SEISMOGRAM SYNTHESIS AND ... - Wiley Online Library

Geophysical Prospecting 40,31-70, 1992

SEISMOGRAM SYNTHESIS A N D RECOMPRESSION O F DISPERSIVE IN-SEAM SEISMIC M U L T I M O D E DATA U S I N G A N O R M A L - M O D E S U P E R P O S I T I O N APPROACH M O N I K A BREITZKE’

ABSTRACT BREITZKE, M. 1992. Seismogram synthesis and recompression of dispersive in-seam seismic multimode data using a normal-mode superposition approach. Geophysical Prospecting 40, 31-70. In spite of a geometrical rotation into radial and transverse parts, two- or threecomponent in-seam seismic data used for underground fault detection often suffer from the problem of overmoding ‘noise ’. Special recompression filters are required to remove this multimode dispersion so that conventional reflection seismic data processing methods, e.g. CMP stacking techniques, can be applied afterwards. A normal-mode superposition approach is used to design such multimode recompression filters. Based on the determination of the Green’s function in the far-field, the normal-mode superposition approach is usually used for the computation of synthetic single- and multimode (transmission) seismograms for vertically layered media. From the filter theory’s point of view these Green’s functions can be considered as dispersion filters which are convolved with a source wavelet to produce the synthetic seismograms. Thus, the design of multimode recompression filters can be reduced to a determination of the inverse of the Green’s function. Two methods are introduced to derive these inverse filters. The first operates in the frequency domain and is based on the amplitude and phase spectrum of the Green’s function. The second starts with the Green’s function in the time domain and calculates two-sided recursive filters. To test the performance of the normal-mode superposition approach for in-seam seismic problems, it is first compared and applied to synthetic finite-difference seismograms of the Love-type which include a complete solution of the wave equation. It becomes obvious that in the case of one and two superposing normal modes, the synthetic Love seam-wave seismograms based on the normal-mode superposition approach agree exactly with the finitedifference data if the travel distance exceeds two dominant wavelengths. Similarly, the application of the one- and two-mode recompression filters to the finite-difference data results 1

2

Received October 1990, revision accepted July 1991. Formerly Institut fur Geophysik, Ruhr-Universitat Bochum, P.O. Box 102148, 4630 Bochum 1, F.R. Germany

31

32

M O N I K A BREITZKE

in an almost perfect reconstruction of the source wavelet already two dominant wavelengths away from the source. Subsequently, based on the dispersion analysis of an in-seam seismic transmission survey, the normal-mode superposition approach is used both to compute one- and multimode synthetic seismograms and to apply one- and multimode recompression filters to the field data. The comparison of the one- and two-mode synthetic seismograms with the in-seam seismic transmission data reveals that arrival times, duration and shape of the wavegroups and their relative excitation strengths could well be modelled by the normal-mode superposition approach. The one-mode recompressions of the transmission seismograms result in non-dispersive wavelets whose temporal resolution and signal-to-noise ratio could clearly be improved. The simultaneous two-mode recompressions of the underground transmission data show that, probably due to band-limitation, the dispersion characteristics of the single modes could not be evaluated sufficiently accurately from the field data in the high-frequency range. Additional techniques which overcome the problem of band-limitation by modelling all of the enclosed single-mode dispersion characteristics up to the Nyquist frequency will be mandatory for future multimode applications.

1. INTRODUCTION The detection and location of small underground tectonic or atectonic faults using in-seam seismics require special data processing methods. The high-frequency content (modern firedamp-proof instrumentation can record frequencies up to 2000 Hz) and the modal dispersion requires either a modification of reflection seismic data processing methods so that phase- and group velocities are taken into account, or a development of new processing methods which remove dispersion so that conventional processing methods can be used afterwards. Prestack techniques, applied to in-seam seismic single-shot sections to increase temporal resolution and to improve signal-to-noise ratio, are mandatory. CMP stacking would result in a destruction of dispersive wave groups rather than in an improvement of the signalto-noise ratio of the input data. This paper deals with the second possibility, that of treating dispersive in-seam seismic data. It describes a method of designing inverse or time-variable deconvolution filters which remove dispersion. This is usually known as recompression filtering. In contrast to conventional deconvolution methods, e.g. spiking or shaping filters which necessitate source-wavelet estimation or at least require the input traces to be minimum phase, these recompression filters do not make any demands on the spectral properties of the input signals. Several authors have described techniques of designing such recompression filters. Three different mathematical approaches can be distinguished. (i) The first approach describes a frequency-domain method which is known as ‘spectral warping’. It can be applied to both transmission and reflection data since it does not depend on travel distance. Based on a non-linear mapping from the frequency- to the wavenumber domain (Booer et al. 1976; Booer, Chambers and Mason 1977; Booer, Beresford-Smith and Mason 1978) or the use of a frequency domain operator (Beresford-Smith and Mason 1980; Beresford-Smith and Rango 1988) it removes the part of dispersion

DISPERSIVE SEISMOGRAM SYNTHESIS

33

that modulates the envelope shape. Special stacking and migration methods taking the stationary envelopes into account were developed (Mason, Buchanan and Booer 1980a, b; Buchanan et al. 1981a, b; Buchanan and Jackson 1983). (ii) The second approach derives two-sided filters in the time-domain which completely remove dispersion. Since they include the travel distance they are preferably applied to transmission data. The phase spectra of these filters are determined by an integration of the groupvelocity curve with respect to travel distance (Marschall 1982). The amplitude spectra are considered to be constant or, in the case of absorption, damped and band-limited. Since the travel distance can be considered to be positive or negative this technique provides both dispersion and recompression filters. (iii) The third approach includes all deconvolution and filter techniques not specially developed for the recompression of in-seam seismic data but rather for an improvement of the signal-to-noise ratio and temporal resolution of other dispersive data. Firstly, time-variable inverse filters designed to deconvolve signals with dispersion due to absorption must be mentioned (Robinson 1979). Secondly, the class of matched filters (Turin 1960; Robinson and Treitel 1980) should be considered. Tolstoy and Clay (1966), Capon, Greenfield and Lacoss (1969), Herrin and Goforth (1977) and Goforth and Herrin (1979), for instance, described applications and examples of this type of cross-correlation filter. These methods all have in common the fact that they can only be applied to single-mode data and, apart from Buchanan and Jackson’s (1983) approach, neglect the influence of the source. However, in spite of geometrically rotating two- or three-component in-seam seismic data into their radial and transverse parts each component sometimes still shows interfering modes of the same or different wavetype. (i) Coal seam layer sequences of large thickness often show several normal modes of the same Love or Rayleigh wavetype. (ii) Inhomogeneities, disaggregations near the roadways or backwall scattering sometimes produce normal modes of different Love and Rayleigh wavetype (Krajewski et al. 1987). (iii) Specific petrophysical properties of the layer sequence support the propagation of normal and leaky modes (BreitBke et al. 1987). Thus, a method based on normal-mode superposition (Harkrider 1964; Harvey 1981; Panza 1985) is introduced which takes these multimode problems into account. In contrast to seismology, which needs from six (Swanger and Boore 1978) to 200 modes (Panza 1985; Suhadolc and Panza 1985; Chiaruttini, Costa and Panza 1985) to simulate synthetic earthquake seismograms, very few modes need be considered here. Additionally, frequency- and time-domain techniques to design multimode recompression filters by an inversion of the synthetic seismogram algorithm are described. First, this normal-mode superposition method is compared and applied to the finite-difference method which includes a complete solution of the wave equation. Since it was developed as a far-field approach, these investigations allow us to deter-

34

MONIKA BREITZKE

mine: (i) if, and from which travel distance, both modelling methods coincide; (ii) if a reconstruction of the source wavelet is possible by recompression filters based on the normal-mode superposition method. Subsequently, synthetic single- and multimode seismograms and recompressions are computed for seismograms of an underground transmission survey revealing a leaky- and a normal mode Love seam-wave group. The dispersion characteristics are not known a priori but are evaluated from the field data by two methods. The first combines multiple-filter dispersion analysis techniques with trial-and-error modelling of the best-match theoretical dispersion curve. The second derives the (band-limited) dispersion characteristics directly from the contour map representation of the Gabor matrix. The objectives are to investigate: (i) if normal-mode Love seam-wave groups and leaky-mode wave groups can be modelled and recompressed as single modes and as two superposing modes using the normal mode superposition approach; (ii) if the dispersion characteristics of the layer sequence can be evaluated sufficiently accurately from the field data dispersion analysis; (iii) if additional modelling techniques are necessary for the computation of theoretical dispersion curves up to the Nyquist frequency.

