EXPERIMENTAL ESTIMATES OF STRESS SENSITIVITY OF CRUST IN THE REGION OF
LAKE BAIKAL, FROM DATA OF ACTIVE VIBROSEISMIC MONITORING AND ELASTIC
TIDE
V.I.Yushin, V.V.Velinskii, N.I.Geza, and V.S.Savvinykh
Institute of Geophysics SB RAS, prosp. Akad. Koptyuga, 3, Novosibirsk, 630 090, Russia
ABSTRACT
The paper presents an attempt to estimate the upper limit of velocity and amplitude stress
sensitivity of the crust in a highly seismic area of the Baikal rift on the basis of data from 10-day
long active experiment using of a 100-ton vibrator. Recorded were waves reflected from the crustal
base at a distance of 125 km from the source. The obtained series of wave travel time and amplitude
variations were correlated with elastic tide effects considered as a source of periodic changes of
internal stresses in the crust. The upper limit of velocity stress sensitivity showed to be about an
order of magnitude higher than its indirect theoretical estimates. A technique is discussed for
revealing statistical relationships between variations of wave propagation parameters.
Baikal rift zone, crust, elastic tide, stress sensitivity, vibroseismic monitoring.
INTRODUCTION
The problem of monitoring variations in seismic wave propagation arose in seismology in
relation to earthquake prediction, which according to Stacey [1] means search for appropriate
methods of identification of elastic stresses. Dependence of wave velocities on stresses inside a rock
massif is obvious but the subtlety of expected effects requires special approaches to monitoring and
data interpretation. There are two similar parameters proposed to estimate sensitivity of seismic
velocities to internal stresses in a rock massif [2–4]. The first one is called 'stress sensitivity of
velocity' or 'pressure coefficient of velocity' and is expressed as
(1)
where V is velocity as a function of pressure (stress) P. Western scientists usually use parameter v.
In the Russian literature it is mostly a nonlinear parameter K determined by a non-dimensional
equation [5–9]
(2)
where ρ is density. The two parameters are related as
(3)
Inasmuch as v is often estimated in bars (kg·s/cm2), a non-systematic stress dimension, and
relative velocity variations Δ V/V are sometimes expressed in %, the relationship (3) can involve a
coefficient 10-7:
(4)
The parameters v and K express nonlinearity of the medium, which does not cause loss of
wave energy. At the same time, absorption can also be nonlinear and depend on wave amplitude.
Nazarov [7] proposed to distinguish the two types of non-linearity as a reactive and a dissipative
ones, respectively.
The velocity-stress relationships for different rocks for pressures under 30 kbar (that
corresponds to depths till 100 km) have been well known from laboratory experiments [10, 11] and
were in general substantiated by deep seismic field studies. However, the problem of absolute
critical stress is open to discussion, as the proposed estimates differ by orders of magnitude, from 10
to 1000 bar [1, 12]. Hence, there is another no less important problem of quantitative relationship
between observed velocity variation and the related in situ stress change. In this respect, studies of
seismic velocity variations related to solid Earth tides can be a helpful tool, as the latter can serve
as a natural calibrator of tectonic stress.
The known theoretical feasibility to detect tidal effects by seismic method consists in the
following [2–4]. Gravity variations Δ g/g of the order of 2·10-7 cause crustal strain Δ l/l of the order
of 2·10-8. Empirical mean rigidity m of consolidated crust is about 5·105 bar. Thus, the double peakto-peak amplitude of tidal stress changes in the crust Δ P = m·Δ l/l is about 0.01 bar (F.Stacey [1]
gives 0.05 bar). Now, in order to estimate the tidal component of velocity changes Δ V/V we have to
know stress sensitivity of seismic velocity (1). It is known to vary over a broad range in function of
rock lithology, fracturing, and depth-variable lithostatic pressure (300 bar/km). Maximum v shown
in laboratory tests is 0.1 %/bar and is attributed to specimens cut with cracks. These conditions are
restricted in situ to depths as shallow as a few tens of meters. Laboratory tests of triaxial
compression of rock samples under pressures from 0.1 to 12 kbar corrsponding to depths from 0.3
to 40 km, showed v varying from 0.01 to 0.001 %/bar, and even smaller. The integral estimate of
velocity stress sensitivity of the crust can be obtained by another way, independent of laboratory
experiments, uniquely from seismic data if seismic velocities at different depths are known. Write
expression (1) as
(5)
and assume that v = v = const. By integrating this equation in the sense of Stilties we obtain mean
stress sensitivity of velocity for the given crustal thickness:
(6)
where V1, V2, P1, P2 are velocties and pressures on the surface and on a deep reflector, respectively.
