Work Plan for testing crustal thickness inversion with Stingray
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Create smooth 1D starting model
a. Extend the smooth 1D velocity model through the model space and add a
lower crustal velocity of 7.2 km/s
b. Define a smooth Moho relative to the seafloor by convolving the
srModel.elevation field with a 2-D Gaussian function where the sum of the
function adds to unity.
c. Use this to construct a Moho defined by model depth. In this case, 6 km
beneath the median filtered seafloor.
d. Create a welt of thicker crust with a function that takes the following
inputs:
i. The origin in model space
ii. Dimensions
iii. Rotation in degrees from north = 90 degrees
iv. Welt amplitude = 1 km
e. The bulge is formulated using an exponential, which allows me to define a
bulging surface with a major axis, a minor axis and total amplitude in the
model space.
f. This gives me a matrix that can be added to the Moho matrix created from
the elevation data.
Create predictions with from forward modeling arrivals based on the new
model using the 2D tlPert, srStation and srEvent that intersect the bulge in the
new synthetic model.
Take the tlOutput from the forward problem and make synthetic picks using
the function tlOutput2tlPick.m
Put these synthetic picks into tlArrival file that mimics the pick distribution of
the real data i.e. create the range limitations for source and receiver pairs that I
would expect in my own picks. Set the tlArrival.error to a non-zero value.
Create model with no bulge as a starting model for inversions using the
synthetic tlArrival file to test interface parameters.
Using this model I can test the sensitivity of user defined parameters using
synthetic data and determine trade offs between smoothing and resolution
with a known input.
a. The parameters to explore:
i. Smoothing
1. Interface smoothing (test from 5:50000 in order of sized
magnitude steps)
ii. Penalties
1. Interface penalty (Lagrangian multiplier for norm of
interface perturbations; test from .001:1000 in order of
magnitude sized steps)
Create model with no bulge and modified velocities to test slowness
parameters. To start with I have taken the starting model and applied a 5%
velocity change to the lower crust. This will force the inversion to choose
between crustal thickness and velocity.
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Using this model I can test the sensitivity of user defined parameters using
synthetic data and determine trade offs between smoothing and resolution
with a known input.
a. The parameters to explore:
i. Smoothing
1. Slowness smoothing in xy and z. (test from 5:50000 in
order of magnitude sized steps)
ii. Penalties
1. Slowness penalty (Lagrangian multiplier of the model
norm; test from .001:1000 in order of magnitude sized
steps)
Limit iterations to three while testing parameters so that I can minimize
computational time and utilize precompiled rays.
Once an ideal set of parameters has been identified redo inversions with a four
other starting models:
a. 7 km and 5 km starting moho depths
b. Vary the lower crustal velocity (6.8 km/s plus and minus 5 %)
Create additional synthetic models to test sensitivity to other geologic
possibilities (i.e. sloping interface, shingled interface etc.)