2. THEORETICAL BACKGROUND The seismogram synthesis and the computation of multimode recompression filters are based on the determination of the Green's function for a vertically layered medium subjected to a unidirectional unit impulse in the 2D and 3D cases. This discrimination between 2D and 3IT models refers mainly to the source type used. In the 2D case a line source parallel to the x,-axis (Fig. 1) excites cylindrical waves. In the 3D case a point source positioned on the x3-axis at depth h excites spherical waves. The mathematical background for the determination of the Green's function has been described by several authors, e.g.- Harkrider (1964), Harvey (1981) and Panza (1985) in the case of surface waves, and Hudson and Douglas (1975) and Buchanan (1986) in the case of seam waves. Thus, only a summary of the formulae used in this paper is given here. In the 2D case the mathematical approach is based on the reciprocity and representation theorem and leads to a far-field expression for the Love-wave terms of the Green's function (Aki and Richards 1980):

x exp (i

x1

")

+ 1. -2 ,

for x1

0. (1)

In the 3D case the wavenumber or slowness integral known from the reflectivity method (Fuchs 1968; Fuchs and Muller 1971; Muller 1985) is evaluated for its residue contributions and leads to the far-field expression for the Love-wave terms

DISPERSIVE S E I S M O G R A M S Y N T H E S I S

35

FIG.1. Sketch of the layer-cake model and coordinate system used for the computation of the Green's function by superposition of seam-wave normal modes. cp is the azimuth, h the source depth, 0 the origin of the coordinate system.

of the Green's function with an azimuth of cp = 0" (Aki and Richards 1980):

In both equations the first index of the Green's function refers to the displacement component and the second index to the direction of the unit impulse. The first coordinate pair (xl, x3) describes the receiver and the second coordinate pair (0, h) the source position, Z(w, k, , h) and Z(o, k, , x3) are the eigenfunction values in the source and receiver depth h and x 3 , computed for the angular frequency w and the nth normal-mode eigenvalue k,. C,(o) and U,(w) are the nth normal-mode phaseand group-velocity curves. x1 is the travel distance between source and receiver. ZLl(w, k,) describes an energy integral which can be evaluated according to

From both expressions for the Green's function it becomes obvious that in the far-field it can be described as a linear superposition of the spectral impulse responses of each single normal mode. Their contributions can be expressed in

36

MONIKA BREITZKE

terms of a phase spectrum, given by the argument of the exponential function, and an amplitude spectrum, given by the fraction in front of the exponential function in (1) and (2). In practice, only those modes whose cut-off frequencies lie within the frequency band of the source spectrum must be taken into account. From the filter theory’s point of view, these Green’s functions can be regarded as multimode dispersion filters used for forward modelling. Hence, synthetic seismograms due to a particular source wavelet are given by a convolution in the time domain. Accordingly, the convolution model provides a starting point for the design of recompression filters. Since they remove the dispersion from the complete seismograms so that only (a delayed version of) the source wavelet remains, a convolution of the dispersive seismogram with the inverse of the Green’s function effects this recompression. To determine the inverse of the Green’s function, two approaches are suggested. The first operates in the frequency domain and is based on the multimode amplitude and phase spectra A + @ ) and $+(CO) of the Green’s function,

A + ( 4 = I G + ( 4I , ++(CO)= arctan

[E$3.

(4)

The amplitude and phase spectra of the multimode recompression filter K ( o ) and 4-(w) are given by the reciprocal value of this amplitude spectrum and by the negative value of this phase spectrum, simulating waves travelling backwards from the receiver to the source, K ( w )= (A+(o))-’, $-(CO)

= -f$+(o).

(5)

An inverse Fourier transform results in two-sided recompression filters which allow the simultaneous recompression of n normal modes. If the amplitude spectrum of the Green’s function includes zeros or rather small values, a prewhitening or at least an elevation of these values to a higher level is necessary. The second approach operates in the time domain and is based on the z transform of the Green’s function G+(z). Two-sided recursive Wiener filters are then computed as recompression filters G-(z) (Marschall 1982; Marschall (pers. comm.)), given by

G;(z) is the minimum-phase correspondent of the z-transform of the Green’s function G ‘(z). It is determined by computing the Wiener-Levinson’s spike deconvolution twice (Marschall (pers. comm.)). Using the Green’s function G+(z) as input time series, the first application of the spike deconvolution yields the inverse of the minimum-phase correspondent of the input signal as filter coefficients (Claerbout 1976). Using this inverse of G,+(z)as input time series again, the second computation


37

of the spike deconvolution provides the required minimum-phase correspondent G:(z) of the Green’s function as filter coefficients. Care must be taken over the filter length. Since both the frequency- and the time-domain techniques lead to two-sided filters, their lengths must at least amount to twice the seismogram length to be recompressed. Additionally, the convolution of a recompression filter with a dispersive input seismogram ideally leads to a non-dispersive wavelet whose first arrival occurs at zero time. To facilitate the comparison between recompressed and dispersive signals, whose first arrivals appear after a non-zero propagation time, a reduction velocity is introduced to delay the recompressed traces linearly, according to their travel distance.

3. A P P L I C A T I O TNO F I N I T E - D I F F E R E NSCEEI S M O G R A M S

3.1. Numerical and model parameters Finite-difference and normal-mode superposition seismograms were computed for a 2D model of a coal seam embedded between half-spaces with the petrophysical parameters given in Table 1. TABLE1. Petrophysical parameters of the symmetrical layer sequence, rock (R) - coal (C) - rock (R) used for the computation of the finitedifference and the normal-mode superposition seismograms. U, = shear-wave velocity, p = density, H = layer thickness.

The model size for the finite-difference seismogram computations amounted to 888 x 225 grid points with a spacing of 0.07576 m. The coal seam was represented by 33 grid points and the upper and lower rock ‘half spaces ’ by 96 grid points. The source was positioned in the centre of the coal-seam, 250 grid points away from the left model boundary. It simulated a line force which extended and acted in the x,-direction. The receiver profile, also laid out in the centre of the coal seam, consisted of 150 geophone positions with a spacing of four grid points. The finite-difference seismogram computations were based on the ‘homogeneous formulation’ (Alterman and Karal 1968; Alford, Kelly and Boore 1974; Kelly et al. 1976; Korn and Stock1 1982). Reflections from the artificial model boundaries were weakened by Reynolds’ (1978) method.

38

MONIKA BREITZKE

The critical sample interval of 0.02ms was used to ensure numerical stability (Boore 1972; Alford et al. 1974; Kerner and Dresen 1985). A narrow- and a broadbanded Kupper wavelet (Kupper 1958) with two amplitude extrema and durations of 5.0 ms and 2.5 ms served as source time functions. In order to save computer mass storage, the finite-difference seismograms were resampled after their numerical computation with an interval of 0.1 ms. To eliminate reflections from the artificial model boundaries that were not numerically suppressed by Reynolds’ (1978) method, the finite-difference seismogram sections (Figs 4 and 6 ) were tapered by a linearly moving rectangular window with a passband between 0 and 20 ms for 0 m and between 0 and 60 ms for 45.2 m travel distance. The normal-mode superposition seismograms were based on the 2D Green’s function. The Love seam-wave eigenvalues and eigenfunctions were calculated by Rader et al.’s (1985) recursive algorithm. The numerical integration of the energy integral was performed by the trapezoidal rule. For the computation of the recompression filters in the frequency domain, spectral amplitude values smaller than 10% of the maximum were elevated to this level.