As an example we shall need later, let us use this method to estimate the integral velocity
stress sensitivity for a wave reflected from the Moho in the area of San Andreas Fault (California)
and propagating in the crust. According to [13], P-wave velocity V1 in the near-surface layer is
about 3 km/s, boundary velocity V2 at the crustal base ( H = 25 km, P2 = 7500 bar) is 7.85 km/s.
Substituting these values into (6) and assuming that P1 = 1 bar, we obtain v ≈ 0.013 %/bar (K =
130).
For the Baikal region where V1 = 3 km/s, V2 = 8.1 km/s, H2 = 40 km, P2 = 12,000 bar [14],
the same value v estimated by formula (6) is about 0.008 %/bar, or K = 75. Hence, the tidal traveltime change Δ t/t = Δ V/V of a wave reflected from the Moho must be, according to (5), about
1.3·10-6 and 0.8·10-6 for California and Baikal, respectively. Such subtle changes can be detected at
a resolution at least 0.2·10-6. A lower resolution is acceptable for shallower depths where v can
attain 0.1 %/bar but it should be above 10-5 anyway [3, 4]. Given that the available resolution of
seismic methods is no better than 10-4, seismic detection of tidal effects would be thought
impossible. However, broadly published experimental results [2–4, 9, 16, 17] evidence of the
reverse. We shall consider three works [2, 3, 16], which in our view are the best reliable and report
high quality experiments.
The experiment described in [2] was performed along a roughly vertical shaft of a mine cut
in coarse-grained calcite (marble). Seismic signals were generated by a hydraulic vibrostand,
"shaker", operated at a quartz-normalized frequency of 500 Hz. Measured was phase difference
between two geophones: the remote geophone 30 m below the surface and the reference one
separated by about 300 m along the mine shaft; the shaker was placed 37 m further down from the
reference geophone. Signal amplitude surveys showed that the principal seismic mode was
represented by a Rayleigh wave-like tube wave with a phase velocity of 3000 m/s. The experiment
lasted 37 hours and recorded a periodic phase change corresponding, as calculated, to a velocity
change of Δ V/V = 10-3 at a precision of the order of 10-4. A comparison of the observed velocity
changes with the actual earth-tidal strain in three horizontal directions showed a good correlation in
one azimuth. (De Fazio et al. find this correlation satisfactory. We however think that their plots are
little reason for optimism because of a striking discord between the main periods of velocity and
strain changes, also noted by the authors themselves.) Such a great velocity contrast, if it really was
caused by an elastic tide, would correspond to v = 10 %/bar or K = 20,000 according to (1) and (3).
At the same time, inasmuch as velocity stress sensitivity v from laboratory tests on similar rock is in
a range of 0.01 to 0.1 %/bar at pressures under 100 bar, ΔV/V must be 2 or 3 orders of magnitude
lower than it was observed in that experiment. De Fazio et al. [2] explain the discrepancy by the
probable presence of much larger cracks in the rock in situ, which makes doubtful any direct
extrapolation from laboratory tests of small samples.
Another experiment [3] was performed in a granite quarry. Signals came from an air gun
suspended in a water-filled cylindrical hole and were received by an array of geophones at a
distance of 200 m. Measured was the time interval between the onset of the pulse at a reference
near-field accelerometer and the first arrival of the wave at the geophone. The phase velocity of the
direct wave is 1.2 km/s, travel time is 170 m/s. Averaging over 300 shots for each seismogram
yielded a mean square deviation of 3·10-4. The experiment revealed a visible periodic travel time
variation with a double peak-to-peak amplitude about 1 ms, which corresponds to a velocity change
of ΔV/V ≈ 5·10-3 (much greater than in the previous experiment). Taking into account the observed
strain, which likewise showed to be greater, Reasenberg and Aki [3] estimated the in situ velocity
stress sensitivity as 20 %/bar.
The two experiments were restricted to the shallow crust but were carried out in crystalline
rocks typical of deeper crust as well, and so are of interest. As far as the true crustal variations are
concerned, the greatest number of known works [see, for instance 9, 18] deals with processing of
earthquake records based on poor-accuracy raw data and the results differ strongly from those
obtained by more precise active methods. A surprising reverse relationship between the amplitude
of observed velocity changes and precision was noted by Soloviev [15] who proposes to consider
these estimates as just boundary values representing the detection limit of seismic methods.
