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Second draft version  5th October 1995



Program VELEST USER玈 GUIDE - Short Introduction



E. Kissling



Institute of Geophysics, ETH Zuerich





This short introduction corresponds to the VELEST Version 3.1 (10.4.95) by:



Edi KISSLING, Urs KRADOLFER, and Hansrudi MAURER

Institute of Geophysics and Swiss Seismological Service, ETH-Hoenggerberg

CH-8093 Zurich, Switzerland

Phone: [phone]; Fax  : [phone]; Telex: 823480 eheb ch

E-Mail addresses:	[e-mail]

(Internet)	[e-mail]      

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1.  Purpose and history of  VELEST



Program VELEST is a FORTRAN77 routine that has been designed to derive 1-

D velocity models for earthquake location procedures and as initial reference 

models for seismic tomography (Kissling 1988; Kissling et al. 1994). Originally 

written in 1976 by W.L. Ellsworth and S. Roecker for seismic tomography 

studies (under program name HYPO2D, see Ellsworth 1977; Roecker, 1978) 

VELEST has been modified by R. Nowack (who also gave it its current name), 

C. Thurber, and R. Comer who implemented (among other things) the layered-

model raytracer (Thurber 1981). In 1984 E. Kissling and W. L. Ellsworth after 

modifications of the flow structure and implementation of several new options 

used it to calculate a 'Minimum 1-D model' (i.e., a well-suited 1-D velocity 

model for earthquake location and for 3-D seismic tomography) for Long Valley 

area, California (Kissling et al., 1984). Since then VELEST has been applied to 

local earthquake and controled-source data from several areas in California, 

Alaska, Wyoming, Utah, and the Alps (Kissling 1988; Kradolfer 1989; Kissling 

and Lahr 1991; Maurer 1993). U. Kradolfer implemented the option to use 

VELEST as single-event-location routine and H. Maurer reintroduced the option 

to use both P- and S-wave data, separately or combined. Thanks to the cleaning 

efforts of U. Kradolfer and of H. Maurer the code no longer suffers from quick-

and-risky programming by too many authors. The current version of VELEST 

has been tested to correctly run under both UNIX (HP and SUN) and VMS 

(DEC) operating systems with (optimized) standard FORTRAN77 compilers.



If you need a reference please use Kissling et al. (1994) (see reference list) or the 

appropriate of the ones mentioned above. In order to avoid misunderstandings it 

is recommended that you also mention the version of the program.







2.  	Simultaneous Inversion and Coupled Hypocenter-Velocity Model 

Problem



This USER玈 GUIDE to VELEST is intended to provide a brief introduction on 

how to run and use the program to simultaneously locate earthquakes and to 

calculate 1-D (layered) velocity models with station corrections. As an 

introduction to the coupled hypocenter-velocity model problem the reader is 

referred to Crosson (1976), Ellsworth (1977), and Thurber (1981). The concept 

of a 'Minimum 1-D model' is described in detail by Kissling (1988) and Kissling 

et al. (1995), who also provide several examples of applications of such 1-D 

velocity models for both improved earthquake locations and as initial reference 

models for 3-D seismic tomography. Kissling et al. (1994) -after describing 

the effects of initial reference models on 3-D tomographic results- in an 

appendix provide a brief overview over the procedure to be followed 

to calculate a 'Minimum 1-D model' with VELEST. The following 

USER玈 GUIDE is written under the assumption that the reader is vaguely 

familiar with the problems and solutions described in the above mentioned 

publications (see reference list). Here only a brief overview will be given.



Program VELEST (iteratively, i.e., "non-linearly") solves

 

 * in 'simultaneous mode': 	the coupled hypocenter-velocity model problem 

for local earthquakes, quarry blasts, and shots; for 

fixed velocity model and station corrections 

VELEST in simultaneous mode performs the 

Joint-Hypocenter-Determination (JHD).



 * in 'single-event-mode': 	the location problem for local earthquakes, blasts, 

and shots.



The model consists of a (layered) 1-D velocity model and station corrections. In 

both modes the forward problem is solved by ray tracing from source to 

receiver, computing the direct, refracted, and (optionally) the reflected rays 

passing through the 1-D model. In both modes the inverse problem is solved by 

full inversion of the damped least squares matrix [AtA+L] (A= Jacobi matrix, 

At=transposed Jacobi matrix; L=damping matrix). Because the inverse 

problem is non-linear, the solution is obtained iteratively, where one 

iteration consists of solving both the complete forward problem and the 

complete inverse problem once (see Fig. 1). In 'single-event-mode' an 

additional singular value decomposition of the symmetric matrix AtA (in 

this case a 4*4 matrix only) is performed in order to calculate the 

eigenvalues.