3.2. Excitation of modes Since the single-mode amplitude spectra of the Green’s function include the energy integral (3), which describes the total energy trapped in the complete layersequence, they provide information on the relative excitation strength of each single mode depending on the source and receiver positions. Considering the symmetrical layer sequence, rock-coal-rock, Figs 2a and b display these amplitude spectra for the first to the fifth normal mode of the Love seam waves and a source and receiver position in the centre of the coal-seam. They show an excitation of only the odd-numbered normal modes because of the antisymmetry of the even-numbered normal-mode eigenfunctions (Rader et al. 1985). Similar to Hudson and Douglas’ (1975) Rayleigh-wave investigations, each spectrum reveals a distinct maximum which coincides with the group velocity minimum in the corresponding dispersion curve (Fig. 2c). In the 2D case the maximum excitation strength of the third mode only amounts to about 40% and that of the fifth mode only to about 30% of the maximum excitation strength of the first mode. Additionally, the amplitude spectra computed for the 3D case and a travel distance set to 1 demonstrate an amplification of the high frequencies by )*/, (see (1) and (2)). However, the high-frequency spectral amplitude ratios of the third to the first and of the fifth to the third and first mode do not differ significantly from those in the 2D case. Nevertheless, for the calculation of synthetic seismograms or the practical underground excitation of Love seam waves, it must be remembered that these amplitude spectra only reveal the relative excitation strengths of modes due to a unit impulse. In the case of an arbitrary, band-limited source wavelet, the effective excitation strengths will still be modified by the source spectral components according to the convolution model.

DISPERSIVE S E I S M O G R A M SYNTHESIS

Frequency [ Hz ]

c

PI

4 . . 0

39

Frequency [Hz]

. -5001

1

- 1000 *

1

.

1500

Frequency [ H z l

FIG.2. Symmetrical rockxoal-rock layer sequence. (a) 2D and (b) 3D single-mode amplitude spectra and (c) phase- and group-velocity dispersion curves, of the first to the fifth normal mode of Love seam waves. The source and receiver were positioned in the centre of the coal-seam. The numbers 1-5 indicate the mode number.

3.3. Single-mode computations The first synthetic seismograms were calculated using the narrow-banded Kiipper wavelet of 5 ms duration as a source wavelet having a frequency band up to about 600 Hz with a dominant frequency of about 300 Hz. A comparison with the cut-off frequencies of the amplitude spectra in Fig. 2 shows that only the first mode of the Love seam waves could be excited. Figure 3 presents an example of the dispersion and recompression filters computed in the frequency domain. Based on the 2D amplitude spectrum and the dispersion curve of the first mode, dispersion and recompression filters were calculated for each tenth receiver position of the profile in the finite-difference grid model.


40

3

Dispersion Filter

Recompression Filter

Distance [m]

Distance [m]

2

3

2

FIG3. Symmetrical rock-coal-rock layer sequence. (a) Dispersion and (b) recompression filters of the first normal mode of the Love seam waves. The recompression filters were determined in the frequency domain.

Since the phase spectra of both filter types are equal in value and opposite in sign, the dispersion filters predominantly appear at causal, positive arrival times, while the recompression filters predominantly reveal significant amplitudes at acausal, negative arrival times. Additionally, apart from low-frequency components which clearly disperse with increasing travel distance, in the case of the dispersion filters both filter types show a high-frequency, impulse-like arrival which belongs to the Airy phase. Subsequently, the first mode dispersion filters of each receiver position were convolved with the narrow-banded Kiipper wavelet (Fig. 4b) and compared to the corresponding finite-difference seismogram section (Fig. 4a). It becomes obvious that both modelling techniques agree very well if the source-receiver distance exceeds about 5 m or two dominant wavelengths, referred to the first-mode Airy-phase frequency of 300 Hz and the corresponding group velocity of 1000m/s.


Normal Mode Superposition

Finite-Difference Distance t m l

(a) 0

10

20

30

Distance [ml 40

41

(b)

0

0

10

20

40

50

FIG.4. Symmetrical rock-coal-rock layer sequence. Comparison of (a) the finite-difference and (b) the normal mode superposition seismogram section computed with the narrowbanded Kupper wavelet of 5.0 ms duration as source signal. The seismogram sections were normalized to the 45 m trace.

Finally, the quality of the first-mode recompression filters is studied. They were computed in the frequency and time domains and applied to the finite-difference seismograms. In Fig. 5 the recompressed seismogram sections based on both types of recompression filters are compared. The host rock shear-wave velocity of 2300 m/s was used as a reduction velocity according to the velocity of the critically refracted shear wave. Both seismogram sections reveal short, recompressed, nondispersive wavelets. Apart from same slight changes in the amplitudes, the recompressed wavelet shapes seem to be constant for source-receiver distances greater than about 5 m in case of the frequency-domain recompression filters and greater than about 10 m in case of the time-domain recompression filters.

42

MONIKA BREITZKE

F-Domain Recompression Filter T-Domain Recompression Filter

0

10

20

30

40

50

FIG.5. Symmetrical rock-coal-rock layer sequence. Recompression of the finite-difference seismogram section of Fig. 4a. The recompression filters of the first normal mode of the Love seam waves were computed in (a) the frequency domain and (b) the time domain with a reduction velocity of 2300 m/s. The seismogram sections were normalized to the 45 m trace.

3.4. Multimode computations The results derived from the single-mode computations are investigated to discover if they are also valid for the multimode seismogram synthesis and for the simultaneous recompression of several superposing normal modes. Therefore, the broad-banded Kiipper wavelet of 2.5 ms duration was used as a source wavelet having a frequency band up to approximately 1200 Hz with a dominant frequency of approximately 600 Hz. Thus, normal modes up to the third could be excited, but the second mode is zero due to the source and receiver positions in the centre of the coal-seam.


Finite-Difference (a)

D i s t a n c e [ml

43

Normal Mode Superposition D i s t a n c e [ml

(b)

FIG.6. Symmetrical rock-coal-rock layer sequence. Comparison of (a) the finite-difference and (b) the normal-mode superposition seismogram section computed with the broad-banded Kupper wavelet of 2.5 ms duration as source signal. The seismogram sections were normalized to the 45 m trace.

In Fig. 6 the finite-difference and the normal-mode superposition seismogram sections are opposed. Similarly to the single-mode computations, both modelling methods agree for travel distances greater than about 5 m or two dominant wavelengths in the multimode case. Additionally, amplitude spectra of six single traces using both methods were calculated and compared in Fig. 7. They confirm the time-domain result of Fig. 6. While the amplitude spectra of the finite-difference (FD) and the normal-mode superposition seismograms (NMS) still differ significantly for a 1 m travel distance, they already agree fairly well for a 5 m travel distance, and for travel distances greater than 15 m they coincide almost completely. Furthermore, in contrast to

44

MONIKA BREITZKE

-FD -NMS

I .

F r e q u e n c y [ Hz]

'

. . '.

. .

'

' . .

.

I

F r e q u e n c y [Hz]

FIG.7. Symmetrical rock-coal-rock layer sequence. Comparison of the amplitude spectra of the finite-difference (FD) and the normal-mode superposition seismograms (NMS) for the 1 m, 5 m, 15 m, 25 m, 35 m and 45 m traces. Trace normalization before spectral analysis according to Fig. 6.


