CC BY
9
УДК 550.34
DOI: 10.18303/2618-981X-2018-3-11-16
АВТОМАТИЗАЦИЯ СПЕКТРАЛЬНОГО АНАЛИЗА ДАННЫХ ПОВЕРХНОСТНЫХ ВОЛН
Александр Викторович Яблоков
Институт нефтегазовой геологии и геофизики им. А. А. Трофимука СО РАН, 630090, Россия, г. Новосибирск, пр. Академика Коптюга, 3, инженер; Институт горного дела им. Н. А. Чина-кала СО РАН, 630091, Россия, г. Новосибирск, Красный пр., 54, младший научный сотрудник, e-mail: YablokovAV@ipgg.sbras.ru
Александр Сергеевич Сердюков
Институт нефтегазовой геологии и геофизики им. А. А. Трофимука СО РАН, 630090, Россия, г. Новосибирск, пр. Академика Коптюга, 3, кандидат физико-математических наук, старший научный сотрудник; Институт горного дела им. Н. А. Чинакала СО РАН, 630091, Россия, г. Новосибирск, Красный пр., 54, младший научный сотрудник, e-mail: SerdyukovAS@ipgg.sbras.ru
В работе рассматривается метод многоканального анализа поверхностных волн (MASW) и предлагается использовать новый подход к извлечению дисперсионных кривых поверхностных волн из записей сейсмических наблюдений. Идея подхода состоит в усилении пакетов поверхностных волн, используя временно-частотные представление сейсмических данных на основе преобразования Стоквелла и оценки волнового числа путем помехоустойчивого пространственного спектрального анализа.
Ключевые слова: сейсморазведка, поверхностные волны, спектральный анализ.
AUTOMATIZATION OF SPECTRAL ANALYSIS OF SURFACE WAVE DATA
Alexandr V. Yablokov
Trofimuk Institute of Petroleum Geology and Geophysics SB RAS, 3, Prospect Аkademik Koptyug St., Novosibirsk, 630090, Russia, Engineer; Chinakal Institute of Mining SB RAS, 54, Krasny Prospect St., Novosibirsk, 630091, Russia, Junior Researcher, e-mail: YablokovAV@ipgg.sbras.ru
Aleksander S. Serdyukov
Trofimuk Institute of Petroleum Geology and Geophysics SB RAS, 3, Prospect Аkademik Koptyug St., Novosibirsk, 630090, Russia, Ph. D., Senior Researcher; Chinakal Institute of Mining SB RAS, 54, Krasny Prospect St., Novosibirsk, 630091, Russia, Junior Researcher, e-mail: SerdyukovAS@ipgg.sbras.ru
We consider the multichannel analysis of surface wave (MASW) method and propose to use a new automated surface wave dispersion curves picking method. The idea is to amplify the surface waves packets, using S-transform based time-frequency representation of seismic data, and then estimate wavenumber by robust spatial spectral analysis. The proposed method showed good results when processing field data.
Key words: seismic exploration, surface waves, spectral analysis.
We consider the multichannel analysis of surface wave (MASW) method [8]. This method is based on utilizing the dispersion curves of phase surface wave velocity dependence on time frequency. The dispersion curves are extracted from multichannel seismic records (typically linear acquisition systems are used), containing broadband Rayleigh wave data. The MASW method has been intensively developed and applied over past two decades [10, 12-15]. MASW is mainly aimed on estimating subsoil structure for geotechnical purposes. In the field of hydrocarbon seismic exploration surface wave analysis also can be used to compute receiver static corrections for body waves processing [6, 9]. Commonly, the dispersion curves are inverted for S-wave ID-velocity profiles [12]. The reconstruction of lateral near surface variations may be crucial for a number of applications. Pseudo-2D (3D) S-wave velocity sections are constructed from a sets of 1D models by using spatial interpolation [3, 4].
Theoretically, in most situations the fundamental mode Rayleigh surface wave curve can be extracted by picking the f-k spectral maximums. However, other waves and noise can lead to the presence of other local spectrum maximums. Due to the limited length of the seismic acquisition array the spectral leakage takes palace and close picks can merge. Because of these effects, in most MASW implementations, the dispersion curves are picked manually. Experienced operator can guess how to plot a smooth and realistic dispersion curve.
Usually the surface waves are generated by impulse sources. The seismic oscillations are non-stationary in this case. In practice, the surface wave packet is often extracted for the subsequent spectral analysis by cutting out the corresponding part of the seismograms. This procedure is done manually within time-offset representation of the seismic recordings. High energy triangle area, expanding by time and offset axis (thanks to the dispersion of surface waves velocities) is taken. That is the straightforward intuitive way to amplify the surface wave. A more advanced method is to consider time-frequency representation of seismic data.
We present the automated picking method, providing smooth and realistic dispersion curves. The proposed processing method has two steps. In the first step the surface wave packet is extracted using S-transform [11] of seismic signal. At the second step the phase velocities are determined by spectral analysis of the extracted wave packet. The proposed method showed good results when processing field data.
