Application of numerical modeling for analysis of
underground recordings of seismic events
Dmitriy A. Malovichko
Schmidt United Institute of Physics of the Earth, Russian Academy of Sciences;
Yuriy V. Baranov
Mining Institute, Ural Branch, Russian Academy of Sciences;
78a, Sibirskaya St., Perm, Russia, 614007
tel: 7 3422 160984
fax: 7 3422 167502
E-mail: [email protected]
SYNOPSIS
Waveforms obtained during underground seismic activity monitoring at the mines
of Upper Kama potash deposit (UKPD) exhibit an interesting structure. Intensive lowfrequency (f < 4 Hz) wavetrains are found at the final parts of seismograms except for
compressional (P) and shear (S) waves. Numerical modeling was carried out with the
aim of clearing the nature of the low-frequency waves. Process of seismic waves
propagation from a point source on the mine level was modeled using the
pseudospectral method. The results of calculation show that the low-frequency part of
the source’s signal excites energetic surface waves over the range 0.5 – 4 Hz. The
amplitude of these waves is comparable to the amplitudes of body (P and S) waves at
the level of mine openings. Thus registered low-frequency waves are interpreted as
surface waves.
Standard formulas of modal decomposition may be used for the description of
low-frequency surface waves. This is demonstrated by comparing of seismograms
calculated by pseudospectral method with harmonics of Rayleigh waves obtained by
modal decomposition method. Thus the low-frequency part of the wave field excited by
seismic events at UKPD is well described by the harmonics of Rayleigh waves. This
feature gives opportunity to use low-frequency waves for the study of seismic events
sources.
INTRODUCTION
Seismic monitoring is performed on the 6 mines of Upper Kama potash deposit
(UKPD). Every mine network represents an array of broadband (0.5 – 30 Hz) vertical
velocimeters SM3-KV deployed in underground openings (at the depth 250-350 m).
The area covered by the array could reach 10 km2. Signals from the sensors are
transmissed in a frequency modulated form to a digital recording system at the surface.
Monitoring networks of UKPD can record the seismic effect from the following
types of sources:
- teleseismic earthquakes. Usually compressional waves at first arrivals are
registered over the frequency range 0.5 – 2 Hz. Waveforms of teleseismic
earthquakes are used in identity checking of recording channels;
- quarry explosions at distances 30 – 180 km. The mass of the explosive
material varies in the interval from 1 to 15 tons;
- seismic events and explosions at the Upper Kama potash mines. The number
of events registered during 1995-2000 reaches 5000. Waveforms of typical
seismic events are shown in Figure 1 and Figure 2.
Figure 1. Seismic event recorded at the Berezniki-1 mine on October 11, 2000.
Figure 2. Seismic event recorded at the Solikamsk-1 mine on June 12, 1999.
Generally 3 types of seismic waves could be distinguished in accordance with the
waveforms of seismic events at mines:
1) Compressional (P) waves at first arrivals. These waves have frequencies in
the range 10 - 30 Hz and velocities of propagation - 3.8 – 4.4 km/s;
2) Shear (S) waves. These carry energy in the frequency range 8 – 20 Hz with
velocity 2.1 – 2.7 km/s. Generally the amplitude of S waves is higher then that of P
waves from the same source;
3) Intensive oscillations are observed in the final parts of the seismograms of
large seismic events and explosions. These waves are labeled by R in Figure 1 and
Figure 2. Their frequencies are 0.5 – 4 Hz and phase velocities - 1.6 – 2.0 km/s. The
amplitudes of R waves are comparable with the amplitudes of P and S waves.
FULL SEISMIC WAVEFIELD MODELING
A numerical modeling was carried out to investigate the fine structure of
waveforms and to reveal the nature of R waves.
The process of propagation of seismic waves was modeled using a pseudospectral
method (Kosloff et al., 1990) for a vertically inhomogeneous medium. A velocity and
density depth dependence which is typical for UKPD was used in the calculations (left
upper plots in Figure 3). A vertical force applied on the same level as the mine openings
(at the depth 300 m) was selected as the source. Figure 3 shows the development with
time of the divergent component of the calculated wavefield for a vertical section of
medium. It’s clearly seen on the initial snapshots (from t = 0.025 s to t = 0.25 s) that
high-frequency part of the source signal (f > 8 Hz) excites body wave with length about
100 m. Direct compressional wave labeled as P. Direct body waves are reflected from
the free surface with monotype (pP, sS) and converted waves (pS, sP) generation.
