Modelo de evaluación institucional

Events with greater angular coverage ( > 25°) have less error in the resolved source orientations (< 35°) than events with less angular coverage (Table 3.1, Figure 3.1). This relationship is apparent regardless of event frequency, indicating that the resolvability of the source orientation is dependent on receiver angular coverage (Figure 3.1). However, it is important to the note the relationship between the expected source radiation pattern and receiver angular coverage of that source (Figure 3.2). The angular coverage of events at locations 3d and 3e provides sampling of both sides of the fault planes such that both first- motion up and first-motion down P-wave polarities are detected at the receivers (Figure 3.2b-c). The orientation of the focal mechanism is constrained using these P-wave polarities (Dahm & Krüger, 2014, p. 29). The auxiliary plane is resolved for events at location 1b because of the symmetric radiation pattern of the DC source (Figure 3.2a).

When including the intermediate- and near-field terms in an unconstrained moment tensor inversion, the isotropic source has the least error (< 13%) in the resolved source mechanism because the least-squares minimization is finding a fit to a source with only P- wave amplitudes in the seismograms (Table 3.1).

Table 3.1: Full-wavefield moment tensor inversion results of synthetic seismograms with pure DC (top row), pure CLVD (middle row), and pure ISO (bottom row) sources generated in an isotropic medium and with a dominant event frequency of 125 Hz. The first column shows the input mechanism. The coordinates below each beach-ball indicate the output location from ISOLA where 0 m E, 0 m N is the true source location. The second, third, and fourth columns represent sources occurring at locations 1b, 3d, and 3e, respectively and are in order of increasing angular coverage and decreasing source-receiver distance from left to right. No constraints on the source mechanism are applied to the inversion. The beach-balls are colored by the amount of the resolved DC mechanism such that 100% DC is black and 0% DC is yellow.

Input Output

Figure 3.1: Error in source strike from results of full-wavefield moment tensor inversion of synthetic seismograms for a) DC sources and b) CLVD sources. Sources with greater angular coverage (locations 3d and 3e) have less error in the resolved source strike than sources with less angular coverage (location 1b). This relationship is apparent in all three of the tested dominant source frequencies: 50 Hz (red), 125 Hz (blue), and 175 Hz (green).

Figure 3.2: Lower-hemisphere stereographic projection of the P-wave radiation pattern of a DC source with strike of 66°, dip of 90°, and rake of 0° (dashed black line) with the angular coverage of the geophones (highlighted in white) relative to the source for an event at a) location 1b, b) location 3d, and c) location 3e. The auxiliary plane is perpendicular to the source orientation with a strike of 156° (purple dashed line). The orange areas represent the surrounding material moving outward from the source and the green areas represent the surrounding material moving inward to the source.

The results of the grid search for the moment tensor inversion of DC and CLVD sources at location 1b show a trade-off between correlation, resolved mechanism, and resolved strike

such that with increasing correlation, there is less error in the resolved mechanism but greater error in the resolved strike (Figure 3.3). This trade-off is only apparent at the location with the least angular coverage (Figure 3.3). The error in calculated source mechanism percentages is less for sources with small source-receiver distances (~300 m) and containing lower frequencies because of the less attenuated intermediate- and near- field amplitudes.

Figure 3.3: Plot of correlation versus resolved mechanism percentage for a DC source occurring at input locations a) 1b and b) 3e for all moment tensor inversion results in the grid search. The squares, diamonds, and triangles represent the results from the moment tensor inversion when the dominant source frequency is 50, 125, and 175 Hz, respectively. The points are colored by the error in the estimated strike where blue is greater error (up to 90°) and red is less error (0°).

The addition of 5% random Gaussian noise to the seismograms does not significantly alter the results of full-wavefield moment tensor inversion from that of the results of the noise- free seismograms (Figure 3.4).

Figure 3.4: Plots of comparison of the full-wavefield moment tensor inversion results for added noise (x-axes) versus noise-free (y-axes) cases for all three tested locations (1b, 3d, and 3e) and all results in the grid search. The addition of 5% random Gaussian noise does not have a significant effect on neither the a) resolved source mechanism nor b) the resolved strike of the source. The dash blacked line is the line with the equation x=y.

There is a relationship between event location and angular coverage of the source such that location 3e with the greatest angular coverage always has the minimum location error of zero meters except in the anisotropy and low frequency cases (Figure 3.5). Location 3d consistently has an error in location of approximately 50-55 m (Figure 3.5) and has the moderate angular coverage of the three test locations. Location 1b, with the worst angular coverage, has the most varied error in location (~32-70 m) (Figure 3.5).

