GEOPHYSICAL JOURNAL INTERNATIONAL DOI: 10.1093/GJI/GGU029

MICROEARTHQUAKE MECHANISM FROM WAVE AMPLITUDES RECORDED BY A CLOSE-TO-SURFACE SEISMIC ARRAY AT OCNELE MARI, ROMANIA

Z. Jechumtálová, J. Šílený

Institute of Geophysics, Acad. Sci. of Czech Rep., Prague, Czech Republic

C-I. Trifu

ESG Solutions, Kingston, Canada

The resolution of event mechanism is investigated in terms of the unconstrained moment tensor source model and the shear-

tensile crack source model representing a slip along the fault with an off-plane component. Data is simulated as recorded by

the actual seismic array installed at Ocnele Mari (Romania), where sensors are placed in shallow boreholes. Noise is included

as superimposed on synthetic data, and the analysis explores how the results are influenced (i) by data recorded by the

complete seismic array compared to that provided by the sub-array of surface sensors, (ii) by using three- or one-component

sensors, and (iii) by inverting P- and S-wave amplitudes vs. P-wave amplitudes only. The orientation of the pure shear fracture

component is resolved almost always well. On the other hand, the noise increase distorts the non-double-couple components

(non-DC) of the moment tensor unless a high quality dataset is available. The shear-tensile crack source model yields

considerably less spurious non-shear fracture components. Incorporating recordings at deeper sensors in addition to those

obtained from the surface ones allows for the processing of noisier data. Performance of the network equipped with three-

component sensors is only slightly better than that with uniaxial sensors. Inverting both P- and S- wave amplitudes compared

to the inversion of P-wave amplitudes only markedly improves the resolution of the orientation of the source mechanism.

Comparison of the inversion results for the two alternative source models permits the assessment of the reliability of non-shear

components retrieved. As example, the approach is investigated on three microseismic events occurred at Ocnele Mari, where

both large and small non-DC components were found. The analysis confirms a tensile fracturing for two of these events, and a

shear slip for the third.

INTRODUCTION

Determination of source parameters requires good receiver coverage of the focal sphere. This condition is often difficult to

meet in case of induced microearthquakes, which are usually weak, with recordings characterized by low signal-to-noise ratio,

thus reducing the amount of data suitable for analysis. Monitoring of microseismicity can sometimes be carried out using a

seismic array that incorporates surface and borehole sensors. Surface sensors are easy to install, operate, and maintain, but their

ability to record very weak events is limited by noise. Borehole sensors provide higher quality data, but cost of drilling can be

substantial. In order to make the drilling cost effective, several sensors can be installed at different depths in each borehole.

Any three dimensional seismic array will be the result of a trade off between performance and cost.

A close-to-surface microseismic array was supplied and installed by ESG Solutions at Ocnele Mari (Romania) in 2005 for

the monitoring of the microseismicity generated during a controlled collapse of a large cavern in a solution mining field. This

array was specifically designed to identify, locate, and report in real-time the occurrence of microseismic activity. It included

36 one-component, 15 Hz omnidirectional geophones installed in 12 boreholes 160 to 360 m deep, three sensors per hole (Fig.

1). The boreholes were drilled vertically and were cased to about 80 m to avoid their closure. The depth of each hole was

designed to ensure that the bottom sensor is located within the salt layer.

Figure 1 Ocnele Mari microseismic array and coverage of the focal sphere (in equal-area, lower-hemisphere projection).

Between July 2005 and March 2006, approximately 2,400 seismic events with Mw -2.6 to 0.2 were recorded and located

with an average accuracy of 18 m (Trifu & Shumila, 2010). Most of the seismicity is related to the fragmentation and falling of

the major cavern roof, but smaller clusters are likely related to roof fragmentations of smaller, nearby caverns. Variations in

the b-value and the branching ratio suggest that the fracture process initiated in a linear pattern, and once the roof

fragmentation process began the fracturing continued super-critically (Trifu & Shumila, 2010).

