Optimizing Source Wavelets Extracted from the Chirp Sub-Bottom Profiler Using an Adaptive Filter with Machine Learning

Abstract

In this study, we extracted three source wavelets of a Chirp sub-bottom profiler (SBP), which is widely used for high-resolution marine seismic exploration, using a MATLAB-based graphical user interface tool for computational processing. To extract the source wavelet for general seismic exploration data processing techniques, including that for Chirp SBPs, we first evaluated source wavelet extraction techniques using an adaptive machine learning filter. Subsequently, we performed deterministic deconvolution by extracting the optimal source wavelet from the raw data of Chirp SBP. This source wavelet was generated by applying an adaptive filter. Various methods have been studied to solve the multivariate optimization problem of minimizing the error; in this study, a least-mean-square algorithm was selected owing to its suitability for application to geophysical time-series data. Extracting the source wavelet is a crucial part of high-resolution marine seismic wave exploration data processing. Our results highlight the effectiveness of performing deterministic deconvolution by extracting source wavelets using adaptive filters, and we believe that our method is useful for marine seismic exploration data processing.

1. Introduction

Marine seismic exploration involves the investigation and analysis of acoustic waves reflected or refracted from the seafloor and recording them through a receiver. This is performed by artificially generating seismic waves from the source wavelet and then directly receiving reflected and refracted waves to analyze the wavelet and transmission time. This technique is used in submarine geological surveys, energy resource profiling for oil and gas hydrate development, profiling for offshore plant construction coastal development, and underwater archaeology surveys [1,2,3,4]. For example, research involving 3D seismic surveys has been reported recently; in Korea, Kim et al. [5] reported the interim results of a small vehicle-integrated 3D seismic survey that can be used for engineering purposes. Several international studies have been reported on buried archaeological ships using 3D high-resolution sub-bottom seismic surveys [6,7,8]. However, careful selection of techniques is needed according to the purpose [1,9]. The high-frequency Chirp sub-bottom profiler (SBP) transmits sweep pulses, whose frequency characteristics change over time, unlike boomers, pingers, and sparkers—sources using a single frequency [10]. Chirp SBPs have been successfully applied in Quaternary geological studies because it is possible to obtain information about envelope profiling without additional data processing [11,12]. In addition, the attenuation of the Chirp signal acoustic characteristics may be analyzed and applied to seafloor classification [5,13,14,15,16,17]. Research into underwater acoustics on the seafloor is on-going, with two different approaches employed: (1) irradiating the seafloor using acoustics and (2) determining the effect of the seafloor on the behavior of sound waves. Both approaches include the acoustic properties of sediments as parameters.

As mentioned above, research associated with the processing of 3D seismic surveys using Chirp SBPs for the analysis of buried objects has resulted in various achievements, including resolution improvement through computational processing, and seabed and sediment analysis using acoustic characteristics such as reflection and attenuation. However, to date, methods for extracting the source wavelet from Chirp SBPs and for data processing have proven to be insufficient for obtaining cross-sectional views of the lower part of the seafloor at high resolution. If the source wavelet of Chirp SBPs can be extracted, deterministic deconvolution can be applied using the extracted source wavelet. Therefore, obtaining a high-resolution stratum cross-section is possible using a data analysis program with simple coding.

An efficient strategy for the extraction of the source wavelet and subsequent conversion into a Klauder wavelet through correlation is essential for computerizing data from Chirp SBP. The Klauder wavelet, named after the American mathematician John Rider Klauder (1932), indicates the “autocorrelation of a vibroseis sweep. The vibroseis (q.v.) process of injecting a sweep of frequencies into the ground and then correlating them with the sweep pattern to yield a seismic record is equivalent to convolving the reflectivity with the autocorrelation of the vibroseis sweep so that the Klauder wavelet is in effect the seismic source waveform for correlated vibroseis records. It is not restricted to linear sweeps because a nonlinear sweep can be thought of as the superposition of linear sweeps”(Dictionary: Klauder wavelet-SEG Wiki.) [18]. Currently, source waveforms are applied to a method for calculating and using an operator that converts the reflection coefficient into a waveform by comparing the reflection coefficient log data to the field acoustic wave record [7,18]. However, to date, the program has not been put into practical use owing to the difficulty associated with developing algorithms that correlate two variables. An alternative method involves the calculation of a zero-phase sound source waveform by matching the amplitude spectrum with the acoustic wave record using the field acoustic wave record.

For such source wavelet recording and analysis technology, professional profiling institutions (e.g., Bolt in the USA, WesternGeco in Norway, and the Geological Survey in Canada) store source wavelets for thorough quality control of marine seismic profiling. Currently, the Korean Institute of Geoscience and Mineral Resources is also attempting to secure proprietary technology by measuring and analyzing air gun source wavelets [19].

In this study, we aimed to use an adaptive filter to extract source wavelets from a Chirp SBP for seismic profiling data. We extracted source wavelets in three different ways and applied them to raw data to analyze their suitability. The amplitude values of the profile data of Chirp SBPs were compared and used for validation. To verify the efficacy of the technique, we investigated its field applicability for sub-bottom profiling and buried-object detection.