In this respect we should mention the work by Clymer and McEvilly [16] that concerns longterm travel-time monitoring of reflected waves including Moho reflections. The work contains plots
of two experiments 2-days long each with combined strain and travel-time records, which do not
show any evident correlation between the two processes. Clymer and McEvilly [16] mentioned that
"an apparent response of the travel time to the solid earth tide was observed during the first three ...
experiments, which will be discussed in a separate paper". However, as Dr. McEvilly informed us,
they refused the promised publication having realized that what they observed were shallow effects.
Inasmuch as the experiments focused on diurnal travel time trends for waves reflected from the
Moho, we tried to draw boundary information from therefrom. The first one coincided in time with
a nearly maximum tide (0.22 mGal), so there were no reasons to expect greater tide effects in other
experiments. It is reasonable to assume that the hypothetical tide effect in those three more
experiments may have been detected due to lower noise. Therefore, the upper limit of tidal effects
can be determined from maximum travel time difference recorded in those "failed" experiments
(about 3 ms at a traveltime of 8 s) and estimated at 0.4·10-3. Assuming that the tidal stress change
ΔP is 0.01 bar, n obtained for California from a wave ray reflected from the Moho, according to (1)
should be within 4 %/bar. This result contrasts sharply against the indirect estimate of 0.013 %/bar.
However, taking into consideration the private explanation by Clymer and McEvilly, we have to
classify their work as one where no tidal effects in consolidated crust were observed, and the
estimate of 4 %/bar should be considered a boundary value in terms of instrumental and
methodological potentials.
In October 1991 we ran a two-week active monitoring in a seismic area of the southern
Baikal in order to study tidal effects on seismic velocities in the consolidated crust; some
preliminary results were published in [21]. Repeated vibroseismic soundings were carried out along
a 125.5 km long profile from the southeastern side of Lake Baikal (town of Babushkin)
northwestward to village of Kharat, with the use of an electromechanic 100-ton vibrator operated at
frequencies of 5 to 10 Hz.
No tidal effects were detected in spite of a high precision exceeding the known from
previous works. The present paper is a result of more detailed processing of the extensive data from
that experiment in search for more precise boundary estimates of nonlinear parameters and stress
sensitivity of seismic velocity in the crust of a highly hazardous seismic region.
DATA TREATMENT, INVERSION OF WAVE FIELD AND CHOICE OF SUBJECTS FOR
ANALYSIS OF VARIATIONS IN WAVE PROPAGATION
Four typical seismograms obtained by repeated soundings are shown in Fig. 1. Each of them
is a result of real time correlation of vibroseismic signals directly during soundings. The signals
were received by a 12-channel inline geophone array oriented azimuthally toward the source. The
upper three channels recorded respectively X, Y, and Z components of a three-component geophone.
The other nine channels recorded Z components. The geophones were arranged into bunches of 11
for each channel, and spaced at 10 m within a group. The bunches were oriented along the profile
and spaced at 100 m (distance between the centers). Differences in these seismograms can be
noticed only by very careful examination. After rejection, 60 seismograms were selected for
statistical analysis.
In spite of a fairly high signal-to-noise ratio on individual seismograms, inversion was
performed using a seismogram, specially filtered from any incoherent noise, obtained as a
channelwise sum of 16 records. Because of a strongly increased dynamic range, the seismogram was
displayed with the use of a transient-scale imaging (Fig. 2). Interpretation involved comparison with
DSS results for this region [14]. The true first arrival showed to be from a low-amplitude P-wave
refracted at the base of the sediment cover with a travel time of 21.6 s, which is visible only on the
summed seismogram (see Fig. 2). This wave is bad for monitoring because of poor signal-to-noise
ratio (note by the way that it is poorly detectable even if induced by explosions). The wave is
followed by several refraction waves (one with a travel time of 22.94 c is labeled as W1 in Fig. 3 and
included into the analyzed selection). The travel time of 23.6 corresponds to a prominent arrival of a
Moho reflection labeled as W2 whose parameters are analyzed later on from its maximum second
phase. The other five waves ( W3 - W7), included into the selection, cannot be unambiguously
interpreted but are certainly of deep origin, as evidenced by high apparent velocities (8–9 km/s).