45

single-mode spectra, the multimode spectra depend on the travel distance. Above the third mode cut-off frequency of about 600 Hz, they show distinct interferences between the first and third mode with an increasing number of maxima and minima for increasing travel distance. The travel distance dependence and interferences become particularly obvious if the expressions for the amplitude and phase spectrum of a two-mode dispersion filter are calculated explicitly according to (4). Let A : ( o ) and A l ( o ) be the amplitudes and 4:(o) and +:(CO) be the phase spectra of both single-mode dispersion filters. The amplitude and phase spectrum of the two-mode dispersion filter, A + ( w ) and 4+(w),can be computed from the expressions

+ ( A : ( o ) ) 2 + 2A:(o)A;(w) cos (4:(o) sin +:(CO)+ &(U) sin +;(CO) A:(w) cos +:(U) + A&) cos Cjl(o)

A+(w)= [ ( A : ( o ) ) 2

4+(o)= arctan

- 4:(o))]1'2,

(7)

These expressions demonstrate that (i) the amplitude and phase spectra of a twomode dispersion filter depend on the amplitude and phase spectra of both single modes; (ii) the amplitude spectrum of the two-mode dispersion filter depends on the travel distance due to the travel distance dependence of the phase spectra of the single modes; (iii) the expression for the amplitude spectrum of the two-mode dispersion filter contains an interference term, cos (4:(o) - 4;(o)), which describes the interferences of the single modes; (iv) an exact knowledge of the amplitude and phase spectra of the single modes is necessary. If the phase difference, 4:(o) - 4;(o), is inaccurate, the interference maxima of the recompression filters do not fill up the interference minima of the dispersive wavetrain but will produce additional peaks in the amplitude spectrum of the ' recompressed ' trace, which then cause more or less numerical noise. Finally, the effect of a multimode recompression is investigated. The filters were computed in the frequency domain, and the recompressed wavelets were delayed by a velocity of 2300 m/s. Figure 8a displays the finite-difference seismogram section of Fig. 6a after the simultaneous recompression of the first and third modes. For travel distances greater than 2 m, constant, short, recompressed wavelets can be distinguished. The effect of a one-mode recompression applied to multimode data is illustrated in Fig. 8b. Only the first normal mode of the finite-difference seismograms was recompressed. Again, the shape of the source wavelet could be fairly well reconstructed but these recompressed wavelets now trail a dispersive wave group which results from the missing recompression of the third mode.

4. APPLICATION T O IN-SEAMSEISMIC T R A N S M I S S IDATA ON 4.1. Survey site, layout and recording parameters Figure 9 shows a map of the underground survey site and layout. A transmission survey was carried out between both parallel roadways to investigate: (i) if one or several of the faults of 0.3 m to 3.2 m throw, extend to the coal-seam in front of the

MONIKA BREITZKE

46

1. - 3. Mode Recompression

1. Mode Recompression Distance [ml

Distance [m] 0

10

20

30

(b)

40

10

40

50

FIG.8. Symmetrical rock-coal-rock layer sequence. Comparison of a simultaneous recompression of (a) the first to the third normal mode and (b) only the first normal mode of the Love seam waves in the finite-difference seismogram section of Fig. 6a. The recompression filters were computed in the frequency domain with a reduction velocity of 2300 m/s. The seismogram sections were normalized to the 45 m trace.

face; (ii) if other faults occur in front of the face; (iii) if seam-wave transmission was possibly obstructed by such a fault. 84 shots were fired from points S1 to S84 on the upper roadway, at horizontal distances of 427 m (Sl) to 862 m (S84) from the origin 0, to a fixed two-component geophone station G on the lower roadway. The roadway spacing was 234.5 m and the shotpoint spacing was 5 m. Both horizontal components were recorded, the one orientated parallel, the other perpendicular to the roadways. The recording time lasted over 600 ms with a sample interval of 0.25 ms. An antialias filter with a cut-off at half the Nyquist frequency and a slope of 54 dB/octave was used. An additional high-pass filter with a lower cut-off frequency of 120 Hz and an 18 dB/ octave slope suppressed very low-frequency noise.

41


.

/ /

0.3m

*,

1.0 m

*,

1.8 m

0.4m 3.2m

I,./

L/ 1.3 m /

6

I

0

Layer-Sequence Scale: 1:5000 Coal 1 (Cl)

3t- Shot Position V Geophone Position

j (D)

:2)

/ 1.3 m:Fault

FIG.9. Map of the site and layout of the in-seam seismic transmission survey. The transmission fan includes 84 shotpoints S1 to S84 in the upper roadway and a fixed two-component geophone station G in the lower roadway. The orientation of the radial Y*-component and the transverse X*-component after their geometrical rotation is indicated by the arrows. 0 is the origin of the coordinate system.

The layer sequence displayed in Fig. 9 was given by mine geologists and reflects the mean stratification of the coal-seam. It consists of two seams C1 and C2 of thicknesses 0 . 8 M . 8 5 m and 0.354.45 m respectively, enclosing a thin dirt band D of thickness 0.1-0.5 m. P- or S-wave velocities and densities were not known. The shotpoints and the geophone station were positioned in the centre of the complete layer sequence Cl-D-C2.

4.2. Preprocessing Firstly, trace balancing was carried out by a time-invariant, two-component rms-amplitude-scaling (Yilmaz 1987). Subsequently, the data was rotated into its radial Y* and transverse X* parts, as indicated by the pair of arrows in Fig. 9. Thus, apart from effects due to backwall scattering, disaggregations or inhomogeneities near the roadways, P-waves and the vertical component of the Rayleigh waves predominantly appear in the Y* component and SH and Love seam waves predominantly in the X*-component. Finally, to amplify low amplitude signals, a time-variable, two-component instantaneous automatic gain control (Yilmaz 1987) of window length 200 ms was applied so that the amplitude ratio of the X * - and Y*-components was preserved.

48


4.3. Wave-group, mode and petrophysical parameter analysis Figure 10 shows the seismogram sections of both components after preprocessing. Three dispersive wave groups appear. (i) A fast, strong amplitude wave group which results from critical P-wave refraction at the coal-seam/rock interface and from the following leaky modes (as defined by Dresen and Freystatter 1976). (ii) A second, lower-frequency wave group which probably belongs to the lowfrequency part of the Love seam waves. (iii) A slow, very high-frequency wave group which probably belongs to the Airy phase of the Love seam waves. To examine the mode contents and to verify this wave-group identification, a multiple-filter group-slowness analysis (Dziewonski, Bloch and Landisman 1969) was carried out for both components. 40 traces between the distances, 452 m and 652 m, padded by zeros to 4096 samples, were used as input data. The resulting Gabor matrices were stacked, each normalized to loo%, and displayed as contour maps (Fig. 11). Superimposed are theoretical Love seam-wave dispersion curves of the first to the third normal mode which were computed using Rader et al.’s (1985) recursive algorithm. The petrophysical parameters (Table 2) underlying these dispersions curves were derived by trial-and-error so that the first-mode group-slowness curve corresponds best with the X*-component contour map and, in spite of the geometrical rotation, also with the Y*-component contour map. The second low-frequency and the third high-frequency wave group of both seismogram sections could thus be identified as belonging to the first normal mode of the Love seam waves. Higher Love or any Rayleigh seam-wave normal modes are not evident in either of the two components. Only in the group-slowness range below the normal modes can the strong amplitude maximum of the P- and leaky-mode wave groups be distinguished between about 200 and 400 Hz and between 0.2 and 0.4 s/km (250&5000 m/s). TABLE2. Petrophysical parameters of the underground coal-seam layer sequence, Cl-D-C2 (coal lklirt band-coal 2), and the host rock (R) evaluated from the multiple-filter analysis of the transmission survey. U, = shear-wave velocity, p = density, H = layer thickness.

