Response to Reviewers
Reviewer 1: Dr. Martin Mai
+ Line 57: The statement "treated as point sources" is not correct in general; a number of
researchers treat the inside of subfaults independently, placing 4, 9, even 16 point-sources in each
sub fault which then rupture with pre-defined "internal" rupture speed which could be different from
the overall rupture propagation. See works by Delouis and others, and also Sekiguchi and others.
We have modified the text accordingly to avoid any misunderstandings.
+ Line 61: I would a short comment on the typical choices made to parameterize the elementary sliprate functions (boxcar, triangle etc pp)
Such a comment already exists in the discussion under the title “Resolution of Rise-time Function”.
In order to avoid redundancies, we decided to keep the text as it is.
+ Line 70-72: This sentence seems to imply that Husseini et al already had access to and studied
kinematic rupture models, which is not the case; their work is related to fracture mechanics as
applied to earthquakes. Rephrase for clarification.
We have rephrased the sentence to avoid any confusion.
+ Line 108: I found this statement related to "non-contiguous fault + patches" a bit confusing. In a
non-linear inversion in which rupture speed is a free parameters, this is possible. Also in a multi-time
window inversion in which the propagation speed of the first time window is specified, fault patches
can slip essentially at any time, independent of neighboring patches. One may argue to what extent
this is likely to happen, but numerous dynamic rupture model show such behavior.
Although codes seem to have that capability, it does not usually resolve that detail. We have
modified the sentence to avoid this unclarity.
+ Line 137: I am not sure I understand why more complicated dynamic rupture models would make it
difficult to isolate the main sources of uncertainty in kinematic inversion. Perhaps the authors can
clarify this further .. in particular since their end-member models are in fact quite complicated
already.
We have clarified that part in the main text.
+ Line 155: Not correct! There are many earthquakes by now for which we have abundant near-field
GPS and strong-motion data to perform finite-fault inversions. By using only 9, later 18 stations,
apparently homogeneously distributed, the authors limit themselves in a very peculiar way, and
actually deviate quite a bit from the current deployments we have. This point should perhaps be
discussed in more detail in later parts of the paper.
We have removed the sentences implying that this number of stations is a lot compared to the real
cases.
+ Line 166: Scenario V in itself is a very interesting case, as it is -- to my knowledge -- the first time
that a dynamic rupture simulation is carried out in a 3D random media. While the authors claim this
is "to test the effect of inadequate Greens functions" (Line 188), I have to object. The resulting
dynamic rupture model in itself is quite different, if we look at the details of Figure 9 and Figure 18
(top right): slip is higher, rupture is faster, near-surface rupture seems different, and presumably the
on-fault slip-rate functions at identical points are also quite different. In this case, the inversions
"struggle" with unknown Earth structure AND source complexity. It would thus be more correct to
place the slip-rate functions from Scenario III into a 3D-finite-difference code and simply propagate
the waves through the medium.
While we undertand the reviewer’s concern on “testing the effect of inadequate Greens functions” in
a strick sense, the reviewer’s suggestion does not solve this issue either. If we were to use the same
slip distriubtion with a different elastic structure, there will be an internal inconsistency in the
dynamic rupture model. Once we modify the elastic structure, that will affect the resulting rupture
propagation, that is, the same initial condition with a different elastic structure does not result in the
same slip distribution. This is why in Scenario 5, we have slightly modified the initial condition such
that the essential features of the source are similar to the ones in Scenario 3, as already described in
the text.
+ Line 178: is that the correct reference, to Ampuero (2002); seems like it should be Ampuero
(2008)?
The reference was incorrect. It should be Ampuero (2002) (his PhD thesis), and we have modified it
accordingly.
+ L 221: what determines the choice of the subfault dimensions?
We now explain this in the paragraph as “. The subfault size is set to 1.8 km along strike and 1.5 km
along dip which is chosen based on experience to be small enough to resolve the details of the
rupture with the given station distribution, while large enough to avoid longer computation time”.
+ Line 206: This is an interesting point: while the seismograms are "numerically" accurate at, say 0.2s
= 5 Hz, does the source excite these frequencies efficiently? Did you check the spectral amplitude
decay? We ran dynamic simulations in the past, where we thought we excited frequencies up to 4-5
Hz, but the overall smoothness of the rupture only lead to excitation below ~ 1 Hz ?
+ L 236: related to my above comment -- are the short periods (0.75s) actually excited by the source?
Where the synthetics filtered in any way before the inversion?