Two most prominent ones (W3 and W4), are tentatively attributed to the mantle ( PM1ref and PM2ref,
respectively).
In order to enhance the signal-to-noise ratio, the obtained multichannel inline seismograms
was transformed into a single-channel areal record by means of summation over the 9 paths from
identical transversally positioned Z-channel geophones. The channels were summed with a time
shift of one selection (10 ms), which corresponded to orientation of the radiation pattern maximum
with respect to the apparent velocity of 10 km/s. Theoretically this permitted a three-fold increase in
signal-to-noise ratio and each synthetic record was a result of directed reception of a single sweep
by a 800 x 100 m array of 99 geophones.
The fragment of a synthetic seismogram of 60 summed paths shown in Fig. 3 covers six of
the seven analyzed sweeps.
MEASUREMENTS AND CORRECTION OF TRAVEL TIME AND AMPLITUDE
VARIATIONS
Plots of traveltime and amplitude variations obtained from a processed synthetic
seismogram recorded during 10-day monitoring are shown in Figs. 4–6, together with a theoretical
plot of a tidal force. Below we are giving some explanations on the plotting procedure.
Precise measurement of travel time fluctuations recorded at different sessions was achieved
by calculation of reciprocal phase spectra of the respective wave pulses. Wave amplitude was found
as a maximum absolute discrete counting of a given pulse. Residual noise was estimated separately
for each wavepath as a mean square deviation σn on the time interval before P-wave first arrivals.
Inasmuch as the source and receiver were automatically synchronized (by a special quartz timer of
precision 5·10-9), their misfit reflected on seismograms as an arrival shift common to all waves. The
timer was repeatedly verified or adjusted against radiosignals of the national time survey, and the
respective corrections were introduced into the measured arrivals during data processing.
Figure 4 shows travel time variations for the reference wave W4 corrected for clock misfit
and a theoretical plot of tidal force. Travel time variations of the other six waves are shown in Fig. 4
and 5 as differences ( ti - t4) between these travel times Wi and the reference wave W4 after
subtraction of invariable components. It is obvious that in this case only wave W4 bears time effects
common to the entire seismogram. These effects may be produced by synchronization errors
remained after data correction, by local rheologic changes at the source and receiver areas due for
instance to weather effects on the ground and, finally, by a tidal component shared by all waves.
These components will be not evident in travel time differences ( ti - t4). However, since the rays of
different waves do not follow the same paths, the tidal effects on them will be dissimilar and so the
travel time difference variations will bear individual features of these effects, in a clearer form than
the variation t4.
Without three anomalous arrivals of W4 on October 15, 16, and 18, the time series t4
involves a slow positive trend (dashed line in Fig. 4, a) against which random deviations of
measured travel times are within 1 ms. Over the first day the increment reached +3 ms and then
stabilized at +4 ms with respect to the original state. The trend may in principle have tectonic
causes, but is most likely produced by shallow rheologic effects due to weather influence and longlasting compression of the soil under the vibrator. Isolated anomalies, possibly produced by
synchronizartion errors as they have no match in adjacent records, are not evident in travel time
difference series and residual noise at the respective seismograms was even below the mean.
Amplitudes of the same six waves are plotted in Fig. 6. Note that unlike the travel-time
plots, the amplitudes are shown as absolute rather than relative values.
STATISTICAL ANALYSIS OF WAVE ARRIVAL AND AMPLITUDE SERIES. BOUNDARY
ESTIMATES
Visual examination. As a rule, variations distinguished during continuous surveys require
further analysis to reveal inherent relationships, latent periodicity, trends, etc. Except for the abovementioned visible slow trend of traveltimes of wave W4, the series shown in Fig. 5 and 6 look
chaotic. No correlation is seen with the tidal gravity variations either.
It is known from numerous psycho-physical experiments that a harmonic signal with
amplitude B can be visually distinguished against ambient noise of the same frequency with mean
square deviation σ, on condition that the signal-to-noise ratio (on the basis of the mean square
amplitude) is above 2:
(7)
In this limit case, scattering ... of the observed values of series Y equals to the total magnitude of a
harmonic signal and random noise
(8)
whereform it follows, with regard to condition (7), that if a harmonic component cannot be
distinguished by visual analysis, its amplitude does not exceed the value
(9)
In particular, having subtracted the positive trend from the series {t4} (see Fig. 4, a) we
obtained ... = 0.5 ms. Inasmuch as no visible relationship with tide effects is observed, we can state
according to (9) that the amplitude of the tidal component, if it exists, does not exceed
(10)
which corresponds to a relative variation of W4 phase velocity (t = 24.74 s) smaller than
... or 2.5·10-3 %
(11)
Analysis of causes of random scatter of travel times. Ambient noise in seismograms is the
first physically evident cause of travel time scatter. Its effect can be predicted using the known
formula [2]
(12)
where σt is the mean square deviation of travel times of a given wave with amplitude A, σ N is the
mean square deviation of ambient noise, f0 is the predominate signal frequency.
