This electronic supplement expands on the process we used to choose the source length for the deconvolution in producing the teleseismic virtual-source reflection (TVR) images. The first step is to align and stack the recordings of an event at all stations to produce a stacked source (SS). The dark line in Figure S1 is an example of a stacked source function, with the 29 individual traces plotted in grey. By doing this, we improve the signal-to-noise ratio of the source while eliminating the significance of phases that arrive at different times at each station. This removes the contribution of horizontal-flat layers from the source functions. As a result, after deconvolution the appearance of flat layers from the source function is reduced or removed, and only the interfaces with 2D and 3D structures beneath the receivers remain in the TVR image.
We then scan the SS for the proper source length. The term scan refers to a process by which we truncate the SS to a length that spans from −2 s to a value that is obviously too short and produce a truncated stacked source functions (TSS). The TSS is first deconvolved from each recording of this event at each of the stations then convolved with the temporary estimate of the PPdp receiver function (RF) and subtracted from the original data. The residual data (RD, what is left after this subtraction) is presumed to be noise. We use the average of the RDs (ARD) from all the recordings as an estimate of how much signal is left in the data. Ideally,
ARD=RD(real signal) + RD(noise).
(S1)
By lengthening the TSS a slight amount through each iteration, the removal of the real signal becomes more efficient, and a plot of the ARD for all iterations would ideally flatten when we find the correct source length. However, in practice, adding unwanted signal into a source can add noise to the ARD plot, and the line may oscillate or increase in value again. The iterations stop once the ARD line has flattened and/or started to increase in value.
Figure S2 shows the plot of the ARD values for iterations from 0.8 s through 14 s for each of the four source functions used in the main paper. In the ARD plot for each function, the residual is small, while the TSS is obviously too short to include the main signal. Then, when the TSS is long enough to include the first peak but not the entire source function, it identifies every peak or trough as a signal and results in an RF that includes any repetition in the source functions. When this overly complicated RF is used to make ARD, it leaks a lot of this noise into the ARD and results in a very large value. As the length used to estimate the source function increases, the ARD value will drop and will ideally be a minimum when the source length is correct. Considering equation (S1), removing the RD of the real signal would ideally leave only the RD of the noise; and, once the minimum was reached, it should stay small. In practice, however, when the source length is too long, it can cause erroneous peaks to appear in the RF and result in an increase in the ARD. In these cases, the RD will increase in value and then drop again. Every event can behave differently. The peak residual values appear at different source lengths (4.2, 1.8, 1.2, and 1.2 s), but the TSS lengths are chosen by where this curve is at the maximum. In Figure S2a, we find that, as we hypothesized, the line flattened once an appropriate length was achieved. We chose 12 s as the source length for this event. Event 1 has the largest magnitude, Mb 7.3, while the others have similar magnitude, around Mb 5. This indicates that magnitude does have some influence on the length of the source wavelet in our case. We find that the ARD plot in Figure S2b flattens, but peaks rise back up from noise when the source length is longer than necessary. We chose a source length of 6 s for source 2. The ARD plots for sources 3 and 4 (Figures S2c and S2d, respectively) bottom out and then have a general increase in noise as the source length gets longer than necessary. This selection can be automated by either choosing the flattest spot (as in Figure S2a) or, in more common cases in which the ARD line increased in value after the local minimum was reached, pick the most significant local minimum before the ARD value starts to significantly increase. If we look at Figure S1, the obvious window that includes all phases common to the recording from every station was 4 s. On Figure S2b, the first local minimum after the major peak was also at 4 s. However, when we processed these data, we chose the window length of 6 s, which was based on the second local minimum (or just past it). We will show later that either choice may have worked well.
Figure S3 shows single-event TVR images produced by deconvolving the recordings of event 3 by the TSS with various source lengths. Figure S3a and S3b show the TVR profile for the shorter source lengths of 1.2 s (based on the first peak) and 2.2 s (at the first local minimum), respectively. In those figures, there are obvious flat reflectors that were not removed and are likely reflective of repetition in the source function, since they cross some of the curved horizons (which we interpret to be the real basin structure). However, the TVR in Figure S3b was based on a local minimum, so it included enough of the source function that the basin structure appears to be strong. We highlighted features common to Figures S3b–d in grey. The top flat horizon is believed to be a side lobe to the direct P, but the deeper curved horizons are likely noisy versions of real horizons. Note that these are strong on all plots with TSS longer than the first local minimum, which emphasizes the point that the TVR for event 2 using 4 and 6 s source lengths did not differ much (not shown here). The TVR in Figure S3c was based on the second minimum and appears the cleanest of the four plots. Figures S3b and S3d both have areas with strong noise (outlined in a dashed line) that are artifacts of using unfavorable TSS lengths. The TVR in Figure S3c has the simplest structure that is common to Figures S3b–d, which will lead to the least fantastic interpretations. This is consistent with the philosophy practiced in much of geophysics of favoring the simple model (i.e., inverting for smooth velocity gradients). As a result, we tend to favor TSS based on the second local minimum. The noise reduction made possible by stacking TVR from several events produces nearly the same stacked TVR if we choose the TSS based on the first or second local minimum.
Figure S1. Example of the stacked source function for event 2, using 29 individual traces. Notice how the first peak of the stack matches all the individual traces. The trough at 0.5 s is also clearly part of the real source function. The only remaining peak that is common to all traces is the positive peak at 2.2 s. A good source length here might be 3.5 s to 4 s or just after the third peak. We chose 6 s as the source length to include the entire source signal.
Figure S2. The relation of residual amplitude after deconvolution and the length of source wavelet. Panels (a), (b), (c), and (d) show the residual curves of events 1, 2, 3, and 4, respectively. The residual curve in each panel was normalized with the maximum value. The black dashed line shows the selected source length. The blue dashed lines show the source lengths selected for the comparison of TVR images in Figure S3. The residual is normalized for the comparison at difference source lengths.
Figure S3. TVR images constructed at different source lengths for event 3: (a) source length = 1.2 s; (b) source length = 2.2 s; (c) source length = 5 s; (d) source length = 8 s.
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