(1) Effective wave and interference wave
In the field construction of seismic exploration, seismograph can record all disturbances near the observation point. Among these interferences, the waves used to solve the proposed geological task are called effective waves, while those waves that have nothing to do with the exploration task and hinder the tracking and identification of effective waves belong to interference waves. Interference wave is sometimes a relative concept. For example, in the reflected wave method, refracted waves are often regarded as interference waves.
Interference waves can be roughly divided into two types: regular interference waves with obvious propagation laws, such as acoustic waves, surface waves, industrial electrical interference, shallow refraction waves, multiple reflection waves and so on. Vibration without obvious propagation law is called irregular interference wave (also called random interference wave), such as microseisms, wind, waves and random fluctuations of human factors in earthquake records. In field collection and data processing, various measures have been taken to highlight effective waves and suppress interference waves.
(B) the principle of digital filtering
The process that an original signal becomes a new signal after passing through a device is called filtering: the original signal is called input, the new signal is called output, and the device passing through it is called filter. The "signal" and "device" mentioned here should be broadly understood: they can be concrete (such as "signal" of current and "device" composed of inductance, capacitance, resistance and other elements) or abstract (such as counting and mathematical operation).
Figure 1-4 1 Response characteristics of different filters
When the input is unit pulse Δ t, the output signal is the impulse response of the filter, and the waveform of the response is different from that of the input; When the same unit pulse is input into different filters, the waveform of the output pulse response is also different, as shown in figure 1-4 1. That is, the characteristics of the filter can change the input signal. Therefore, we can choose the characteristics of the filter or design the filter coefficients according to the expected output waveform.
The so-called digital filtering is to change the discrete sampling of the input signal into a digital signal, design the characteristics of the system into a mathematical function (called a weight function), and then perform mathematical operations on the digital signal and the mathematical function to obtain a new digital signal output.
Now let's briefly discuss the specific process of digital signal filtering.
For * * * reflection point data, the effective wave is a reflection wave. If the seismic record X(t) is written as the sum of two parts, i.e.
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Where: S(t) and n(t) represent effective wave and noise respectively. According to the linearity of digital filtering, the output can be expressed as
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That is, it is equivalent to the sum of the digital filtering results of S(t) and n(t) respectively, but our purpose is to suppress noise and increase noise.
Strong effective wave. To this end, we hope that
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From the perspective of frequency domain, it is expected that
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The above formula is equivalent to
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If the frequency spectra of signal S(t) and noise n(t) are separated and do not overlap, then
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When H(f) is determined, h(t) can be obtained according to Fourier transform. In this way, Y(f) is obtained by the product of H(f) and X(f), i.e.
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According to the convolution theorem, the product of frequency domain is the convolution of time domain, that is
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The results show that time domain filtering is realized by convolution operation of input signal X(t) and filter impulse response h(t).
In seismic exploration, sometimes the spectral components of effective wave and interference wave are very close or even coincident, so it is impossible to suppress interference by frequency filtering, and it is necessary to filter by using the differences between effective wave and interference wave in other aspects. If the apparent velocities are different, the apparent velocities can be filtered. Because convolution operation involves two variables, time and space, it is called two-dimensional filtering.
When seismic waves propagate underground, the earth medium is equivalent to a filter, which filters out the higher frequency components and retains the lower frequency components. This is the so-called "earth filtering". The loss of high-frequency components narrows the frequency spectrum and prolongs the duration of short pulses excited after earth filtering, so the formation can be regarded as a filter with low-pass frequency characteristics.
In order to improve the resolution and signal-to-noise ratio of seismic records, the extended waveform is compressed into a pulse wavelet that is close to that without earth filtering. This process is called inverse filtering. The inverse filtering process is just the opposite of the previous filtering process.