If a seismogram is a result of correlation of a vibrosignal, as in the given case, f0 is, as a rule,
the central frequency of the noise spectrum. Expression (12) is valid for singnal-to-noise ratios over
10 being the usual case, otherwise monitoring does not make sense.
Noise in travel time difference series {ti - tJ} is estimated by formula
(13)
where rN ( ti - tJ) is the background-normalized noise component. Inasmuch as rN < 1, this
expression is always valid. Comparing the obtained σt' with σt calculated immediately from the
series {ti - tj}, we can conclude that if σt ≈ σt', the scatter is chiefly caused by ambient noise; if σt >>
σt', some other significant causes should be searched. The case when σt < σt' is physically impossible
and attests to a serious error in processing.
Revealing of latent relationships by the correlation method. The correlation analysis
permits to reveal a relationship between two series or between a series and a known function
obscured by random measurement errors. It is better suitable for discontinuous time series than the
spectral analysis. In order to estimate the hypothetical tidal component in variations of some
parameters, the following statistical problem should be considered.
Let X and Y be two arbitrary values, derived from two other independed arbitrary values Φ
and N as
(14)
(15)
where G and B are constants. G is assumed known (amplitude of gravity variations), N (random
error in measurements of some parameter Y of a seismic wave) has normal distribution with mean
square deviation σN, Φ is distributed uniformly over the range (0.2 π). We are to estimate a constant
B in a selection of n independent measurements (number of measurements taken during the
monitoring period, or the length of the series). Physically value Φ models a tidal phase, which is
certainly not a random component. However, if consider that measurements are taken at arbitrary
moments of time, such an approach is valid, because this assumption does not improve the final
estimate with respect to the real situation. Solution of this problem leads to the following result. The
correlation coefficient of arbitrary values X and Y (14), (15) is determined by expression
(16)
where γ is the amplitude signal-to-noise ratio in observation series
(17)
The relationship (16) permits to constrain the original signal-to-noise ratio (17) via the
estimate of correlation coefficient of series X and Y:
(18)
where the true value rXY can be replaced by its empirical estimate. Thus, the algorithm of statistical
evaluation of the tidal component B includes the following steps:
1) calcualtion of mean square deviation of series Y;
2) calculation of rXY;
3) calculation of the initial signal-to-noise ratio γ by formula (18);
4) evaluation of B by formula obtained from (17):
(19)
where, since γ << 1, measurement errors σN can be replaced with mean square deviation of series Y.
The accuracy and stability of this estimate can be verified via the mean square deviation σr of the
empirical correlation coefficient, which is known [25] to depend on the volume of selection n as
(20)
The value of the constant G is in this case of no significance.
Let us now estimate the tidal component in travel time change of the reference wave W4
using these equations and real data. The highest correlation between tidal effect and variation t4
(excluding the trend) was at r* = 0.17 and associated with a 4-hour shift of the travel time series
{t4} relative to the tide curve. The rms error in this estimate showed to be σr = 0.12 according to
(20), i.e. of low statistical significance. Nevertheless, assuming the empirical value r* = 0.17 to be
the most reliable, find the respective signal-to-noise ratio γ ≈ r = 0.17 and the amplitude of the tidal
component by (18) and (19):
(21)
Therefore, using an additional correlation analysis we arrived at a detectable limit of the
tidal component more than five times lower than its visible magnitude (10), till a travel-time relative
value of 0.5·10-5.
The obtained result should be considered in terms of probability. It means that if a
correlation between travel time and tide does exist, it can be estimated by the above value which
agrees with observations, but these experimental data and the volume of selection are insufficient
for a more detailed conclusion. Moreover, the rough statistical estimates of relationship between the
two series appear too optimistic, as they misregard the true probability of data distribution
remaining unattainable.