Refraction of body waves takes place in high-velocity carbonates at the depth 800 – 900
m. Refracted compressional wave for time t = 0.25 s and t = 0.375 s is labeled as Ph.
Later body waves form complex interference structure on the horizontal distances more
then 1 km due to superposition of multiple reflections and refractions.
Low-frequency part of the source signal (f < 4 Hz) takes part in the creation of
seismic wavefield in essentially different way. Both free surface and near-surface lowvelocity waveguide influence strongly on a propagation of low-frequency signals. Lowfrequency oscillations are concentrated near free surface (from t = 0.625 s to t = 1.25 s)
and represent standing waves in vertical direction and progressive ones - in horizontal.
So low-frequency oscillations demonstrate basic property of surface waves. It’s clearly
seen that low-frequency surface waves have considerable amplitude on the depth of
mine openings, thus they must be registered by seismic sensors installed there.
The results of the above calculation are shown in a form of seismic waveforms in
Figure 4. The vertical components of the synthetic waveforms for receivers at depth 300
m are represented in gray color. One can see that the structure of synthetic waveforms is
similar to the structure of observed ones (Figure 1 and Figure 2), namely: highfrequency body waves are noticed in the initial parts followed by a dispersive wave
train of low-frequency surface waves.
Figure 3. Velocity and density models and snapshots of the divergent part of
calculated seismic wavefield.
MATHEMATICAL FORMULATION OF SURFACE WAVES AT UKPD
The availability of surface waves for the interpretation of seismic monitoring data
requires a mathematical tool for description of their behavior. Usually the method of
modal decomposition is employed for this purpose. Surface waves are represented as a
sum of Love and Rayleigh harmonics (Levshin, 1973). The method of modal
decomposition is valid only when the distances between source and receiver are large
compared to the wavelengths of surface waves. Source-to-receiver distances for typical
seismic events at UKPD are of the order of 0.1 - 10 km and surface waves have
wavelengths from 400 m to 3 km. Thus these values are of the same order of magnitude
and the validity of the modal decomposition seems doubtful in this case.
Nevertheless standard formulas of modal decomposition may be used in the lowfrequency range for surface waves description even close to a source for a simple model
of the source (single or double-couple force). The results of the reported calculations
confirm this assumption. The 1st and the 2nd harmonics of Rayleigh waves were
calculated for the medium and the source models represented above. Vertical
components of 1st and 2nd Rayleigh harmonics are shown in Figure 4 in black color.
It’s obvious that the low-frequency part of the full wavefield is described well by
Rayleigh harmonics even near a source (as close as 1000 m).
CONCLUSIONS
Numerical modeling allows to understand the structure of seismic wavefield for
seismic events at Upper Kama potash deposit. Low-frequency waves (f < 4 Hz)
observed on the seismograms of large explosions and seismic events are interpreted as
surface waves.
It’s shown that the method of modal decomposition is suitable for the
mathematical formulation of surface waves, for the medium and seismic source
parameters typical for the UKPD, even near the source (at a distance of 1000 m).
The conventional processing of seismic events waveforms is based only on P and
S waves. The information about the seismic source and contained in the low-frequency
waves isn’t used at present. There are plans to use low-frequency waves in study of the
sources of seismic events at UKPD mines.
ACKNOWLEDGMENTS
This work was supported by the Russian Foundation for Basic Research (Grant N
01-05-65509).
REFERENCES
Kosloff, D., Kessler, D., and Filho, A. Solution of the equations of dynamic elasticity
by a Chebychev spectral method. Geophysics, vol. 55. 1990. Pp. 734-748.
Levshin, A.L. Surface and guided seismic waves. Moscow: Nauka. 1973. 176 P. (in
Russian).
Figure 4. Synthetic waveforms of the vertical components for different source-toreceiver distances:
a) 1st and 2nd harmonics of Rayleigh waves by modal decomposition method;
b) full wavefield by pseudospectral method.