A synthetic case study simulating seismic observations at Ocnele Mari is carried out. The analysis investigates the

resolution of microearthquake mechanism inversion, including the ability to detect real events, as well as the orientation of

pure-shear, and the content of non-shear fracture components. The latter are indicative of potential volumetric changes that

occur at the source as a result of a cavity collapse, pillar burst, crack opening or closing, etc. Two types of source models are

employed: a general moment tensor model and a shear-tensile crack model, both allowing for the presence of non-shear

fracture components. The effects of incorporating S-wave amplitudes in the dataset, deep sensors, one- (uniaxial) or three

component (triaxial) sensors, and the influence of noise contamination are analyzed. The study will also focus on the geometry

of principal strains, i.e., the orientation of the tension (T), pressure (P), and null (N) axes, and the capacity to identify non-

shear fracture components. Synthetic experiments are accomplished using data generated by (i) two types of shear-slip sources

(vertical strike-slip and 450 dip-slip), and (ii) a vertical single force. Finally, wave amplitudes determined by Trifu & Shumila

(2010) for a few events are processed in terms of the two source models, and the reliability of the derived parameters is

discussed, with particular reference to the non-shear component of the slip vector.

INVERSION METHODS

The analysis of weak micro-earthquakes often implies that the number of seismic sensors decreases, compared to those

used for larger seismic events, with the potential to render the inversion unstable. In addition, signal-to-noise ratio can be low,

and thus the phase picks have larger errors. To better understand the reliability of retrieved non-pure-shear fracture

components, we simulate data based on two alternative source models. First, an unconstrained moment tensor (MT) source

model is considered. The constraining on the amplitude inversion causes that we do not need to search for the source function.

Thus the relationship between wave amplitudes and the source parameters is a linear function through amplitudes of the

Green’s function (Aki & Richards, 1980; Langston et al., 1982). The formulation of linear inverse problem is straightforward

(e.g., Menke, 1989) and allows a fast retrieval of the six independent components M11, M22, M33, M12, M13 and M23 using the

singular value decomposition (Press et al., 1992).

Second, we invert for a source model which simulates a shear slip combined with a tensile crack. We call it a shear-tensile

crack (STC) source model. The STC may be a good model both for natural earthquakes and induced events. The design of the

STC model was based on the concept of a tensile crack originated at the tip of a fault where a shear slip occurs due to a loading

mechanism (Kozák & Šílený, 1985). Slip along the fault creates a stress concentration at its tip resulting in the tensile

fracturing, which radiates seismic energy almost synchronously with the shear slip. The reverse sequence with a fault slip near

a mined-out cavity represents the shear-implosive source model (Teisseyre, 1980; Rudajev & Šílený, 1985). A modified idea

of a shear slip along a fault accompanied by its simultaneous opening/closing due to the fault bending or surface roughness

yields the source model of a slip non-parallel to the fault (Dufumier & Rivera, 1997; Vavryčuk, 2001; Minson et al., 2007;

Vavryčuk, 2011), as shown in Fig.2. A slip along the fault with an off-plane component can be described by four angles,

pointing to the fault plane normal and non-orthogonal slip vector, namely the strike, dip, rake, and slope () angles, and a

magnitude. Decreasing the number of model parameter from six (general model) to five improves the inversion robustness,

even for less input parameters, but renders it non-linear, which is far more time consuming. In particular, we apply a two-step

grid search, combining a coarse grid across the entire model space with a fine grid in the low-misfit regions. Note that the

slope angle can be determined analytically from the MT solution (Dufumier & Rivera, 1997; Vavryčuk, 2001). However, since

the slope angle retrieval is unstable for small values of (Vavryčuk, 2001) STC results were derived using a numerical

approach. All STC parameters, i.e.four angles (strike, dip, rake and slope) and the scalar moment are searched for in a two-step

grid search (in turn, a coarse grid across the whole model space, and a fine grid in the vicinity of the best point from step 1).

Then, theMT corresponding to the STC solution is evaluated from them. This procedure is stable also for small values of the

slope angle.

Figure 2 STC source model: combination of shear-slip and tensile crack represented by the slip vector off the fault plane

and the slope angle α (α = 0° is pure shear slip, and α = 90° is a tensile crack).