Figure 3.5: Bar plots of location errors for a) DC sources, b) CLVD sources, and c) ISO sources. The five different test cases are plotted along the x-axis in order of: isotropy, anisotropy, noise, frequency of 50 Hz, and frequency of 175 Hz. Each case is separated into three different bars representing each location: 1b (red), 3d (purple), and 3e (green).

a) b)

3.1.1 Source Constraints

When using full-wavefield moment tensor inversion and applying the deviatoric constraint, the results for CLVD sources with greater angular coverage (> 25°) have less error in the estimated source mechanisms than the DC sources (Table 3.2). The source orientation is accurately resolved for the CLVD source located closest to the receivers (location 1b) because of the inclusion of the intermediate- and near-field terms and correct application of the deviatoric constraint (Table 3.2). However, the other two locations (3d and 3e) have greater error in the source orientation with the deviatoric constraint applied than the results of the unconstrained full-wavefield moment tensor inversion (Table 3.1).

Table 3.2: Full-wavefield moment tensor inversion results of synthetic seismograms with pure DC (top row) and pure CLVD (bottom row) sources generated in an isotropic medium and with a dominant event frequency of 125 Hz. The first column shows the input mechanism. The coordinates below each beach-ball indicate the output location from ISOLA where 0 m E, 0 m N is the true source location. The second, third, and fourth columns represent sources occurring at locations 1b, 3d, and 3e, respectively and are in order of increasing angular coverage and decreasing source-receiver distance from left to right. A deviatoric constraint in which the ISO component is assumed to be 0% is applied to the inversion. The beach-balls are colored by the amount of the resolved DC mechanism such that 100% DC is black and 0% DC is yellow.

Input Output

For the ISO source, there is an appearance of non-DC components in the outputted results for the events with greater angular coverage (> 25°) with the DC constraint applied (Table 3.3). On the other hand, the location with the least angular coverage (1b) resolves a dominantly DC source. The incorrect application of the DC constraint for moment tensor inversion of tensile sources results in greater error for sources with less angular coverage (14°) than for sources with greater angular coverage (> 25°).

Table 3.3: Full-wavefield moment tensor inversion results of synthetic seismograms with a pure ISO source generated in an isotropic medium and with a dominant event frequency of 125 Hz. The first column shows the input mechanism. The coordinates below each beach- ball indicate the output location from ISOLA where 0 m E, 0 m N is the true source location. The second, third, and fourth columns represent sources occurring at locations 1b, 3d, and 3e, respectively and are in order of increasing angular coverage and decreasing source- receiver distance from left to right. A DC constraint in which both the CLVD and ISO components are assumed to be 0% is applied to the inversion. The beach-balls are colored by the amount of the resolved DC mechanism such that 100% DC is black and 0% DC is yellow.

3.1.2 Anisotropy

The majority of the full-wavefield moment tensor inversion results in the entire grid search have less than a 15° difference in the resolved source strike between the isotropic and anisotropic cases (Figure 3.6a). On the other hand, the resolved strength of the DC mechanism has a greater difference of ~25%. These differences indicate that the neglect of

Input Output

anisotropy in the velocity model for moment tensor inversion introduces greater variation in the resolved source mechanism than the resolved source orientation (Figure 3.6b).

Figure 3.6: Comparison of full-wavefield moment tensor inversion (assumes isotropic seismic velocities) results for sources occurring in anisotropic (x-axes) and isotropic (y- axes) media. a) Comparison of the strike of the DC source shows little variability (< 15°) for all locations in the grid search. b) Comparison of the strength of the resolved DC mechanism shows greater variability (~25%). These results indicate that the neglect of anisotropy in the velocity model has a greater effect on the resolved mechanism percentages than the resolved source orientation. The dash blacked line is the line with the equation x=y.

The final outputted result for an ISO source at the location with the least angular coverage appears to be dominantly DC. However, the output mechanism is the only result in the entire grid search of the moment tensor inversion with the overestimated DC component (Figure 3.7). The source mislocation is a result of the neglect of anisotropy in the seismic velocities for the moment tensor inversion.

Figure 3.7: Full-wavefield moment tensor inversion results for an isotropic source occurring at location 1b with a dominant source frequency of 125 Hz in a 5% VTI anisotropic medium. The true source location is at 0,0. All locations in the grid search have resolved a high ISO component except for the output location selected as the location with the highest correlation.