H

vs

P

Layer

(mh)

(kg/m3)

(4

R c1 D C2 R

2200 1020 1950 1020 2200

2300 1300 2000 1300 2300

0.85 0.05 0.48

CO

CO


49

50

MONIKA BREITZKE %

l o o . 00

1.2

50.00

1.0

10.00 5.00

0.8 1.00

x*

0.50

0.6

0.10

0.4

0.05 0.2

0.01

Frequency [HzI %

l o o * 00

1.

50.00 1.

10.00 5.00

0.

1.00

y*

0.50

0.

0.10 0.

0.05 0.01

0.

Frequency [Hzl FIG.11. In-seam seismic transmission survey. 40-fold stacked Gabor matrices of the multiplefilter analysis computed for (a) the X*-component and (b) the Y*-component traces between 452 m and 652 m. The Gaussian filter bandwidth amounted to 391 Hz between both - 100 dB points. The contour maps were each normalized to 100%. The best-match theoretical Love seam-wave group-slowness curves of the first to the third normal mode are superimposed.


51

As far as the resolution of the petrophysical parameters is concerned, the shearwave velocities and thicknesses of both coal-seams, C1 and C2, may vary by only about 20 m/s and 0.02 m respectively, as discussed by Breitzke et al. (1987). The dirt-band parameters could be resolved to about 50 m/s and 0.2-0.3 m. The shearwave velocity of the host rock could only be evaluated approximately within a range of +_ 2W300 m/s. Variations in the density values do not influence the dispersion curve behaviour significantly, so that typical values of the Ruhr area carbon were assumed for the model parameters in Table 2.

4.4. Polarizationjltering In the following, the petrophysical parameters given in Table 2 were used to calculate synthetic Love seam-wave seismograms for a vertically layered model and to recompress the transmission data. Assuming that normal and leaky modes can also be superposed linearly, the transmission seismograms can be considered as twomode data with the first normal mode of the Love seam waves as first mode and the leaky modes as second mode. Initially, synthetic one-mode seismograms and one-mode recompression tests were tried, and a polarization filter, as described by Montalbetti and Kanasewich (1970), was applied to the transmission data. It causes the low- and high-frequency Love seam-wave groups to occur only on the ‘proper’ X*-component (Fig. 12a), the P- and leaky-mode wave group only on the ‘proper’ Y*-component (Fig. 12b). The length of the moving time window used to evaluate the polarization characteristics was 20ms. The direction functions of the filter were smoothed over 5 ms. These two single-mode seismogram sections were used as input data for the following one-mode computations.

4.5.Synthetic one-mode seismograms Since the amplitude spectrum of the Green’s function depends on the vertical source and geophone positions, the influence of three different positions within the layer-sequence Cl-D-C2 on the excitation of the first to the third mode of the Love seam waves is shown (Fig. 13). Position 1 represents a source and geophone in the centre of the complete layer sequence Cl-D-C2. Position 2 is in the centre of the upper coal-seam C1 and position 3 is 0.1 m beneath the centre of C1. From the corresponding single-mode amplitude spectra of the 3D Green’s function, it becomes obvious that, if the source and geophone positions are shifted from the centre of the layer sequence, the excitation strength of the second mode increases and more high-frequency components of the first mode are excited. On the other hand, the synthetic seismogram sections, based on these amplitude spectra (Fig. 14) do not significantly depend on the source and geophone positions due to their band-limitation. As with the field data, the synthetic seismogram sections also reveal a fast, low-frequency and a slow, high-frequency wave group belonging to the low-frequency part and the Airy phase of the first mode. Only in

h

e 0 0 CO

3

E

Y

a, U

c (d

c,

rn

-4

a

0

0 W

-E a, U C

rd rn

U

-4

a

0

0

In

52

:U

"3

0 Ln

0

c.J 0

.c E?

0

g

0 Ln

rn

0 0

In

U-

'jl

0

53


rn

0.4

0.2 0

z

0.0 0

250

500

750

F r e q u e n c y [ Hz] 0)

40

loo00

250

500

750

1000


1.0

-4

4

2. .

* Pos. 2 * Pos. 3

0.6

* Pos. 1

U

U

rn

E

0.4

D

0.2

c2

0

z

0.0

F r e q u e n c y [ Hz] FIG.13. In-seam seismic transmission survey. Single-mode amplitude spectra of the first to the third normal mode of Love-seam waves in the layer sequence Cl-D-C2. The source and receiver were positioned in the centre of the complete layer sequence Cl-D-C2 (Pos. l), in the centre of C1 (Pos. 2) and 0.1 m below the centre of C1 (Pos. 3).

the case of position 2 does another slow, high-frequency wave group of the second mode follow the first mode Airy phase. However, its amplitude is so low that it can hardly be identified in case of noisy field data. So, for all further computations the source and geophone position 1 in the centre of the complete layer-sequence Cl-WC2 are chosen. Figure 15 shows which dominant frequency of the source wavelet (a Ricker wavelet) was chosen to give the best agreement between synthetic and field data. Three dominant frequencies, 120 Hz, 150 Hz and 300 Hz, were selected. The syn-

W N

e W 4 U

z

0

E

E W

U

Y

C

m

(0

U -rl

a

E

Y

W U

C ld

m

U

a

-4

0 0

W

I . . . . . ., . ,,..U!..,

0 0

-r

!

...............................................

0

0

0 N

0 r-

0

0 0

m

0 0

e

. . . , ,-. . . -. r i . . . . . . . . . . . . ... .y,,," . ..................................... .............................

.............................

-................. ...................... 0

r

d .-0

E

. U

I a

0

2

8

c 0

a

3

.-c

cd

x

8

c

3

s

b)

b)

-c:

> 3

Id


Distance [m]

Distance [ml 500 0

600

55

loo

--

600

10

c: loc Love 7-7

2

Y

z

20c

-4 E-

Airy

3

30C

400

0

loo

2

U

z

200

-4 B

300

400

-FIG.15. In-seam seismic transmission survey. Comparison of the polarization-filtered seismogram section of the X*-component with the synthetic normal-mode superposition seismogram sections of the Love seam waves computed with Ricker wavelets of 120 Hz, 150 Hz and 300 Hz dominant frequencies as source wavelets. Source and receiver position 1 in the centre of the complete layer-sequence Cl-D-C2. Instantaneous AGC-normalization by a window of 200 ms duration.

56


thetic seismogram section calculated with a Ricker wavelet of 120 Hz dominant frequency shows a predominant excitation of the low-frequency part of the first mode while the Airy phase occurs separately with weak amplitudes in accordance with the field data. In the case of a dominant frequency of 150Hz, significantly higher-frequency components were excited in a continuous wave group, and in the case of a dominant frequency of 300 Hz the Airy phase appears predominantly. Figures 16 and 17 deal with the calculation of synthetic leaky-mode seismograms for the Y*-component using the same computation scheme with amplitude and phase spectra as for the normal modes. However, since the amplitude spectrum and dispersion curve for the leaky modes could not be calculated by algorithms such as Rader et al.'s (1985) or Thomson-Haskell's matrix formalism (Haskell 1953) they were estimated directly from the field data. For the determination of the dispersion characteristics, a multiple-filter analysis was carried out for the leaky-mode group-slowness range between 0.2 and 0.5 s/km (2000-5000 m/s) (Fig. 16a), having used the same processing parameters as for Fig. 11. The solid line superimposed on the contour map indicates the analysed leaky-mode group-slowness curve which was derived by picking the maximum amplitude of each frequency. The leaky-mode amplitude spectrum shown in Fig. 16b is composed of these maximum amplitude values, smoothed over 11 points and interpolated by cubic spline functions. In contrast to the amplitude spectra calculated for the normal modes, this leaky-mode spectrum encloses both the transfer function of the underground layer sequence and the source characteristics. Thus, for synthetic seismogram computations, a convolution with a source wavelet is not necessary. In Fig. 17 the synthetic leaky-mode seismograms derived from these dispersion and amplitude characteristics are compared to a part (487 m to 712 m) of the polarization-filtered seismogram section of the Y*-component. It becomes obvious that both seismogram sections agree very well in their group traveltime and wavegroup shape.