SYNTHETIC TESTS

By simulating the configuration of the Ocnele Mari microseismic array, several synthetic tests are performed to explore

how the resolution of the mechanism inversion is influenced by the data quality. The epicentre of the synthetic event is situated

within the seismic array, in order to ensure a good coverage of the focal sphere (Fig. 1). Worth noting, the majority of the

actual recorded seismic events were located nearby. All datasets were independently inverted for both the MT and STC

models. Two types of theoretical sources were chosen to generate synthetic amplitudes: (i) a shear source with a vertical strike-

slip and a 450 dip-slip faulting, exactly described by both models, and (ii) a vertical single force that cannot be described by

either model. The latter is an interesting case when the data are incompatible with the source model employed in the inversion,

which leads to a systematic error in the retrieved mechanism. Further analysis will explore how this incompatibility is

projected into the parameters of the MT and STC source models, and evaluate the associated results regardless the

incompatible modelling. The effects of (1) inverting P- and S-wave amplitudes or P-wave amplitudes only, (2) using uniaxial

or triaxial sensors, (3) employing data from a combined array or surface sensors only, and (4) noise data contamination are

investigated. Our aim was simply to perturb the different sets of synthetic data (amplitudes of different waves, different sensors

or different station coverage), invert them and observe how they differ from the model used to generate the synthetic data. In

other words, to observe how random errors – a noise - in the data are projected into the model space – the parameters, in turn,

of the MT and the STC model. We were looking how the data perturbation by the noise affects the orientation of the retrieved

mechanism, and its content in terms of the “elementary mechanisms” into which it is decomposed, namely ISO, DC and

CLVD. We visualize the former by plotting the T,P,N axes, and the latter by using the Hudson plot. Since no detailed velocity

model is available for the region under study, computations are performed for a homogeneous half-space.

Shear slips

For pure strike-slip and dip-slip source mechanisms (Fig. 3), synthetic three-component P- and S-wave amplitudes are

computed at the sensors of the respective array (Aki & Richards, 1980). These amplitudes are then altered by artificial random

white noise with the maximum amplitude equal to 10, 20, 30, 40 and 50% of the maximum amplitude in the dataset. A total of

100 datasets are generated for each level of noise. Then, both P- and S-wave, and P-wave amplitude only datasets are inverted

using uniaxial or triaxial sensors of the combined network or the surface sensors only. Due to the noise, the resolved

mechanism is distorted. To visualize the deviation of the orientation, we display the principal axes T, P, N on the focal sphere,

the DC vs. non-DC content is shown in the Hudson plot (Hudson et al., 1989). The 100 resolved source mechanisms are

compared against the source for which the synthetic data were generated in terms of both the orientation and contents of the

non-shear components.

Figure 3 Source mechanism models: (a) strike-slip (dip 900, strike 2300, rake 00), and (b) dip-slip (dip 450, strike 3500,

rake 900) fault-plane solutions in equal-area projection of lower focal hemisphere; (c) Hudson plot of the decomposition of the

corresponding moment tensor; (d) histogram of the slope angle values.

The resolution of the event mechanism solution is assessed in terms of the orientation of the shear slip, as well as the

mechanism decomposition in principal fracture components. The shear-slip (double-couple or DC) part of the derived source

mechanism is shown by using the principal strain T, P and N axes projected onto the focal sphere. The non-shear component of

the derived source mechanisms is displayed differently for each of the source models. The widespread way of display of the

MT decomposition is the Hudson plot (Hudson et al., 1989). This is a two-dimensional equal-area projection showing the

contents of the decomposed parts of the MT by means of relative position of a dot to the locations of the fundamental source

types within a diamond-shaped patch. The pure-shear is located in the middle of the diamond, whereas the volumetric (V)

source is displayed on top (explosion) or bottom (implosion). The crack, dipole and compensated linear-vector dipole (CLVD),

both explosion and implosion, are situated on long edges of the diamond. In terms of the STC source model, there is only one

parameter describing a departure from the shear-slip, namely the slope angle . Distribution of the slope angle values

representing solutions of one hundred different noise samples superimposed onto the input amplitudes is presented as a

histogram.

The orientation of the DC component is determined quite well in almost all cases when both P- and S-wave amplitudes

were inverted (Fig. 4). This, however, deteriorates when P-wave amplitudes only are available, as the orientations of the

principal T, P and N axes are not constrained satisfactorily even for a relatively low noise contamination. For the strike-slip

source the effect of incorporating S-wave amplitudes is larger than employing triaxial sensors (Fig. 5). For dip-slip source the

orientation of the shear component is resolved much better than for strike-slip if only P-wave amplitudes are inverted (Fig. 6).