Due to the intrinsic ambiguity of the inverse problem the final solutions 

obtained by VELEST are but a small part -and often the least significant 

part- of all the output of this program. VELEST has been designed to allow 

great flexibility in the approach and, therefore, a large number of options 

and control parameters must be set and properly adjusted in the process. 

Though default values may be obtained from the examples provided with 

the source code, the calculation of a Minimum 1-D model requires multiple 

runs with VELEST to select and test control parameters appropriate to the 

data set and to the problem. If you are in a hurry or if you are used to the 

idea that proper computer programs always provide a unique solution that 

is either obviously inappropriate or precise and correct, please accept the 

warning: To calculate a Minimum 1-D model a single or even a few VELEST 

runs are useless, as they normally do not provide any information on the 

model space (see chapt. 4)!



The principal procedure for simultaneous mode (and with minor modifica-

tions also for single_event_mode) is summarized in the flowchart given in 

Fig. 1. The main (print) output of VELEST reflects this procedure and 

provides detailed information about many intermediate calculation steps 

even within one single iteration step. It is mainly from these intermediate 

results that the appropriate control parameters are obtained through many 

runs of VELEST.

Please do not use resolution calculation in simultaneous mode. There is a 

bug in this part that will be fixed in version VELEST 3.2 by end of 1995.

           



          Fig. 1     Overview of procedure VELEST



3.  Installation of FORTRAN program VELEST:



VELEST version 3.1 may be obtained for UNIX (SUN and HP) machines and for 

VAX/VMS (DEC) systems. Please check that you get the appropriate source code 

among the files

-	VELESTUNIXSUN.F

-	VELESTUNIXHP.F

-	VELESTVMS.F  .

In each case you also need the file VEL_COM.F that contains the common bloc 

variables.

The difference between the UNIX and VMS version are the I/O - file attachments 

("open" - calls) only. Thus, in the UNIX versions you will find aside of each 

active line for opening call an additional line beginning with "cvms" with the 

open calls in the VMS-system and vice versa in the VMS version are lines 

beginning with "cunix" and the open calls for UNIX.

The only system-dependent calls are found in the two subroutines DATETIME 

and CPUTIMER; so if the program should be moved onto another machine, only 

these two small subroutines located at end of the source code have to be changed. 

Alternatively, delete all calls to these two routines which are not essential for the 

main calculations (they just provide run-time information). 



VELEST is currently set up to invert data in simultaneous mode from a maxi-

mum of 658 earthquakes (iepmax=658) and max. 50 shots or quary blasts 

(inshotsmax=50) with max. 500 observations per event (maxobsperevent 

=500). Current setting also allow a max. number of 500 stations in the 

station list (istmax=500), max. 2 velocity models (itotmodels=2) with max. 

100 layers per velocity model (inltot=100).

If you decide to need other dimensions please only adjust the parameters at the 

beginning of the file VEL_COM.F and compile the source with an (optimized) 

F77 compiler.



In addition to the source you should also get a set of files providing examples of 

input and output data for simultaneous mode. To each example there belong 5 

types of files:

Input:	-	*.cmn 	(control parameters)

	-	*.sta     	(station list)

	-	*.mod	(initial velocity model)

	-	*.cnv	(local earthquake data)

Output:	-	*.out	(main print output)





4.  Calculation of Minimum 1-D model (simultaneous mode)



Solutions to the coupled hypocenter-velocity model problem consist of the 

hypocenters, the velocity model, and station corrections. Each such solution may 

be rated by comparing its corresponding (calculated) travel times with the 

measured (observed) travel times. These travel time differences are called the 

misfit (or residuals) of the solution and we may measure the total misfit by using 

any Norm. Most often the RMS (root-mean-squared)-misfit of the solution is 

used.

