List of data files:
~~~~~~~~~~~~~~~~~~~
'cv.txt' is this text on the arrival time data by James Rutledge,
and on the data files resulting from the attempts to locate the
sources. This set of data files is denoted by 'cv' according to
the site name 'Cotton Valley'.
'cv-arr.dat', 'cv-stn.dat' and 'cv-list.dat' are the original data
files by James Rutledge. Their original file names were
'leo_75events_arrivals.dat', 'stn_list_loc.dat' and
'leo_top75_event_list.dat'.
'cv-arr.dat' contains the P-wave and S-wave arrival times of 75
events recorded at 13 receivers. For each event there are 14 lines.
The 1st line is the event name, next 13 lines are the picks and
hodogram azimuths to source, if reliably determined:
station, Ptime, Stime, az
A value of zero means no pick or no azimuth determined.
Time is in seconds from the start of record, az in degrees clockwise
from north.
'cv-stn.dat' contains the names and coordinates of 13 receivers:
stn_name, N, E, Z (ft)
The receivers are located in 2 vertical wells.
'cv-list.dat' is the list of the names of 75 events.
'cv-arr.for' is a simple program reading file 'cv-arr.dat' ,
separating P-wave and S-wave arrival times and writing them
into files 'cv-arrp.dat' and 'cv-arrs.dat'.
'cv-arrp.dat' and 'cv-arrs.dat' are the P-wave and S-wave arrival
times from file 'cv-arr.dat', reformatted for the SW3D software.
'cv-rec.dat' are the receiver positions from file 'cv-stn.dat',
reformatted for the SW3D software.
'cv-src.for' is a program resulting from not very successful
attempt to analytically perform simultaneous inversion for
hypocenters in a homogeneous velocity model.
'cv-src.dat' contains hypocentral coordinates and times resulting
from the above mentioned attempt at simultaneous inversion.
A questionable manual location using program 'cv-src.for' was
used to estimate an initial homogeneous model and initial source
positions for linearized simultaneous inversion.
After first tests, the vP/vS ratio was fixed to SQRT(3),
and a range of trial vP velocities was estimated.
For a given vP velocity, hypocentres were roughly estimated
by means of program 'cv-src.for' and arrival time residuals
were calculated. The homogeneous model and hypocentres with
the smallest residuals were selected. The velocities are
vP=18034 and vS= 10412.
File 'cv-src.dat' contains the roughly estimated hypocentral
coordinates and times.
'cv-crt.dat', 'cv-cod.dat', 'cv-rpa.dat', 'cv-writ.dat' are
the data for ray tracing by program 'crt.for'.
'cv-crt.h' is the history file to perform two-point ray tracing
in a model temporarily named 'cv-mod.out'. The file with source
coordinates is temporarily named 'cv-src.out'. The receivers
for two-point ray tracing are projected onto the vertical
reference plane approximately given by the 2 vertical wells.
'cv-crtp.dat' and 'cv-crts.dat' are the lists of results of ray
tracing for P and S waves used in the inversion.
'cv-sob.dat' is another data file used in the inversion.
It specifies the Sobolev norm minimizing the horizontal velocity
gradient to find a 3-D model close to 1-D.
'cv-srf.dat' is the auxiliary model file specifying the vertical
reference plane. It is only used during inversion to check the
distances of hypocentres from the reference plane.
'cv-inv1.h' is the history file to perform a single iteration of
simultaneous inversion for a velocity model and hypocentral
coordinates. It uses the results of ray tracing in the initial
model of the iteration. The file with initial source coordinates is
temporarily named 'cv-src.out'. The initial model is temporarily named
'cv-mod.out', and coincides with the template
model describing the parametrization of the final model of the
iteration. The final model of the iteration is also named
'cv-mod.out' and thus overwrites the initial model. The file
with final source coordinates resulting from the iteration
is temporarily named 'cv-srcn.out'.
'cv-inv.h' is the history file repeatedly executing history files
'cv-crt.h' and 'cv-inv1.h' in order to perform the whole simultaneous
inversion for a velocity model and hypocentral coordinates.
The inversion may be performed with various initial models
and with various parametrization of final models (homogeneous,
1-D, 3-D).
'cv-mod0.dat' and 'cv-src0.dat' are files with the initial
homogeneous velocity model and with corresponding initial source
coordinates. File 'cv-src0.dat' differs from file 'cv-src.dat'
by one source slightly shifted away from the reference plane only.
'cv-mod1.dat' and 'cv-src1.dat' are files with the homogeneous
velocity model and with corresponding source coordinates resulting
from 3 iterations starting with model 'cv-mod0.dat' and sources
'cv-src0.dat'. Homogeneous velocity model 'cv-mod1.dat' has been
converted into 1-D parametrization.
'cv-mod2.dat' and 'cv-src2.dat' are files with the 1-D velocity
model and with corresponding source coordinates resulting from
3 iterations starting with model 'cv-mod1.dat' and sources
'cv-src1.dat'. 1-D velocity model 'cv-mod2.dat' has been
converted into 3-D parametrization.
'cv-mod3.dat' and 'cv-src3.dat' are files with the 3-D velocity
model and with corresponding source coordinates resulting from
2 iterations starting with model 'cv-mod2.dat' and sources
'cv-src2.dat'.
'cv-mod04.dat' is just the initial homogeneous velocity model
'cv-mod0.dat' converted into 3-D parametrization.
'cv-mod4.dat' and 'cv-src4.dat' are files with the 3-D velocity
model and with corresponding source coordinates resulting from
9 iterations starting with model 'cv-mod04.dat' and sources
'cv-src0.dat'.
'cv-src.ps', 'cv-src0.ps', 'cv-src1.ps', 'cv-src2.ps', 'cv-src3.ps'
and 'cv-src4.ps' are the plots of horizontal positions of source
points from corresponding data files '*.dat'.
Hypocentral positions in 'cv-src.ps' are colour-coded according
to the P-wave velocity, i.e., all hypocentres have equal colour.
Hypocentral positions in 'cv-src1.ps', 'cv-src2.ps', 'cv-src3.ps'
and 'cv-src4.ps' are colour-coded according to the hypocentral
depth (9000 M, 9070 B, 9140 C, 9210 G, 9280 Y, 9350 R).
Conclusions
~~~~~~~~~~~
It is obvious from the above mentioned numerical experiments that
the arrival times are not sufficient to simultaneously estimate
both the velocity model and hypocentral coordinates. The arrival
times would be sufficient to approximately determine hypocentral
coordinates in a given velocity model. On the other hand, the
simultaneous inversion can simply adjust the velocity model to
given hypocentral coordinates.
The arrival times combined with velocities from well logs may be
used to estimate a 1-D mean velocity model. The velocities from
well logs may then be used to estimate the correlation function
describing the inaccuracy of the 1-D mean velocity model.
The location may then be performed in the 1-D mean velocity model.
The inaccuracy of the location may then be estimated using the
correlation function.