The use of deeper sensors in the event mechanism inversion allows the processing of a little noisier data (Fig. 7). Inversion

results are similar for both alternative source models (Figs. 8 and 9).

Figure 4 Comparison of MT solutions obtained for strike-slip source model by inverting noisy P- and S-wave amplitudes

or P-wave amplitudes only, considering the complete network in the setup of triaxial sensors. The orientation of the MT is

shown by its principal axes T (red), P (blue) and N (green), and non-shear part displayed in the Hudson plot.

Figure 5 Comparison of STC solutions obtained for strike-slip source model by inverting noisy data: P-wave amplitudes

from complete network, recorded by either triaxial or uniaxial sensors. The orientation of the STC is shown by its principal

axes T (red), P (blue) and N (green), and its non-shear part displayed using histograms of slope angles and the Hudson plot.

Figure 6 Comparison of MT solutions obtained for strike-slip and dip-slip source models by inverting noisy P-wave

amplitudes recorded by surface triaxial sensors of the array. For details see the caption of Fig. 4.

Figure 7 Comparison of STC solutions obtained for strike-slip source model by inverting noisy P- and S-wave amplitudes

recorded by triaxial sensors at all and surface station locations, respectively. For details see the caption of Fig. 5.

Figure 8 Comparison of MT and STC solutions obtained for strike-slip source model by inverting noisy P- and S-wave

amplitudes recorded by uniaxial sensors at all station locations. The mechanism orientation is shown by its principal axes T

(red), P (blue) and N (green), and its non-shear part is displayed using histograms of the slope angle and the Hudson plot.

Figure 9 Comparison of MT and STC solutions obtained for dip-slip source model by inverting noisy P- and S-wave

amplitude data recorded by triaxial sensors at all station locations. For details see the caption of Fig. 8.

The decomposition of the MT is distorted unless a high quality dataset is available, with noise level under 10-20%,

containing both P- and S-wave amplitudes, and at least uniaxial sensors are employed at all stations within the array, or triaxial

sensors are used at the surface stations (Figs. 8 and 10). If only P-wave amplitudes are inverted (Figs. 6 and 11), noise is

converted mostly into the CLVD component and, considerably less, into the V component. It implies that in the case of noisy

or insufficient data, the procedure creates spurious non-double-couple components of the unconstrained MT.

Figure 10 Comparison of MT solutions obtained for dip-slip source model by inverting noisy P- and S-wave amplitudes

recorded by triaxial and uniaxial sensors at the surface station locations. For details see the caption of Fig. 4.

Figure 11 Comparison of MT solutions obtained for strike-slip source model by inverting noisy P-wave amplitudes

recorded by uniaxial sensors located at all and surface station locations,respectively. For details see the caption of Fig. 4.

The non-shear part of STC source model is expressed by the slope angle . For a better comparison of the results obtained

using the MT and STC models, the Hudson plots for the STC model are also displayed (Fig. 12), in which the data points are

expected to be located along the (-crack,+crack) line only. The most frequent solution, corresponding to the maximum in the

histogram, is equal to the correct value =0° for all datasets, but it has a different width from case to case. The slope angle is

retrieved more precisely using P-wave amplitudes only than using both P- and S-wave amplitudes. This is, however, a

consequence of the fact the noise was constructed as a percentage of the maximum amplitude within the dataset. Since S-

waves are usually stronger than P, and the noise amplitudes are a percentage of the S-wave amplitudes, the noise

contamination of P-waves is larger when P- and S-waves are inverted together than if P-waves are treated alone. It means that

the noise experiments incorporating both P- and S-waves on one hand and experiments with P-waves only are not fully

comparable. Obviously, the noisier the data, the more uncertain is the slope angle. Inversion of triaxial data is moderately

better than that of uniaxial data (Fig. 5). The benefit of incorporating deeper sensors is small (Fig. 7). The non-shear part of the

dip-slip model is resolved worse in comparison with strike-slip model (Fig. 13), which is a consequence of the station

distribution with respect to the particular event: station projections are situated along the margin of the focal sphere, which

constrains better the nodal lines of the strike-slip than of the inclined dip-slip source.