In order to estimate the probable natural scatter of the empirical correlation coefficient in the
case when a series lacks any invariable component, we performed a numerical experiment on
correlation of independent selections of arbitrary numbers at n = 60 as in nature with the real tidal
function. Some selections showed to contain shifted series with a correlation coefficient up to 0.150.2. Therefore, the detectable limit of tidal velocity variation is overestimated, in spite of the above
formal value, and in reality it must be much lower than 0.5·10-5.
Estimates of correlation between travel time differences {ti - tj} of the other six waves and
the tidal component did not show absolute values above that for {t4} and, hence, do not contradict
the obtained upper boundary value.
Boundary estimate of velocity sensitivity to stresses. Let us find, according to (1), "visual"
v1 and "statistical" v2 boundary estimates of velocity stress sensitivity of the consolidated crust in a
given region using the obtained boundary estimates Bmax (10) and (21) of the amplitude of the tidal
component in travel time variations assuming Δ P = 0.01 bar, t0 = 25 s:
(22)
(23)
A comparison of the latter estimate with the implicit value of 0.008 %/bar shows that
positive detection of the tidal effect in variations of P-wave velocities requires about an order of
magnitude higher precision. In addition to improving synchronization and extending time series, the
idea to investigate travel time differences of P- and S-waves that are free from synchronization
errors appears promising but has not been achieved in our experiment.
Analysis of amplitude variations. Observed variations of amplitudes of seven waves are
shown in Fig. 6. Mean and mean square amplitudes for each wave of the selection are given in
columns 4 and 5 of Table 1. Additionally, we determine nosie scatter on wave-free segments (before
first arrivals) of each seismogram ... and the mean over all seismograms ...:
(24)
It is seen from the Table that the amplitude scatter is everywhere above the mean noise (24)
and obviously depends on the respective amplitudes. It indicates that the ambient noise is not the
only cause of scatter but there is a component acting as a random magnifying coefficient. This
component might be related to the tide, but having no obvious correlation between the amplitude
variations and the tidal strain (Fig. 6, a) it is reasonable to check a simpler hypothesis first, that of
vibrator instability. In this case the statistical model of fluctuations can look as a sum of the random
magnifying component of amplitude change and ambient noise.
Consider the following problem. Let amplitudes Ai and Aj of two waves fit statistical
equations
(25)
(26)
where ... and ... are mathematical expectations for amplitudes of Wi and Wj; Ni and Nj are arbitrary
values representing random ambient noise at the moment of measuring amplitudes Ai and Aj,
respectively. Ni and Nj have zero mean values, identical scatter ... and correlation coefficients rN (i,
j); σ is a non-dimensional random value with a zero expectation and mean square deviation Δ << 1,
which characterizes mutually dependent multiplicative fluctuation of amplitudes Ai and Aj. It is
assumed that variation δ is the same for all waves. Physical value (1 + δ) describes the component
of amplitude changes common to all waves which is produced by random fluctuations of the source
(sounding) amplitude. We are to evaluate mean square deviation Δ (multiplicative instability of the
amplitude).
The correlation moment between measured amplitudes of a wave pair represented by (25)
and (26), with regard to the assumptions, after transformation will look as:
(27)
where rN (i, j) is correlation coefficient of noise in one and the same seismogram, apparently, equal
to the backgound-normalized noise at a time shift equal to time difference between arrivals of Wi
and Wj. This function can be easily estimated from seismograms, but to a first approximation it can
be replaced with a theoretucal expression [25]
(28)
where F and f0 are sweep bandpass and mean frequency, respectively. In this case F = 4 Hz, f0 = 7.5
Hz. Substituting into (28) ti and tj for different wave pairs (Table 1, column 3), we can estimate the
respective noise correlation coefficients. If express the mean square deviation from equation
(27) and correlation moment ... as ... and .. mean square deviation and correlation coefficient
of measured amplitudes of two waves, we obtain
(29)
This expression enables to estimate (within the limits of the assumed physical model) the
sweep amplitude instability by separating it from the ambient noise. Inequality of deltas estimated
from different wave pairs (i, j), and more so obtaining imaginary values will attest to invalidity of
the chosen model.