In order to answer that question, we have added Figure S5 and an associated discussion to the
section “Resolution of Rise Time Function”.
+ L 241: how are the weights chosen for each channel?
We have added this sentence to clarify “In this study, we keep the weight on each wavelet channel wj
same.
+ L 255, 1: did you check the sensitivity of the inversion results to the random initial model? Did you
choose the same initial random model for the various scenarios? I think this could be an important
factor to really understand what can be resolved and what remains unresolved.
No, initial model is always randomly generated at the first iteration, independently. This code has
been tested many times, and the authors also tested the initial model test, and since it is a heath
bath algorithm, and we start with high temperature, the output model is independent of the initial
model.
+ L 255, 2: what do you mean by "static error"? misfit in the GPS? Earlier it is stated these tests are
done w/o noise.
We have corrected the wording to clarify that we mean the misfit to the geodetic data.
+ L 259: why 800 iterations? perhaps the # of iterations should be based on some achieved misfit
level?
This is now explained in more detail in this section. We phenomonologically choose it large enought
so that misfit level stabilizes.
+ L 284: are there any rake variations in the dynamic output model? Or is that perfectly
fixed/constrained? The inversions reveal quite visibly rake variations. ..
We already have a sentence about the rake rotation in the dynamic models: `we assume that there is
no rake rotation in all the source scenarios.’
+ L 297: Is that a fair comparison if a 1-parameter rise inversion result is compared to a 2-parameter
inversion? Shouldn't we apply some ABIC-approach to judge which one is statistically better (more
useful)?
As mentioned in the text, the misfit is slightly lower for two parameter rise time case, since there are
more parameters to fit the same dataset. Here the goal is not imply that 2 parameter rise time is
better than 1 parameter rise time. Actually we later mention that adding more parameters does not
improve our understanding the way it is formulized.
+ L 305: the tendency of the rise time to be at the upper end of the + search range is interesting but
also concerning; any idea why that is? What if you expand the search range? A test would be useful
here!
We have performed this test. The resulting model is quite similar to the current model. The test
result is now in Figure S1.
L338: sorry to be so picky, but how do you quantify "satisfactory fit"? Variance reduction > 80% ?
Visually, all waveforms and GPS fit excellent ?.
We have changed this sentence now stating anything about 80% and higher variance reduction is
considered good.
+ L374ff: Figure 13 is -- to me -- the most important graph, as it illustrates (a) the inadequacy of
simplified source-time functions to map the dynamic rupture process (unless at very low frequencies)
and (b) that the inversion maps the arrival time of the peak=slip, but not of the first break of the slipfunction. (b) in fact then relates how we define rupture time. In the dynamic simulations (and
corresponding plots), the rupture time is the first-break of the Kostrov-like slip function, while in the
inversion it is the onset of the low-frequency wavelet. These two HAVE to be very different! If you
mapped the arrival time of the peak slip-rate, how would the inversion compare then? Moreover,
how do we define then "super-shear" rupture speed? Based on the first-break, or the time of peakslip? If on the first break, we may not care at all since there is little radiation coming off the fault,
while if the point of peak-slip-rate propagates fast, this is different. Goto & Sawada discuss this, but
note also Oglesby and Mai (2012) on this aspect.
+ Line 403: I cannot see anything in Fig 16 that is mentioned in this piece of text. Note also that the
waveforms seems to be very noisy in Fig 16 -- so something strange is going on ? please check and
clarify?
There is a paragraph on Figure 16, which probably the reviewer missed. There are multiple
references to Figure 16a and b. The waveforms have high frequency components due to rapid
changes in rise time, which is now added to the end of the section on Scenario IV.
+ Line 421: The equation is wrong .. the exponent should be (2+H)
For a three dimension, the exponent should be (3/2+H) as it is already shown. But, there should not
be a `=’ sign in the equation. So we have corrected the typo.
+ Line 467: Sorry, but I am unable to follow the argument here on the time smoothness ? related to
my comment (L 374) above? Please clarify!
+ Line 472: I am not sure I agree. Some inversion do use the absolute timing of seismograms, if it is
available. The statement also triggers the question how the authors have aligned their synthetic
seismograms? In this context, I would like to remark that the style of plotting for the seismic
waveforms (synthetics and predicted from inversion) is very unfortunate, as they don't show the
absolute timing, and hence decipher which ones are the near and which ones are the far-distant
stations (the letter-codes in the maps are too small, and not all stations are used).
Also, it is not clear how long a time series is fit; several seismograms clearly extend beyond the shown
20s, but this information is not available.