Figure 12 Comparison of STC solutions obtained for dip-slip model by inverting noisy P- and S-wave amplitudes and P-

wave amplitudes only recorded by uniaxial sensors at all station locations. For details see the caption of Fig. 5.

Figure 13 Comparison of STC solutions obtained for strike-slip and dip-slip models by inverting noisy P- and S-wave

amplitudes recorded by uniaxial sensors at surface station locations. For details see the caption of Fig. 5.

Non-shear source: single force

The next series of synthetic tests is performed with data generated by a single force, representing a source departing from

both the MT and STC models, which characterize dipole sources. In both cases the data are inverted using an inconsistent

model. The motivation is to test how able are these models to report features of the true source. The cavity collapse was

modelled by the use of a vertical single force of 2106 N pointing downward. Its radiation pattern in P- and SV-waves is shown

in Fig. 14. The single vertical force has a bipolar P-wave radiation pattern which can never appear in the case of the MT and

STC models.

Figure 14 Wireframe diagrams displaying the radiation pattern of P- and SV-waves due to a vertical single force pointing

downward. P-wave (left): compressions – red, dilatations – blue; the vertical component of polarization vector of the SV-wave

points downward.

Similarly to the shear-slip source model in the previous section, synthetic one- and three-component P- and S-wave

amplitudes are evaluated at the sensors of the Ocnele Mari array for the single force. Inversions to derive the MT and STC

source models use both P- and S-wave amplitudes versus P-wave amplitudes alone, data at all sensors versus only at the

surface array locations only, as well as at triaxial versus uniaxial sensors (Fig. 15).

Figure 15 Resolved MT and STC source mechanisms for the single force model. Each source mechanism is displayed in

two ways: (1) a traditional fault-plane solution plot with nodal and source lines of the DC part of the source models,

respectively, directions of fault normal/slip vector (magenta) are also presented for the STC model, along with their principal

axes T, P and N axes (red, blue and green, respectively) in equal-area, lower- hemisphere projection and (2) a radiation

pattern of P-waves as a 3-D wireframe diagram (compression – red, dilatation – blue). The values of normalized residual

mean square (NRMS) are presented as well.

When only the surface sensor (both uniaxial and triaxial) data are incorporated in the inversion, different results are

obtained for both P- and S-wave amplitudes and P-wave amplitudes only. The inversion based on P-wave amplitudes exhibits a

very good fit. It is impossible to recognize the model inconsistency, and the vertical orientation is clearly obtained. The good

fit comes to no surprise as only one hemisphere is seen by these stations. The fit deteriorates significantly in case of inversions

carried out using both P- and S-wave amplitudes. As such, this can be used to identify an inconsistency of the source model

employed.

When data from all sensors are included in the inversion, this ensures a much better coverage of the focal sphere. As such,

source model inconsistency should be apparent in the decreasing of the fit to synthetic data. Results show that the above

discrepancy is slightly pronounced only when inverting from P-wave amplitudes. The addition of S-wave amplitudes

deteriorates the fit, but the vertical orientation of the radiation pattern continues to be clearly retrieved. In summary, there is no

significant difference between the two alternative source models when inverting from amplitudes generated by a model

inconsistent with both of them.

To better simulate actual data, P- and S-wave amplitudes are contaminated with random white noise with maximum

amplitude equal to 10, 20, 30, 40 and 50% of the respective wave amplitude. A total of 100 datasets with different noise

samples are generated for each noise level. MT solutions obtained by inverting both P- and S-wave amplitudes and P-wave

amplitudes only, recorded by triaxial sensors of the combined seismic array, are displayed in Figure 16. A linear trend in the

source mechanism between the compensated linear-vector dipole along P axis (marked –CLVD in the plot) and along T axis

(+CLVD) in the Hudson’s source type plot is apparent for P-amplitude inversions. This is probably caused by the fact that P-

waves, contrary to S-waves, are able to recognize volume changes, thus the resolution of the volume component in P-

inversions is higher. However, the value of this volume change, due to the model inconsistency is fictitious.