The continuous-wavelet transform (CWT) is widely used for seismic data processing [1, 2]. In contrast to the standard short time Fourier transform (STFT), the CWT method does not require preselecting a window length and has a variable time-frequency resolution. Kulesh [7] showed how to estimate both group and phase velocities of a dispersive waves using CWT. Roohollah [9] implemented the similar method based on Stockwell transform [11] (S-transform), which provides frequency-dependent resolution similar to CWT. Unlike the CWT, the S-transform maintain a direct relationship with Fourier spectrum [11]. That is why S-transform is preferable for seismic data processing. In particular, the S-transform features make surface waves attributes estimation more straightforward [9]. The S-transform of a signal h(t) is given by relation:
+< I r\ (l-t)2 f2
S [h(t)(x, f )]=J h(t)fe~ 2 e-2%ftdt, (1)
where f is the time frequency, t and t are both time variables - this notation has been introduced just to separate the integration variable from the parameter under the integral.
Let's observe the surface wave packet. Consider two signals hj and h2, recorded by a couple of receivers of a linear acquisition system (both of the receivers are located on the same source-receiver line). The S-transform of the second signal can be expressed in terms of the S-transform of the first signal:
S h(t)](t, f) = e~n*k (f )le"^(f )lS [h(t)](t - k (f)l, f). (2)
After the application of S-transform, one should find the maximum amplitude (ridge) of the time-frequency distribution for a fixed frequency for both signals. Note,
that — = U (f) is the group velocity. Thus, according to (2) the time difference
k (f)
between the ridges of two transforms equals the group velocity travel-time. the phase
lf
shift between the ridges is connected to phase velocity travel-times: k (f )l = ——
C (f)
where C (f) is the surface wave phase velocity. Roohollah [9] proposed to use these relations to extract surface wave attributes from two receiver recordings.
The phase velocity estimation is more preferable than only the group one. For instance, a situation is often observed when the dependence of the surface wave wavenumber on the frequency becomes linear starting from a certain frequency i.e.
k (f) = k0 + af. The group velocity becomes constant in this case: U (f) = — like in
a
homogeneous medium. The phase velocity is not constant if k0 is nonzero - it can be inverted for some depth depended S-profile.
The MASW method is more suitable for determining the surface wave phase velocities than two receiver approaches. It is more robust. f-k analysis can also help to separate different surface wave modes and estimate their phase velocities independently. That is why we have modified the S-transform approach to apply to multichannel data. Consider the linear acquisition system. Let us implement the S-transform to every receiver record, pick up the maximum and get the phase function:
s ' hj (t)_ (f, ax)
s ' hj (t)_ (f, x1"ax)
p(f, Xj) = -J— = exp(-i 2*(ko + k (f) xj + 8, (3)
where Xj is the j-th receiver offset, hj(t) is the corresponding seismic record and i™*
is the time of the maximum ridge of the observed trace. We assume that the phase of the function P( f, Xj), j = 1...N is determined mainly by the wave number of the fundamental mode k(f), k0 is the source dependent phase shift and s is the signal model error.
The straightforward way to get the wavenumber k(f) is the Fourier transform. Note that since it is assumed that a useful signal (3) contains only one harmonic, it is possible to use more advanced high resolution eigenspace methods [5]. By plotting the wavenumber spectrum of the phase function (3) for a set of time frequencies we obtain the f-k image. This f-k image turns out to be much 'cleaner' than the one, obtained using 2D FT. As showed our experiments, a smooth fundamental mode dispersion curve can be obtained by picking maximum amplitude ridges on the f-k plane.
A field data has been acquired in vicinity of Novosibirsk, Russia. The receiver array was made up of 90 vertical 10 Hz geophones with 5 m spacing. The time domain acquisition parameters were 3 s length and 1ms sampling rate (Fig. 1, a). The data S-transform at frequency f = 10Hz amplitude versus distance is presented in Fig. 1, b. The surface wave packet is shown in red. In order to recover 2D shear wave velocity structures, we used moving rectangular 50m lengths spatial windows during wavenumber spectral analysis.
Distance (m) Distance (m)
Fig. 1. Time-frequency representation of the seismic records: a) raw data; b) S-transform of the data versus distance at Frequency = 10 Hz
Figure 2, a, b shows f-k spectra for the first ten receivers: one obtained using the proposed approach and the second obtained by the standard method. The dispersion curves are shown in black. It can be seen that the first curve, shown in Fig. 2, a, turns to be smoother than the second in Fig 2, b. The first curve is similar to that obtained by numerical modeling in stratified medium. Note, that it is a straight line for higher frequencies. We have used simple linear regression to define the dependence of the wavenumber on the frequency (higher than it was possible to pick).
Fig. 2. f-k spectra and dispersion curve picking:
a) proposed two-step automated method; b) conventional result using time-spatial 2D FFT
The series of dispersion curves were inverted for a set of 1D shear wave profiles. They were gathered to 2D sections by using interpolation. A result, presented in Fig. 3, a, is obtained by the inversion of dispersion curves, automatically picked by proposed method. In Fig. 3, b an inversion of conventional manually picked on 2D FT f-k image dispersion curves is shown. The inversion procedure was the same for both results. Note that the section in Fig. 3, a is almost horizontally homogeneous. This indirectly exposes its reliability.
Fig. 3. Pseudo-2D shear-wave velocity sections by inversion of a series: a) automatically picked dispersion curves; b) conventional manually picked dispersion
curves
A new method for surface wave dispersion curves picking, based on the implementation of S-transform to multichannel data and further robust wavenumber estimation, has been proposed. This method not only automates the processing routine but also significantly improves the reliability of MASW results.
The research was supported by Russian President grant No.MK-6451.2018.5.
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© А. В. Яблоков, А. С. Сердюков, 2018
