pole Butterworth filter with corners at 0.02 and 0.2 Hz to both waveforms. 

Few more iterations by using the scattering-integral and LSQR algorithms on the Mira. We will let you know, once we have a new model.

== Download CVM-SI ==

We have configured a software program called CVMSI_Query may be checked out from SVN with these commands:

 svn co https://source.usc.edu/svn/cvmsi/trunk

An UCVM distribution is available for download here [[UCVM]].

== References ==

# Lee, E., Chen, P., Jordan, T., & Wang, L., 2011.  Rapid full‐wave centroid moment tensor (CMT) inversion in a three‐dimensional earth structure model for earthquakes in Southern California, Geophysical Journal International, 186, 311–330.
# Chen, P., Lee, E., Jordan, T. H., Maechling, P. J., Denolle, M., & Beroza, G. C., 2011, Full-3D Waveform Tomography for Southern California, 2011 SSA Annual Meeting, Memphis, TN
# Lee, E., Chen, P., Jordan, T. H., Maechling, P. J., Denolle, M., & Beroza, G. C., 2010, Full-3D Waveform Tomography for Southern California, 2010 AGU Fall Meeting, San Francisco, CA

== Related Entries ==
*[[Community Velocity Model]]
*[[CVM-SI Inversion Models]]