Figure 16 Comparison of MT solutions obtained for the model of the vertical single force by inverting noisy data P- and

S-wave amplitudes and P-wave amplitudes only available from all triaxial sensors of the array. For details see the caption of

Fig. 4.

Comparison of MT solutions obtained by inverting P- and S-wave amplitudes recorded by triaxial and uniaxial sensors of

the surface stations is shown in Figure 17. As expected, the source mechanisms are scattered more amply for uniaxial sensors.

Unlike the MT decomposition, there is not much difference in retrieving the correct orientation of the vertical source.

Figure 17 Comparison of MT solutions obtained for the model of the single force by inverting noisy P- and S-wave

amplitudes available from triaxial and uniaxial sensors located at the surface station locations of the array. For details see the

caption of Fig. 4.

Figure 18 plots results based on inverting noisy P-wave amplitudes recorded by uniaxial sensors at all station locations,

and only at the surface ones, respectively. In the presence of low noise, the resolution of the event mechanism is improved if

all sensors are used. Interestingly, in case of high noise data, the resolution does not appear to be influenced by the addition of

deeper sensors.

Figure 18 Comparison of MT solutions obtained for the model of the single force by inverting noisy P-wave amplitudes

recorded by uniaxial sensors at all station locations, and at those of the surface ones. For details see the caption of Fig. 4.

STC solutions obtained from combined noisy P- and S-wave amplitudes and noisy P-wave amplitudes only recorded by

uniaxial sensors at the surface array locations are displayed in Figure 19. When using only P-wave amplitudes, the derived

slope angles have only negative values, contrary to both positive and negative values obtained from P- and S-wave amplitudes.

This is not surprising, since the surface sensors “see” only the upper part of the radiation pattern, which is similar for the single

force and the 1-D implosion in P-waves, but not in S-waves. In other words, in P-waves the single force and STC source model

are closer to compatibility than in case of the combined P- and S-waves. The resolution of the mechanism orientation is,

however, opposite: P-axis is stable from P- and S-waves and scattered from P-waves only. This probably coincides with the

conditioning of the inversion, as the solution based on P- and S-waves is definitely better constrained than that based on P-

waves only.

Figure 19 Comparison of STC solutions obtained for the model of the single force by inverting noisy P- and S-wave

amplitudes and P-wave amplitudes only recorded by uniaxial sensors at the surface station locations. For details see the

caption of Fig. 5.

A similar comparison, but employing the complete array (Fig. 20) yields similar results (Figs. 19 and 20). This is because

the surface sensors only “see” the upper part of the P-wave radiation pattern, which is similar for the single force and 1-D

implosion. The inversion results remain largely similar, despite a few discrepant observations related to the lower radiation

patterns, which come from the deeper sensors, located below the event focus.

Figure 20 Comparison of STC solutions obtained for the model of the single force by inverting noisy P- and S-wave

amplitudes and P-wave amplitudes only recorded by triaxial sensors at all station locations. For details see the caption of Fig.

5.

EXAMPLES OF REAL EVENTS

Using the two above mentioned source models, mechanism inversions are carried out for several microseismic events

occurred at Ocnele Mari. All available P- and S-wave amplitudes are employed, with the former ones dominant. The attempt is

to compare the results derived in order to obtain a better insight into the presence of non-shear components in the event

mechanism. This is not an attempt to interpret the mechanisms derived in terms of the phenomena taken place as a result of the

particular operations performed to induce the cavern roof collapse.

Figure 21 presents the MT solutions of three events associated with minor collapses on (i) November 26, 2005 at 15:23,

(ii) December 14, 2005 at 00:07, and (iii) the major cavern collapse on December 23, 2005, at 08:21 (Trifu & Shumila, 2010).