Consider any possible combination of hypocenters, velocity model, and station 

corrections be rated by its RMS misfit for a well-posed problem that would only 

have one solution with minimal RMS. Such a situation could be represented by 

Figure 2a. In the case of the coupled problem with local earthquake data, 

however, such a diagram displaying the RMS misfit for various solutions most 

probably looks more like Figure 2b, where serveral local RMS minima occur. In 

such situations the solution obtained by any iterative algorithm strongly depends 

on the initial model and initial hypocenter locations.



 

Figure 2. 	Quality estimate of solutions to the coupled problem. a: Simple case 

with unique "best fit" solution. b: Normal case with several local 

minima of RMS misfit.



Unfortunately, we do not a priori know this function (Fig. 2b) and, therefore, we 

must search for different solutions with minimal misfit (RMS) by varying initial 

models and hypocenter locations within reasonable but large bounds. Thus, the 

calculation of a Minimum 1-D model amounts to a TRIAL-AND-ERROR process 

(for different initial models) with internal non-linear (iterative) INVERSION 

procedure, performed by VELEST.



Since VELEST does not automatically adjust layer thickness (as opposed to layer 

velocities), the appropriate layering of the model must be found by a trial-and-

error process. Thus the calculation of a Minimum 1-D model normally starts 

with

FINDING AN APPROPRIATE MODEL LAYERING.

Introduce layers according to refraction models and according to main phases 

visible in data when displayed similar to Fig. 3. 

Put the trial layer thickness at 2km for shallow crustal levels and increase 

layer thickness with increasing depth to about 4 to 5 km at Moho depth. Allow 

several 5km-thick layers in the depth range where you expect the crust-mantle 

boundary.



           

Figure 3. 	Phase correlation by refraction seismology type record section for 

stations grouped in sectors seen from epicenter.







SETTING APPROPRIATE DAMPING and CONTROL PARAMETERS



Begin without low velocity layers (LOWVELOCLAY=0) since they have strong 

effects on the ray paths and, thus, they increase the non-linearity of the problem. 

Set VTHET=1.0, STATHET=0.1, and the hypocentral damping parameters to 

0.01. Set INVERTRATIO to 1 and allow between 5 and 9 iterations. Normally, 

do not use shots or quarry blast data. Save this data for later testing (see below). 

The option to include (with special treatement) shot data has been implemented 

for specific VELEST use only.







INITIAL VALUES and FIRST INVERSIONS



INITIAL VELOCITIES: The average velocity for the crust should remain 

within reasonable bounds provided by information from controled-source 

seismology but otherwise try a large varity of initial velocity models. Set 

velocity damping parameters (vdamp) in Model File (*.mod) all equal to 1.0.



INITIAL HYPOCENTERS: Use the locations of best routine location 

procedure.

If your trial velocity model is largely different from the one used to obtain 

initial hypocenter locations you might want to try two VELEST runs, one 

with INVERTRATIO=1 and one with INVERTRATIO=2. In order to allow 

easy comparison do not vary any other parameter. If you feel like your 

hypocenters shift too much in the first iteration steps you might want to hold 

your initial model fixed (VTHET=999.) and let the hyopcenters and station 

corrections approach a local minimum. You may then use these final 

hypocenter locations and station corrections as initial parameters for the next 

run of VELEST where you let the model float again.

Note: Whenever you use final values as initial values for another VELEST run 

you are biasing your solution in a specific way, which is sometimes a good 

thing, since you want the solution to approach one of the minima.



INITIAL STATION CORRECTIONS: Set all of them to zero.





PROBING THE SOLUTION SPACE



Try to first get a feeling for the solution space (Fig. 2b) corresponding to your 

specific problem (stability and diversity of potential solutions) and for the 

robustness of your data.

Possible mathematical solutions to the coupled model-hypocenter problem span a 

much wider range than the physically reasonable solutions. Example: In one case 

a velocity model with one layer having a velocity of nearly zero showed an 

excellent fit to the data. By not allowing low-velocity layers in this first round of 

VELEST runs most such solutions may be avoided. One does, however, like to 

get a feeling for the range of the physically reasonable solutions and, therefore, 

one must try extreme initial velocity models as well. Normally, we have a fairly 

good idea about the probable average crustal velocity and about the Moho depth. 

Try several initial velocity models that fulfill these -even vague- constraints and 

that correspond with petrophysical arguments. Velocities near the surface may be 

as low as 2 km/s and as high as 6.5 km/s. Average velocities of lower crustal 

material may vary between 6 km/s and 7.8 km/s.

To probe the dependence of the solution on the initial model one should try at