The right half of the table contains a matrix of pair correlation of amplitudes for all seven
waves with statistically significant coefficients (above 2σ, which according to (20) is 0.26). Some
waves show fairly strong amplitude correlations, and this appears to confirm the hypothetic model
of their relationship through variations of sweep amplitude. The degree of wave relationship Δ,
calculated by formula (29) is 5-6 % for most waves. However, the fact of statistically significant
negative correlation of the W2 amplitude with some waves is plaguing and cannot be accounted for
by the simple model of (25) and (26). At present we can explain it by an exotic mechanism of
changing radiation pattern which is really able to cause different effects on seismic rays. Actually,
there are no physical reasons for amplitude variations of the unbalanced vibrator as a machine: The
motive force is strictly related to sweep frequency and the latter is reproduced to an accuracy of 10-8.
All really observed variations of sweep amplitude are undoubtedly related to the external effects,
either near-field or remote. If we assume variability of the medium (caused by weather effects or by
vibration itself), we may hypothesize that this influence affects both intensity and pattern of seismic
radiation.
BOUNDARY ESTIMATE OF WAVE AMPLITUDE SENSITIVITY TO CRUST STRESSES
We can obtain the upper limit of wave amplitude stress sensitivity by statistical analysis of
observation series assuming probable existence of a relationship between changes of wave
amplitudes and elastic tidal strain. The approach is similar to that for wave velocity and likewise
involves two types of estimates: from visual examination (a1) and by correlation analysis (a2). For
visual estimate we have to know mean square deviation σA of a wave amplitude change and mean
wave amplitude (both values are given in Table 1). Applying the same derivation as (9), we obtain
that if there is no visible relationship with the tidal strain G, the boundary estimate of the tidal effect
on wave amplitude cannot be above
(30)
where Π is the hypothetical tidal effect on amplitude A, and σ A = 28 units for wave W4 (see Table
1), whereform Π1 < 35 units. A better constrained Π2 can be obtained by analogy with (19) after
calculating the correlation coefficient rGA for a series of observed amplitudes A and tidal component
G:
(31)
The maximum value of rGA 0.2 was observed at a time shift of three hours (0.09 without the
shift). According to (31), Π2 < 8 units. By analogy with velocity stress sensitivity (1), the amplitude
sensitivity can be found as
(32)
Assuming that Δ P = 0.01 bar and substituting Π in (32) with the obtained boundary estimates Π1
and Π2 and mean wave amplitude w4 (... = 504), we find that a1 < 7 bar-1 (700 %/bar) according to
visual estimate and a2 < 1.6 bar-1 (160 %/bar) according to statistical estimate.
Unfortunately, we do not know theoretical predictions for dissipative sensitivity (related to
attenuation) to match the obtained estimates. Therefore, they should be considered as attainable
limit of instrumental detection of elastic tide effects in variations of seismic wave amplitudes
provided the active monitoring is carried out by a continuous vibrator, which is the most stable
source nowadays.
CONCLUSIONS
1. Active vibroseismic monitoring was performed in the region of Lake Baikal with the aim
to test the methodology for revealing stress and strain variations in the crust of hazardous seismic
regions. A specific problem was to determine sensitivity of P-wave velocities in the crust to stress
changes caused by elastic tide.
2. The obtained series of travel times and amplitudes of waves reflected from the crustal
base and uppermost mantle made a basis for statistical and visual analysis of their relationship with
gravity variations.
3. The velocity variations were measured to precision 2·10-5, or nearly two orders of
magnitude better than in earlier experiments by De Fazio, Reasenberg, Aki, etc.
4. The revealed variations of wave velocities and amplitudes are related with external
surface effects and microseismic noise.
5. The absence of an obvious relationship with tide effects however permitted to determine
the upper limit of possible velocity stress sensitivity of the crust, which showed to be an order of
magnitude and a half lower than obtained by other workers. It is 0.15 %/bar, much closer than
elsewhere to the results of laboratory tests on rock samples.
6. In addition to the usual ambient (microseismic) and multiplicative (sourse) fluctuations,
the statistical analysis of wave amplitudes revealed an unexpected effect of negative wave
correlation, which can be physically explained by variability of the radiation pattern.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
F.Stacey. Physics of the Earth [Russian Translation], Moscow, 1972.
T.L. De Fazio, K.Aki, and J.Alba, J. Geophys. Res., vol. 78, no. 8, p.1319, 1973.
P.Reasenberg and K.Aki, J. Geophys. Res., vol. 79, no. 2, p. 399, 1974.
H.Bungum, E.Hjortenberg, and T.Risbo, in: Studies of the Earth by non-explosion seismic
sources [in Russian], p. 248, Moscow, 1981.