For each event the traditional fault-plane solution and principal T, P and N axes (red, blue and green, respectively), are shown

on an equal-area, lower-hemisphere projection. There are also histograms of the individual components of the MT solution,

namely the double-couple (DC), volumetric (V) and compensated linear-vector dipole (CLVD). We used decomposition of

resultant MTs into percentage of the DC, V and CLVD components introduced by Vavryčuk (2001). The actual percentage of

these components in the best fit solution is also mentioned. The colour shades represent the confidence zone areas where the

normalized root mean square (NRMS) remains below a certain percentage of the best value. Dark, medium and light colour

shades correspond to 105, 110 and 125% of the best NRMS. The STC solutions of the same three events are shown in Figure

22. For STC model we display retrieved fault plane and a plane perpendicular to the slip. These two planes are called source

planes (Vavryčuk, 2011) and they are not necessarily perpendicular to each other. For slope angle equal to zero they

correspond to nodal planes. Plots of source lines (Vavryčuk, 2011) and directions of fault normal/slip vector, as well as plots of

principal T, P and N axes (red, blue and green, respectively) are presented in the same projection mentioned above. To have an

error estimate of retrieved source parameters, confidence zones of directions of fault normal/slip vector, principal T, P and N

axes are constructed. Slope angle histograms are displayed too. To compare the confidence level of the MT and STC

solutions, the histograms of the DC, V and CLVD fracture components corresponding to the MT solutions evaluated from the

resolved STC are presented as well. In order to visualize the confidence level, the same percentages are applied as employed

for the MT solutions. There is an excellent agreement in retrieving the orientation of the source using both models, which can

be observed by comparing the principal axes and nodal lines in Figure 21 with source lines in Figure 22.

Figure 21 Source mechanisms of real events (a, b and c) retrieved using the MT source model. The traditional fault-plane

solution and principal T, P and N axes are displayed together with histograms of the individual DC, V and CLVD components.

The confidence zones are represented by the colour shades corresponding to 105, 110 and 125% of the best NRMS.

Figure 22 Source mechanisms of real events (a, b and c) retrieved using a STC model. The source lines along with the

directions of fault normal/slip vector and principal T, P and N axes are displayed together with histograms of the slope angle,

DC, V and CLVD components of the MT source model evaluated from the STC solutions. For details see the caption of Fig. 21.

MT solutions of all three events have roughly the same ratio of shear to non-shear components, but their mechanisms are

different. The first event has a high non-DC, explosion-like component amounting to 31%. The STC model results in the slope

angle of 11.5°, yielding as much as 44% of non-DC component. Its sign is positive, which means crack opening. This result is

consistent in both the MT and STC models. Also, the histograms of V, and CLVD fracture components are fairly narrow

and situated in positive values well above zero. This indicates that tensile fracturing might be the real mechanism of this event.

The consistence of both source models is supported by similarly good match of the synthetic amplitudes to the data in terms of

the NRMS value: 0.23 and 0.32, respectively. The MT solution of the second event has high (40%) V and very low (2%)

CLVD components, which is inconsistent with the crack model requiring V/CLVD = 5/4 for a standard set-up of equal Lamé

constants and . It suggests a combination of shear-slip with a blast. The STC source model offers a comparable match of the

data (0.72 versus 0.63 for the MT), with a combination of shear-slip and tensile cracking. However, the DC histogram is very

wide, indicating an uncertain determination of the shear-slip component. Contrary to that, the V and CLVD histograms are

narrow, suggesting a well constrained tensile crack. According to both the source lines and T-axis, the crack is oriented

horizontally. The confidence zones of the T-axis, the fault normal and the slip vector are stretched largely in the azimuth but

very narrow in the take-off angle, which means that the tensile crack, though rather uncertain in azimuth, keeps a horizontal

orientation of its normal very well. As such, it resembles the tensile crack cited by Hasegawa et al. (1989) and the

manifestation of a potential breaking of the cavern roof due to loading of the overlying strata. The third event is matched

equally by both source models: 0.44 with the MT vs. 0.45 with the STC. Both models yield dominant shear-slip (DC)

component of 73 and 91%, respectively. The value of the best-fit slope is 20, with the confidence interval including the value

zero, which can be interpreted that pure shear (=00) could well be the actual solution.

