IV. MODELS

A critical element in the interpretation of the observational data is the development of models that include varying degrees of assumptions concerning important source processes. Constraint of these models by the observational data sets then provides the mechanism for assessing assumptions implicit in the models. The fundamental components of this problem that are emphasized in these models and the accompanying visualizations are the spatial and temporal aspects of the problem and the relationship to the observations.

Figure 10. Model representing the spatial and temporal characteristics of a typical mining explosion. Uphole time delays are represented by the horizontal burning lines between holes while downhole delays are represented by the vertical burning lines. Explosive red and stemming green.

One of the critical elements of mining explosions that is different from contained, single fired explosions is the process of delay firing individual explosions in an array in order to maximize the fragmentation and throw of rock while minimizing peak ground motions. This blasting pattern forms one fundamental difference for mining explosions that a number of authors [Baumgardt and Ziegler, 1988; Smith,1989; Hedlin et al., 1989] have argued will provide discriminants as well as reduce the size of regional or teleseismic signals. A model that characterizes these spatial and temporal effects is the first step in the interpretation of the observational data. Using a simple ray tracing algorithm that is common in the animation community, the 4x4 array of cylindrical boreholes for which data were displayed earlier (Figure 9) is shown in Figure 10.

MPEG Movie 4. (192x144, 520k) Multi-Shot Model.
MPEG Movie 4. (320x240, 1.5M)

The explosions are imbedded in a shale layer overlying a coal seam that is to be mined (Figure 5). The sixteen explosions in the array are designed to detonate at a sequence of times controlled by a combination of uphole and downhole delays. The uphole delays provide the relative timing among shots and are short in duration (10's msec) while the longer and constant downhole delays (100's msec) are designed in series with the uphole delays so that all uphole delays are completed before any explosive column detonates. To illustrate these effects, the timing in the delay pattern is represented in the model by a series of horizontal (uphole delays) and vertical (downhole delays) lines that 'burn' (stars in Figure 10 which move in the animation) for a time proportional to the design delays. One can animate the blasting process with multiple representations in time of the above model. Implicit in this representation is information concerning the viewing location of the observer, lighting and perspective. Comparison of these models to observational data requires selection of these parameters consistent with the location of observations which will be compared to the models.

MPEG Movie 5. (192x144, 30k) Tyrnyauz Moly Mine Blast in Southern Russia
MPEG Movie 5. (320x240, 66k)

Models such as the one depicted in Figure 10, when compared to observational data provide the mechanism for assessing the importance of these temporal and spatial source effects on the resulting phenomenology. We use a mining explosion documented in Southern Russia (Stump et al., 1994) to illustrate this point. In this case, six rows of explosives are detonated with 40 ms delay between rows. A number of individual explosions were detonated on the surface, producing particularly strong acoustic signals. The three-dimensional structure of the source region as well as the locations of the individual explosions were surveyed by the mine, providing the fundamental geometrical data for the model. In order to track the progression of the explosions in the model, individual explosions are represented by small spheres (blue) in the model prior to detonation and turn red and grow in size at the time of detonation. Each individual explosion then becomes the source of cylindrically spreading compressional (light blue) and acoustic (orange) energy with the velocity of the expanding wavelet constrained by in situ velocity determinations for the compressional energy and 300 m/s for the acoustic energy.

Figure 11. Three dimensional spatial/temporal characteristics of the explosions and mine are illustrated with the propagation of compressional(blue) and acoustic (yellow) energy. Instrument location is designated by purple sphere.

Figure 11 is one time frame from the model. At the time represented by this image, the first row of explosions on the second bench is just detonating as indicated by the red spheres. Compressional waves from the two rows on the lower bench have already propagated away from these explosions toward the seismometer (purple symbol). The time delay between the individual rows in the explosive array is expressed by the spatial separation of compressional energy from each of the first two rows of explosions in this figure. It is the constructive and destructive interference of the energy from each of these rows which may provide an effective discriminant for these types of sources (Baumgardt and Ziegler, 1988; Smith,1989; Hedlin et al., 1989). For the blasting technique employed in this example where a number of explosions are simultaneously detonated, small variations in the individual detonation times will have a minor effect on the constructive and destructive interference between the packets of energy generated by each row. One can also see the effects of spatial finiteness of each row on the radiated compressional waves. The wavefronts whose normals are parallel to the line of explosives are more dispersed than those perpendicular to the line of explosives. The lower velocity of the acoustic waves is also apparent.

Figure 12. Data (left column) and model (right column) from a mining explosion in Southern Russia.

The last step in the modeling effort is comparison with observational data. As an illustration of this process, the model for Southern Russia is combined with video images of the explosions. This integration provides the opportunity for improved interpretation of the actual explosion. Video images of the explosions at the same time intervals as the models are compared in Figure 12.

The model allows one to follow the detonation process in the video images beginning with the first row of explosions in the top image progressing to the last row in the bottom image. The resulting compressional and acoustic energy can be seen in the model visualization. The video and model comparisons indicate that the explosions in each row detonate nearly simultaneously in this experiment.

The video data also provides documentation of the surface explosions and the fact that the individual boreholes are unstemmed as evidenced by the burning gas ejected from each hole. It is this aspect of these explosions that leads to their strong airblast arrival. The last piece of data that must be added to these visualizations is the measured ground motions and acoustic waves to complete the interpretation.

MPEG Movie 6. (192x144, 395k) Tyrnyauz Blast Model
MPEG Movie 6. (320x240, 1M)

Go to Table of Contents or Next Section