4.6. One-mode recompressions Based on the first-mode Love seam-wave dispersion curve and the amplitude spectrum of shot and geophone position 1, recompression filters were applied to the polarization-filtered seismogram section of the X*-component. The frequencydomain method was used for the recompression filter design and 8192 samples were supplied for the FFTs. Spectral amplitudes smaller than 10% of the maximum were elevated to this level, and the shear wave velocity of the host rock served as a reduction velocity. In Fig. 18 the polarization-filtered seismogram section of the X*-component (a) and its recompressed counterpart (b) are shown. The high-frequency Airy-phase wave group has completely vanished after recompression. The low-frequency part of the Love seam wave is focused to a short wave train, whose amplitudes are significantly increased in comparison to the input data.


57

%

l o o * 00

0.5

50.00 10.00

0.4 5.00 Y

1.00

(I) (I)

a,

j:

0

4

0.50

0.3

cn

0.10

a 3

0 &

(3

0.2

2bo.

#

. .400

.

'

'

I

.

600

.

.

-

0.05

0.01

800

Frequency [ Hz]

a,

a

1

U

.. U U

a,

a

cn

E

Frequency [Hzl FIG.16. In-seam seismic transmission survey. (a) 40-fold stacked Gabor matrix of the multiple-filter analysis of the leaky-mode group-slowness range computed for the Y*component traces between 452 m and 652 m. The solid line indicates the evaluated leakymode group-slowness curve derived from the contour map maxima of each frequency. (b) Leaky-mode amplitude spectrum evaluated from the contour map maxima of (a) along the solid line.

MONIKA BREITZKE

58

Y" (a)

synthetic

Distance [ m ] 500

600

Distance [m] 0

(b)

loo

0

P, leaky

loo

2

Y

z

200

Yi

€+

300

400

FIG. 17. In-seam seismic transmission survey. Comparison of the polarization-filteredseismogram section of (a) the Y*-component and (b) the synthetic leaky-mode seismogram section. Instantaneous AGC-normalization by a window of 200 ms duration.

Furthermore, the shape of the recompressed wavelets is almost constant up to about 650m. For larger distances a slight residual dispersion can be seen which might be due to a change in the dispersion characteristics, possibly caused by a change in the underground petrophysical properties and/or faults in front of the face. This distance range approximately encloses that area where three faults were developed in the upper roadway. However, reliable fault detection is not possible if only this single-shot section is taken into account. Next, based on the leaky-mode dispersion curve and amplitude spectrum, a leaky-mode recompression was tried. A velocity of 4000 m/s was used as a reduction velocity. In Fig. 19 the polarization-filtered seismogram section of the Y*-component (a) is compared to its recompressed version (b). Though the signal-to-noise ratio improvement is not as evident as in case of the normal-mode recompression of the Love seam waves, a decrease in the signal duration and thus an improvement in the temporal resolution is obvious. Nevertheless, in this case it is more difficult to distinguish constant, coherent, recompressed wavelets along the complete distance range because some high-frequency noise is superposed. Hence, additional indications of faults above a distance of 650m cannot be derived. Besides, it must be

60


DISPERSIVE S E I S M O G R A M S Y N T H E S I S

61

taken into account that a change in the dispersion characteristics or faults in the coal-seam affect the normal modes, trapped in the coal-seam, more significantly than the leaky modes propagating in the host rock.

4.7. Synthetic two-mode seismograms In order to simulate synthetic two-mode seismograms, with the first normal mode of the Love seam waves as first mode and the leaky modes as second mode, an estimation of their relative excitation strengths on both components is necessary. As in the leaky-mode case, these relative amplitudes were evaluated from the multiple-filter analysis contour maps (Fig. 11) by picking the maximum amplitude of each frequency, once in the normal-mode group-slowness range between 0.45 and 1.25 s/km (800 m/s to 2200 m/s) and again in the leaky-mode group-slowness range below 0.45 s/km (above 2200 m/s). Fig. 20 presents the resulting amplitude spectra of both components, smoothed over 11 points, interpolated by cubic spline functions and each normalized to 1.0. They quantify the description of the leaky- and normal-mode wave groups given at the beginning of section 4.3. In both components the amplitudes of the leaky-mode wave group prevail. Their dominant frequency of about 350 Hz is approximately 150 Hz higher than that of the Love seam waves. The relative excitation strength of the Love seam-wave group amounts to about 50% in the X*-component and only to about 10%in the Y*-component. If one compares these Love seam-wave amplitude spectra evaluated from the field data with the theoretical amplitude spectra of Fig. 13, the influence of the

Frequency [Hz]

Frequency [Hz I

FIG.20. In-seam seismic transmission survey. Amplitude spectra of the first normal mode of the Love seam waves and the leaky modes estimated from the multiple-filter analysis contour map maxima of (a) the X*-component and (b) the Y*-component of Fig. 11 to evaluate the relative excitation strengths of the single modes on both components.

62

MONIKA BREITZKE

source spectrum becomes obvious. The spectra evaluated from the field data are confined to the frequency band of the source spectrum and their high-frequency components are almost completely damped. Based on these evaluated amplitude spectra, the theoretical Love seam wave (Fig. 11) and the estimated leaky-mode dispersion curve (Fig. 16a), synthetic twomode seismograms were calculated for each component. In Fig. 21 a part of these synthetic seismogram sections is compared with the non-polarization-filtered field data. On both components the arrival times, the durations and the relative amplitudes of the three wave groups in the synthetic and the field data agree well. In particular, the relative excitation strength of the low-frequency part of the Love seam waves (second wave group), which is different in both components, could be modelled very well.

4.8.Two-mode recompressions Finally, using the same amplitude spectra and dispersion curves as for the previous modelling of two-mode seismograms, a simultaneous two-mode recompression was tried for the non-polarization-filtered seismogram sections. The parameters for the recompression filter design are equivalent to those in the one-mode case, and a reduction velocity of 4000 m/s was used. Figure 22 shows the seismogram sections of both components after their twomode recompression. Instead of short, recompressed signals they essentially display the input data superposed by strong numerical noise. Figure 23 illustrates why the one-mode recompressions of the polarizationfiltered input data resulted in well-recompressed wavelets but the two-mode recompressions of the non-polarization-filtered seismogram sections only produced additional numerical noise. Amplitude spectra were calculated for the 482 m trace of the input data, namely the non-polarization-filtered seismogram of the X * component (a) and the polarization-filtered seismogram of the X*-component (b) and Y*-component (c), for the corresponding dispersion filters ((dHf)) and for the recompressed traces ((gHi)). The amplitude spectrum of the non-polarization-filtered trace (a) distinctly reveals the amplitude maximum of the leaky-mode wave group at about 3% 400 Hz but also shows rather strong amplitudes in the low- and high-frequency range below about 250 Hz and above 500 Hz, corresponding to the low- and highfrequency components of the Love seam waves. The amplitude spectrum of the dispersion filter (d) displays the interferences discussed in section 3, especially in the frequency range of the Love seam-wave maximum below about 250 Hz. Above about 300 Hz, the spectral amplitudes of the Love seam waves are so weak that the two-mode dispersion filter essentially agrees with the one-mode dispersion filter of the leaky modes (f). Additionally, the ' correct ' spectral amplitudes of the two-mode dispersion filter can hardly be discerned above about 500 Hz due to the band-limitation of the source spectrum enclosed in this dispersion filter spectrum.