Even if the code is capable of including absolute timing, it is usually not used. The reason is that the
timing has to do with the velocity structure and it is more about the velocity structure than the
source processes. So unless a great detail is known about the velocity structure, it is safer to align on
the first arrival time. We have now added this argument to the text.
If we choose to show in absolute time, then the seismograms become too small to see. We chose to
show the details of the seismic waveforms, rather than absolute timing with much smaller
waveforms.
+ Line 476: The discussion on the average stress drop does not add anything useful to the paper;
since we are dealing with dynamic models to begin with, I don't think the stress-drop arguments are
very useful. I suggest to delete this whole section and related entries in Table 2.
+ Line 512: Figure 20 cannot be understood; I suggest to simply show a histogram or some sort of
frequency plot of these random-looking ratios.
We have taken the reviewers suggestion and changed the plots to histogram plots.
------------------------A few additional comments
------------------------+ I think the authors should include a paragraph in the introduction on recent attempts to better
understand the uncertainties in source inversion, by means of changing parameterizations (Hartzell
and co-authors), variable use of the available stations (Custodio et al; Page et al), Bayesian methods
(Monelli et al). It may also be useful to refer to some general discussion on source-inversion issues
(Beresnev, 2003; Ide and Beroza, 200x) ....
We have added such a paragraph to the introduction section.
+ The figure resolution is often quite low, and details remains barely visible (slip-value colorbar;
station names etc)
This is due to the PDF generated by BSSA. The original figures are of high quality.
+ Its is almost impossible to see the difference between green and black labels for stations (Figure 3a)
which I think should indicate which stations have been used for the inversion. Be more clear and
more specific.
We have fixed this problem by increasing the font size, and making plots more legible. We have also
indicated that stations with name in green are the ones used in the seismic inversion.
+ Why do use only 9, later 18, stations? Why a selection based on a regular grid, symmetrically
distributed? What happens if you "randomize" the selection of stations? Do you get the same
inversion results?
We believe that going into the grid size issue can be addressed as further research. Considering large
number of scenarios and the length of this article, it is beyond this study to address the station
distribution issue.
+ Try to cut the number of figures. Although I see that Fig 1-20 seem needed, these are a lot of very
similar plots to digest .. perhaps this can be streamlined ?
We believe that all the figures are essential, and hence we would like to keep them.
Finally: great paper, a pleasure to read and review! I am very much looking forward to the final
version.
Reviewer 2: Anonymous
1. Line 220: Wouldn't it be simpler just to use rupture time instead of distance d to hypocenter and
some velocity V that isn't really what we mean by instantaneous rupture velocity (except when
rupture velocity is constant)?
Obviously these two appproaches are identical. In the nonlinear appproach, it is quite common to
include rupture velocity as a parameter. This approach is useful since one can penalize deviations
from a constant rupture velocity.
2. Line 224: Isn't it true that DS(t) is the slip history? D has units of length and S is dimensionless,
right? If so, then the first sentence on line 224 is not quite right. Please clarify.
Yes there is normalization for S(t). S(t) has a unit area under it. We have clarified this issue now.
3. Equation (3) has strange formatting in the pdf version. I think this is an equation for _S (t), right?
The equation is correct in the original version, the problem is with the PDF creation.
4. Lines 396{397: The inversion is successful when adding more stations and when increasing the
permitted rupture velocity range. Which of these is more important, or are both necessary?
Most important was the range of rupture velocities, but it did not constrain enough, so both are
necessary.
5. Line 412: Are perturbations added also to density, or just wave speed?
The perturbations are only added to the velocity structure.
6. Line 473: I hadn't realized that most (all?) inversions ignore absolute time information, even when
available.
Please see the answer to the other reviewer: “Even if the code is capable of including absolute
timing, it is usually not used. The reason is that the timing has to do with the velocity structure and it
is more about the velocity structure than the source processes. So unless a great detail is known
about the velocity structure, it is safer to align on the first arrival time. We have now added this
argument to the text.”
7. Figure 3 (and similar Could you more carefully put a scalebar on here for the north-south and eastwest distances? There arenumbers on the bottom, 30.5, 31, and 31.5. What do they refer to? Same
for 41 and 41.25 on the left. Maybe this is some artifact of the plotting software?
We have fixed this now and removed which were hypothetical geographic coordinates, and instead
included a scalebar.
8. Line 1030: I think Figure 17 is for Scenario 4, not 3, as stated in the caption.
Thanks we have fixed this now.