Sismologı́a – Tarea 4
1. Project VESE (very expensive seismic experiment) deployed 60 seismometers in a linear array extending 240 km away from a large surface explosion. Despite careful picking of the resulting seismograms, the first-arrival
P-wave travel times (plotted in figure below and also given in the supplemental web material) show considerable scatter.
Fit these points with a series of straight lines and compute the ray parameter p and the delay time ? for each line. The first of these lines should
go through the origin (zero time and range). Be sure to take into account
the reduction velocity of 8 km/s in computing p. Using equation (5.12),
invert these results for a layer-cake P-velocity model of the crust and uppermost mantle. List your model in a table, starting with the surface layer
and continuing downward, with each line consisting of a depth (km) and
a velocity (km/s). Specify the velocity discontinuities between layers by
listing the depth twice, with the first line containing the velocity in the
upper layer and the second line the lower layer velocity. Make sure that
the first column of your table is absolute depth and not layer thickness.
For example, a three-layer model with a 2 km thick top layer of 4 km/s, a
4 km thick middle layer of 6 km/s, and a bottom layer of 8.1 km/s would
be written as: What is the Pn crossover distance? How thick is the crust
Table 1: default
0.0
2.0
2.0
6.0
6.0
4.0
4.0
6.0
6.0
8.1
in your model? How much uncertainty would you assign to your crustal
thickness estimate?
2. (MATLAB) You are given P-wave arrival times for two earthquakes recorded
by a 13-station seismic array. The station locations and times are listed
in Table 5.2 and also given in the supplemental web material.
(a) (a) Write a computer program that performs a grid search to find
the best location for these events. Try every point in a 100 km by
100 km array (x = 0 to 100 km, y = 0 to 100 km). At each point,
compute the range to each of the 13 stations. Convert these ranges to
time by assuming the velocity is 6 km/s (this is a 2-D problem, dont
worry about depth). Compute the average sum of the squares of the
residuals to each grid point (after finding the best-fitting origin time
at the grid point; see below). (b) For each quake, list the best-fitting
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location and origin time. (c) From your answers in (b), estimate the
uncertainties of the individual station residuals (e.g., ?2 in 5.30) for
each quake. (d) For each quake, use (c) to compute ?2 at each of the
grid points. What is ?2 at the best-fitting point in each case? (e)
Identify those values of ?2 that are within the 95% confidence ellipse.
For each quake, make a plot showing the station locations, the best
quake location, and the points within the 95% confidence region. (f)
Note: Dont do a grid search for the origin time! Instead assume an
origin time of zero to start; the best-fitting origin time at each grid
point will be the average of the residuals that you calculate for that
point. Then just subtract this time from all of the residuals to obtain
the final residuals at each point.
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