0 0

m

0 0

W

0 0

W

0 0

v

63

64

MONIKA BREITZKE

-

e 0

0 CO

1

E

U

0

c rd

U v)

-d

a

0 0

W

0 0

In

0 0 CO

Y

0

-d

0

0 0

W

0 0

In

t

,.r,

II

-

I

.

-

-

........

.

.........

...........-3

D I S P E R S I V E S E I S M O G R A M SYNTHESIS

Leaky- and 1. Love Mode

1. Love Mode

65

Leaky -Mode

.rl rl

3 m

0.8

$ 0.6 al *a 0 . 4 a al N .r(

0.2

rl

m

E

0.0

g

1.0

Ll

0.8

0.6 0.4

0.2 0.0

-

tJ 0

250

500

750

F r e q u e n c y [ Hz ]

o

250

500

150


o

250

500

750

F r e q u e n c y [Hz]

FIG.23. In-seam seismic transmission survey. Discussion of the two- and one-mode recompressions of the superposing first normal mode of the Love seam waves and the leaky modes, of the single first normal Love seam-wave mode and of the single leaky modes on the basis of the amplitude spectra of the 482m distance traces. (a)+) Amplitude spectra of the input data. (dHf)Amplitude spectra of the dispersion filters. (gHi) Amplitude spectra of the recompressed traces.

These weak high-frequency amplitudes are most likely to be responsible for much of the numerical noise appearing in the recompressed sections of Fig. 22. Due to the calculation of the reciprocal value of the dispersion filters in the case of recompression, these weak amplitudes amplify the high-frequency components (g), which then occur as strong numerical noise. Furthermore, these ‘inaccurate ’ highfrequency components also affect the phase spectra of the recompression filters so that an incorrect phase delay is probably added to the enhanced amplitudes.

66

MONIKA BREITZKE

The amplitude spectra of the leaky-mode dispersion filter (0 and the corresponding recompressed trace (i) show a similar behaviour. The dispersion filter spectrum also suffers from the band-limitation of the source spectrum and amplifies the highfrequency components of the input data too much. In the recompressed seismogram section (Fig. 19) this problem is not as obvious as in the two-mode case because attention is only paid to one single wave group. Nevertheless, the amplification of the high-frequency components can be recognized as additional noise superposing the recompressed wavelets and in some late arrivals of residual Airy-phase wave groups, but does not greatly affect the improvement of the temporal resolution of the leaky-mode wave group. In contrast, the amplitude spectrum of the Love seam-wave dispersion filter (e), which was calculated theoretically up to the Nyquist frequency, still shows high amplitudes above 500 Hz. Hence, only the low-frequency components of the input data (b) were amplified by the recompression while high-frequency components above 250-300 Hz were significantly attenuated (h).

5. SUMMARY A N D CONCLUSIONS A normal-mode superposition approach for the seismogram synthesis and the recompression of dispersive in-seam seismic data was introduced. Based on singlemode amplitude and phase spectra, the Green’s function is determined by a superposition of the displacement fields of the single normal modes. From filter theory’s point of view the Green’s functions can be considered as dispersion filters. A convolution with a source wavelet provides band-limited synthetic seismograms. The inversion of the Green’s functions results in recompression filters which simultaneously remove the dispersion of any number of superposing normal modes. Two methods were used for the determination of the recompression filters. The first computes the recompression a t e r spectra by an inversion of the dispersion filter spectra in the frequency domain. The second derives two-sided recursive recompression filters in the time or z-domain. The dispersion and recompression filters depend on the travel distance. In the one-mode case this travel distance dependence is confined to the phase spectrum. In the multimode case it affects the modal interference pattern of the amplitude and phase spectrum. The normal-mode superposition approach was applied and compared to finitedifference Love seam-wave seismograms including one and two superposing normal modes, and to field data of an in-seam seismic transmission survey including the first normal mode as first mode and a strong leaky mode as second mode. Comparison of the synthetic one- and two-mode Love seam-wave seismograms shows that the finite-difference and the normal-mode superposition methods agree if the travel distance exceeds two dominant wavelengths. Similarly, the one- and twomode recompressions of the finite-difference data almost completely reconstruct the initial source wavelet for travel distances greater than two dominant wavelengths. One- and two-mode synthetic seismograms and one- and two-mode recompres-


67

sions were computed for the first normal mode of the Love seam waves and the leaky modes of the in-seam seismic field data using the normal-mode superposition scheme for both types of mode. The dispersion curves and amplitude spectra of the single modes were evaluated by two different methods. In the case of the Love seam waves, a theoretical dispersion curve was fitted to a multiple-filter group-slowness analysis by trial-and-error. The resulting layer-cake model was then used to compute the amplitude spectra theoretically. In case of the leaky mode and of two superposing modes, the dispersion curves and amplitude spectra were derived from the contour map maxima of the multiple-filter analysis without any further modelling techniques. The resulting synthetic single-mode seismograms agreed very well with the polarization-filtered field data for both the Love seam waves and the leaky modes, while the synthetic two-mode seismogram sections agreed well with the nonpolarization-filtered data in group traveltimes, lengths and amplitudes of the dispersive wave groups. The relative excitation strengths of the normal Love and the leaky modes were well modelled. A knowledge of the exact source and receiver positions proved to be unimportant. The one-mode recompressions of the Love seam waves and the leaky modes result in coherent, non-dispersive wavelets whose signal-to-noise ratio and temporal resolution were distinctly improved in comparison to the input data. The simultaneous two-mode recompressions of the normal Love and the leaky modes did not lead to a satisfactory result. The recompression filters caused additional numerical noise. The reason is probably due to the band-limitation of the input data which does not permit the estimation of the high-frequency components of the single-mode amplitude spectra with sufficient accuracy. Additionally, a theoretical investigation of the amplitude and phase spectra of a two-mode recompression filter revealed that an exact knowledge of the single-mode spectra is necessary to match the modal interference pattern of the recompression filters with that of the input data and to compensate for the dispersive phase distortion. Thus, in conclusion, the estimation of the dispersion and amplitude characteristics from the multiple-filter analysis is sufficiently accurate to provide a good agreement between synthetic seismograms and field data, whether single- or multimoded. For recompression, the accuracy does not suffice, especially in the highfrequency range, Additional modelling techniques for eigenvalue and eigenfunction computations up to the Nyquist frequency must be recommended to overcome the problem of band-limitation,

ACKNOWLEDGEMENTS This investigation was carried out in co-operation with the Deutsche Montan Technologie (DMT) fur Rohstoff, Energie, Umwelt e.V. Essen. Financial support was given by the BMFT of the Federal Republic of Germany under the contract ' Seismische Reflexionstomographie mit Mehrkomponentenregistrierungen - Modellierung und Bearbeitung dispersiver Flozwellen - Einsatz des flozwellenseismischen Messsystems SEAMEX 85'. I thank Professor Dr Dr h.c. L. Dresen for his encour-

68

MONIKA BREITZKE

agement and support of this study. He and Dr Dieter Krollpfeifer critically read the manuscript and made several valuable suggestions.