V.V.Gushchin and G.M.Shalashov, ibid, p. 144.
A.V.Nikolaev, in: Problems of nonlinear seismics [in Russian], p. 5, Moscow, 1987.
V.E.Nazarov, Akusticheskii zhurnal, vol. 37, no. 6, p. 1177, 1991.
Yu.I.Vasiliev, N.A.Vidmont, A.A.Gvozdev, et al., in: Problems of nonlinear seismics [in
Russian], p. 149, Moscow, 1987.
A.G.Gamburtsev, Seismic monitoring of the lithosphere [in Russian], Moscow, 1992.
S.Clark (Ed.), Handbook of physical constants [Russian Translation], Moscow, 1968.
N.I.Christensen, J. Geophys. Res., vol. 79, no. 2, p. 407, 1974.
F.Press and U.F.Brace, in: Earthquake prediction [Russian Translation], p. 32, Moscow,
1968.
R.Feng and T.V.McEvilly, Bull. Seism. Soc. Amer., vol. 73, p. 1701, 1983.
N.N.Puzyrev (Ed.), The Baikal interior (from seismic data) [in Russian], Novosibirsk, 1981.
V.S.Soloviev, Dokl. RAN, vol. 329, no. 2, p. 166, 1993.
R.W.Clymer and T.V.McEvilly, Bull. Seism. Soc. Amer., vol. 71, no. 6, p. 1903, 1981.
V.Kh.Akhiyarov, L.G.Petrosyan, and Yu.G.Shimelevich, Dokl. RAN, vol. 252, no. 3, p. 577,
1980.
G.A.Popandopulo, Dokl. RAN, vol. 262, no. 3, p. 580, 1982.
L.N.Rykunov, O.B.Khavroshkin, and V.V.Tsyplakov, in: Problems of nonlinear geophysics
[in Russian], p. 109, Moscow, 1981.
R.Tetem, G.Pernel, R.Miller, et al., Proc. Intern. Geoph. Conf. SEG, Moscow-92, Abstracts,
p. 260, Moscow, 1992.
V.I.Yushin, N.I.Geza, V.V.Velinsky et al., J. Earth Pred. Res., no. 3, p. 119, 1994.
A.F.Emanov, A.P.Kuz'menko, M.A.Mokshanov, et al., in: Development of non-explosion
seismic sources [in Russian], p. 48, Moscow, 1989.
V.I.Yushin, G.V.Egorov, N.F.Speranskii, and V.N.Astafiev, Acoustic study of nonlinear and
rheological phenomena in the near zone of seismic vibrator, Geologiya i Geofizika (Russian
Geology and Geophysics), vol. 37, no. 9, p. 156(152), 1996.
E.Karageorgi, R.W.Clymer, and T.V.McEvilly, Bull. Seism. Soc. Amer., vol. 82, no. 3, p.
1388, 1992.
N.A.Livshits and V.N.Pugachev, Probabilistic analysis of automatic control systems [in
Russian], Moscow, 1963.
I.S.Gonorovskii, Radiotechnical circuits and signals [in Russian], Moscow, 1986.
Received 6 July 1998
Accepted 2 November 1998
FIGURE CAPTIONS
Fig. 1. Typical correlated records of active vibroseismic monitoring.
Each seismogram is a result of convolution of a 20-min sweep signal.
Fig. 2. Summed seismogram over 16 sweeps.
Transient visualization scale: amplification smoothly decreases eight-fold between 22 and
23
s.
Fig. 3. Synthetic seismogram of 10-day long monitoring.
Fig. 4. Travel time and tidal strain variations.
a – reference wave W4; b – variations of travel time difference
Fig. 5. Variations of wave amplitudes.
Fig. 6. Amplitudes of seven different waves A1, ..., A7 obtained during 10 days of measurements.
Amplitudes are in conventional units. Diurnal time spans are separated by vertical bars.
Table 1. Statistical analysis of wave amplitude variations
Wave
Amplitude
abbreviation nature travel time, mean
in s
amplitude
Coefficient of amplitude correlation beteen a
pair of waves and its confidence interval**
amplitude scatter*
m.s.d. %
refraction and
harmonic waves
from Moho
and upper mantle
* Mean square deviation of amplitudes is in absolute conventional units and in percents of mean
amplitude of a wave;
** Confidence interval ε = ±3 (1 - rwi, wj) / ...60
+ marks only sign of the correlation coefficient if its value is below confidence interval