CONCLUSIONS

Based on extensive synthetic tests, the resolution of the microearthquake mechanism is explored as a function of the

quality of the dataset in terms of using uni- vs. three-component sensors, employing data from surface sensors only vs. all

sensors in the array, inverting both P- and S-wave amplitudes vs. P-wave amplitudes only, and assuming several levels of noise

contamination. The analysis results obviously depend on the sensor array configuration. This study made use of the

microseismic network deployed at Ocnele Mari, Romania for monitoring the seismicity associated with an induced collapse of

a large cavern generated by solution mining in salt rock. For any particular array configuration, the resolution of the event

mechanism also depends on the particular type of mechanism occurred within the study region. Therefore, two shear-slip

fracture mechanisms were considered, strike-slip and inclined dip-slip. Two source models were employed in the description

of the event mechanism: unconstrained moment tensor (MT) model, resolved through linear inversion, and shear-tensile crack

(STC) model, yielding non-linear inversion but benefiting from less parameters needed for its description. Finally, a single

vertical force was added to the analysis, in order to test the results of mechanism inversions using an inconsistent source

model.

As already reported in numerous studies, the geometry of the mechanism, i.e. its orientation in terms of the MT principal

axes, is remarkably robust, contrary to the elemental fracture components in terms of the mechanism decomposition. The

percentage of the DC vs. non-DC components depends much more of the factors listed above than the DC orientation. The

same feature was found for the STC model, though the spurious non-shear components are notably smaller than in case of the

MT model. In particular, the principal features of the resolution of the retrieved mechanism are as follows: (a) The

performance of the array equipped with three-component sensors is only slightly better than that with only one –component

sensors. (b) Incorporating deep sensors in addition to the surface sensors allows for the processing of noisier data. (c) Inverting

both P- and S-wave amplitudes compared to the inversion of P-wave amplitudes only markedly improves the resolution of the

mechanism orientation.

Detailed conclusions are as follows. For both the MT and STC source models: (a) the orientation of the mechanism is

determined well in all cases investigated except that with extreme noise contamination; (b) for the strike-slip source, the effect

of incorporating S-wave data (i.e., inverting both P and S instead of P only) is more significant than that of employing three-

component in addition to one-component sensors; and (c) dip-slip source model is much better resolved than the strike-slip

model if P data only are employed.

Regarding the decomposition of the unconstrained MT model: (a) results are distorted in most cases if data are

contaminated by noise, with the degree of distortion depending on data scarcity: (i) employing the surface sensors only, (ii)

neglecting horizontal components, (iii) avoiding S-wave readings; (b) if only P-wave amplitudes are inverted, the noise is

converted mostly into the CVLD component; (c) in case of a strike-slip source, the effect of employing three-component, in

addition to one-component sensors is negligibly small, i.e. the benefit of deploying deep sensors is small. In as far as the STC

model is concerned, in particular the determination of the slope angle : (a) the angle suffers from distortion similarly to the

decomposition of the MT, but to a notably less extent; (b) the most frequent solution (peak of the histogram) outlines the

correct value , but mean square error (width of the histogram) differs in particular set-ups; and (c) the inversion of three-

component data is moderately better than that of one component data, i.e. the benefit of incorporating the three-component

sensors is rather small.

Concerning the inversion of data inconsistent with the source model (a vertical single force, contained neither in MT nor

in STC): (a) there is not a significant difference between MT and STC models; (b) if P-wave data from surface sensors only are

employed, there is no chance to recognize the inconsistent source, as inversion yields a very good fit; (c) adding the S-wave

data, the fit deteriorates largely, which offers a tool to recognize an inconsistent source; and (d) regardless of the inability to

retrieve the source type, the feature of its vertical orientation is obtained.

Finally, non-shear components determined for events occurred on November 26, 2005 at 15:23 and December 14, 2005 at

00:07 are found to be in agreement in terms of both the MT and STC models employed. Non-shear components for the event

on December 23, 2005, at 08:21 appeared in the MT model only, and so it is possible that this event was a pure shear slip.

ACKNOWLEDGEMENTS

We are indebted to Editor in Chief J. Trumpert for his personal care about the manuscript which was left pending lengthy

in the review process. The research was supported by the European Community's FP7 Consortium Project AIM 'Advanced

Industrial Microseismic Monitoring', Grant Agreement No. 230669 and by grants of the Grant Agency CR 'Non-double-couple

mechanisms: through induced seismicity to fluid-driven earthquakes', Grant Agreement No. P210/10/1728 and ‘Constrained

models of seismic source: in between a double-couple and moment tensor’, Grant Agreement No. P210/12/2235.

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