REFERENCES AKI, K. and RICHARDS, P.G. 1980. Quantitatioe Seismology, Vols 1 and 2, W. H. Freeman & Co. ALFORD,R.M., KELLY,K.R. and BOORE,D.M. 1974. Accuracy of finite-difference modeling of the acoustic wave equation. Geophysics 39,834-842. ALTERMAN,Z . and KARAL,F.C. 1968. Propagation of elastic waves in layered media by finitedifference methods. Bulletin of the Seismological Society of America 58, 367-398. BEXESFORD-SMITH, G. and MASON,I.M. 1980. A parametric approach to the compression of seismic signals by frequency transformation. Geophysical Prospecting 28, 551-571. BERFSFORD-SMITH, G. and RANGO,R.N. 1988. Dispersive noise removal in t-x space: application to arctic data. Geophysics 53,346-358. BOOER,A.K., BERESFORD-SMITH, G. and MASON,I.M. 1978. ustic imaging in coal seams. Proceedings of Ultrasonics Symposium, 225-228. Ultrasonics Symposium Proceedings, IEEE Cat. no. 78CH 1344-15U. BOOER,A.K., CHAMBERS, J. and MASON,I.M. 1977. Fast numerical algorithm for the recompression of dispersed time signals. Electronics Letters 13,453-456. BOOER,A.K., CHAMBERS, J., MASON,I.M. and LAGASSE, P.E. 1976. Broadband wavefront reconstruction in two-dimensional dispersive space. Proceedings of Ultrasonics Symposium, 160-162. Ultrasonics Symposium Proceedings, IEEE Cat. no. 76CH 1120-5SU. BOORE,D.M. 1972. Finite-difference methods for seismic wave propagation in heterogeneous materials. In: Methods in Computational Physics. B. Alder, S. Fernbach and M. Rotenberg (eds). 11, 1-37. Academic Press, Inc. Id.,DRESEN, L., CSOW, J., GYULAI,A. and ORMOS,T. 1987. Parameter estimation BREITZKE, and fault detection by three-component seismic and geoelectrical surveys in a coal mine. Geophysical Prospecting 35,832-863. BUCHANAN, D.J. 1986. The scattering of SH-channel waves by a fault in a coal seam. Geophysical Prospecting 34, 343-365. BUCHANAN, D.J., DAVIS,R., JACKSON, P.J. and TAYLOR,P.M. 1981a. Fault location by channel wave seismology in United Kingdom coal seams. Geophysics 46,994-1002. P.J. and TAYLOR, P.M. 1981b. Fault location in coal by BUCHANAN, D.J., DAVIS,R., JACKSON, channel wave seismology: Some case histories. Bulletin of the Australian Society of Exploration Geophysicists 12, 13-19. BUCHANAN, D.J. and JACKSON,P.J. 1983. Dispersion relation extraction by multi-trace analysis. Bulletin of the Seismological Society of America 67, 1529-1 540. CAPON,J., GRE~NFIELD, R.J. and LACOSS,R.T. 1969. Long period signal processing results for the large aperture seismic array. Geophysics 34,305-329. C H I A R U ~ NC., I , COSTA,G. and PANZA,G.F. 1985. Wave propagation in multi-layered media: the effect of waveguides in oceanic and continental Earth models. Journal of Geophysics 58, 189-196. CLAER~OUT, J.F. 1976. Fundamentals of Geophysical Data Processing. McGraw-Hill Book Co. DRESEN,L. and FREYSTATTW, S. 1976. Rayleigh-channel waves for the in-seam seismic detection of discontinuities. Journal of Geophysics 42, 111-129. DZIEWONSKI, A., BLOCH,S. and LANDISMAN, M. 1969. A technique for the analysis of transient seismic signals. Bulletin of the Seismological Society of America 59, 427-444.


69

FUCHS, K. 1968. The reflection of spherical waves from transition zones with arbitrary depthdependent elastic moduli and density. Journal of Physics of the Earth 16,2741. FUCHS,K. and MULLER,G. 19’11. Computation of synthetic seismograms with the reflectivity method and comparison with observations. Geophysical Journal of the Royal Astronomical Society 23,417-433. GOFORTH,T. and HERRIN,E. 1979. Phase-matched filters: application to the study of Love waves. Bulletin of the Seismological Society of America 69, 2 7 4 . HARKRIDER, D.G. 1964. Surface waves in multilayered elastic media - I. Rayleigh and Love waves from buried sources in a multilayered elastic half-space. Bulletin of the Seismological Society of America 54,627-679. HARVEY,D.J. 1981. Seismogram synthesis using normal mode superposition : the locked mode approximation. Geophysical Journal of the Royal Astronomical Society 66, 37-69. HASKELL, N.A. 1953. The dispersion of surface waves in multi-layered media. Bulletin of the Seismological Society of America 43, 17-34. HERRIN, E. and GOFORTH,T. 1977. Phase-matched filters: application to the study of Rayleigh waves. Bulletin of the Seismological Society of America 67, 1259-1275. HUDSON,J.A. and DOUGLAS, A. 1975. Rayleigh wave spectra and group velocity minima, and the resonance of P-waves in layered structures. Geophysical Journal of the Royal Astronomical Society 42, 175-188. KELLY,K.R., WARD,R.W., TREITEL,S. and ALFORD,R.M. 1976. Synthetic seismograms: a finite-difference approach. Geophysics 41,2-27. KERNER, C . and DRESEN, L. 1985. The influence of dirt bands and faults on the propagation of Love seam waves. Journal of Geophysics 57,77-89. KORN,M. and STOCKL,H. 1982. Reflection and transmission of Love channel waves at coal seam discontinuities computed with a finite-difference method. Journal of Geophysics 50, 171-176. KRAJEWSKI, P., DRESEN, L., SCHOTT,W. and RUTER,H. 1987. Studies of roadway modes in a coal seam by dispersion and polarization analysis : a case history. Geophysical Prospecting 35,767-786. KUPPER,F.J. 1958. Theoretische Untersuchungen uber die Mehrfachaufstellung von Geophonen. Geophysical Prospecting 6,194-256. MARSCHALL, R. 1982. Verbesserung der seismischen Erkundungsmethoden fur die Seismogrammbearbeitung durch Einbeziehung des seismischen Signals. Bundesministerium fur Forschung und Technologie, Forschungsbericht 03E-3043A Technologische Forschung und Entwicklung-Nichtnukleare Energietechnik. MASON,I.M., BUCHANAN, D.J. and BOOER,A.K. 1980a. Fault location by underground seismic survey. Proceedings of the IEEE 127,322-336. MASON,I.M., BUCHANAN, D.J. and BOOER,A.K. 1980b. Channel wave mapping of coal seams in the United Kingdom. Geophysics 45,1131-1143. MONTALBETTI, J.F. and KANASEWICH, E.R. 1970. Enhancement of teleseismic body phases with polarization filter. Geophysical Journal of the Royal Astronomical Society 21, 119129. MULLER,G. 1985. The reflectivity method: a tutorial. Journal of Geophysics 58, 153-174. PANZA,G.F. 1985. Synthetic seismograms: the Rayleigh waves modal summation. Journal of Geophysics 58, 125-145. RADER,D., SCHOTT,W., DRESEN, L. and RUTER,H. 1985. Calculation of dispersion curves and amplitude-depth distributions of Love channel waves in horizontally-layered media. Geophysical Prospecting 33,800-816. REYNOLDS,A.C. 1978. Boundary conditions for the numerical solution of wave propagation problems. Geophysics 43, 1099-1 110.

70

MONIKA BREITZKE

ROBINSON, J.C. 1979. A technique for the continuous representation of dispersion in seismic data. Geophysics 44, 1345-1351. S. 1980. Geophysical Signal Analysis. Prentice Hall, Inc. ROBINSON, E.A. and TREITEL, SUHADOLC,P. and PANZA,G.F. 1985. Some applications of the seismogram synthesis through the summation of modes of Rayleigh waves. Journal of Geophysics 58, 183-188. SWANGER, H.J. and BOORE,D.M. 1978. Simulation of strong-motion displacements using surface-wave modal superposition. Bulletin of the Seismological Society of America 68, 907-922. TOLSTOY, I. and CLAY,C.S. 1966. Ocean Acoustics. McGraw-Hill Book Co. TURIN,G.L. 1960. An introduction to matched filters. I.R.E. Transactions IT-6, 31 1-329. YILMAZ,8. 1987. Seismic data processing. Inoestigations in Geophysics. E.B. Neitzel (ed.), 2. Society of Exploration Geophysicists.