2. Material and Methods

2.1. Theoretical Background of Adaptive Filters in Machine Learning

For fixed filters, such as the commonly used finite impulse response filters or infinite impulse response (IRR) filters, the basic assumption is that the extent of signal quality degradation is known, or the signals do not change with time. However, in most cases, prior knowledge of the signals or statistical characteristics of the noise are unavailable. Therefore, these commonly used fixed filters cannot be used in a non-stationary environment, where the signal-to-noise ratio is unknown. However, an adaptive filter similar to those widely used in communications can help overcome this problem. Adaptive filters use a type of inverse modeling that automatically adjusts the filter coefficients through iterative calculations without prior knowledge of the signal-to-noise ratio. The procedure of using adaptive filters includes: (1) a filtering process that is applied to a series of sequential data to produce outputs, and (2) an adaptive process that automatically adjusts the filter coefficients [20].

e_i = d_i − y_i

(1)

In most filter applications, the adaptive process is considered to minimize the error function or the objective function e. Here, at timepoint i, the error prediction value e_i was taken as the difference between the desired output, d_i, and the filter output, y_i, for the input signal, x_i, as represented in Equation (1)

y_i = W^T⋅X_i

(2)

where i = 1, 2, N, where N is the length of the input signal vector.

For a non-recursive filter with weight vector W and filter length f, the filter output y_i was obtained as the inner product of the transposed matrix of W and input signal vector X_i.

Selecting the desired output, d, in the adaptive process was related to the area of the filter application. Following previous studies, d was taken as the sum of the signal, s, and random noise, n₀. The signal x contained noise n₁, and this noise was not correlated with the signal s but was considered to be correlated with the noise n₀ in an unknown way. In practical situations, the noise-canceling system is used to obtain an output signal with less noise than the original, which is the least-squares best-fit solution [21].

In this study, a least-mean-square (LMS) algorithm was used to account for multivariate optimization. Hattingh [22] applied the LMS algorithm to geophysical time-series data to successfully separate the signal from noise in two time-series datasets.

Obtaining a noise-free Chirp signal from two Chirp signals, X₁ and X₂ with a length N, containing uncorrelated noise, n₁ and n₂, was described as follows. First, the first trace was set as the basic input signal X₁, and the second trace as the reference input signal X₂. The noise-free signal, S, was obtained by filtering the reference input signal X₂. In this case, the basic input signal X₁ was considered the desired signal d. The mean squared error, e_i², was then the quadratic function of the weight in a non-recursive filter. The effect of weighting parameters on the mean squared error e_i² was taken as a multidimensional parabolic surface in which a minimum point was present. On this error surface, the weight corresponding to the minimum point was defined as the optimal Wiener solution. The value of the weight vector W, calculated using the LMS algorithm, represents an estimate that approaches the Wiener solution as the number of iterations approaches infinity. The simple filter weight vector W proposed by Widrow and Hoff [23] is expressed as Equation (3).

W_{i+ 1} = W_i + 2ue_i X_2i

(3)

The new filter weight W_{i + 1} can be expressed as the sum of the previous filter weight W_i and the second term. The second term is expressed as the product of the step size, u, the reference input signal, X₂, and the error function, e_i. In other words, the error e_i calculated in the previous step is fed back to the system to obtain a new filter. The overall process is illustrated in Figure 1. The convergence factor, u, a fixed value, controls the speed and stability of the algorithm. Conversely, when this value is small, precision increases but the required dataset also becomes larger, thereby increasing the computational time required.

When analyzing the sound source signal and ideal Chirp signal, most of the noise was eliminated and the frequency component was almost identical to the Chirp input signal. However, the amplitude varied over time, which was attributed to the degree of noise contained in the signal.

Owing to the application of adaptive filters, the extraction of the sound source was much more sophisticated than that when reference input signals were available. For Chirp SBP exploration, it is assumed that the reference input signal is also available; as such, it is expected to be a linear Chirp signal with a constant signal length and bandwidth, although not exactly known [6,7,8].

2.2. Acoustic Characteristics of a Chirp Wavelet

As the basic mechanism of Chirp SBPs uses sound waves, appropriate frequency bands should be selected and used according to the characteristics of the surveyed sea and the purpose of the survey. In the case of a high-frequency source, a detailed stratigraphic architecture can be profiled, but with little depth of penetration. In typical data, the depth is expressed as the time it takes for the sound waves to be reflected and received from the sub-bottom strata, not as distance. Therefore, the actual sediment thickness is calculated using the sound velocity or the borehole data for the sediments. It is possible to estimate the precise thickness of the sediments and the depth of bedrock by combining the borehole data with the Chirp SBP data [24].

The Chirp SBP used for field data acquisition acquired seismic exploration data using Z-TAMII from SonarTech Co. Ltd. (Busan, Korea). The frequency band was 2–7 kHz, the center frequency was 4.5 kHz, and the pulse length was 2 ms. Chirp SBPs transmit a sweep pulse with a frequency that changes with time. However, the source wavelet of a typical Chirp SBP has a tapered section, in which the amplitude is reduced in the low- and high-frequency sections. This tapering can be produced with a line, a sine function, a cosine function, or a logistic curve [1]. As tapering reduces the amplitude of the high- and low-frequency sections, it may lead to a large difference from the actual source wavelet. Therefore, when using the taper function, the similarity to the received Chirp SBP signal should be checked before applying the function. Figure 2 shows a Chirp SBP source wavelet by applying a cosine function for 1 ms, which is half of the total pulse length of 2 ms.

In this study, we used a MATLAB-based graphical user interface (GUI) tool to extract the source wavelet of a Chirp SBP. Our procedure consisted of (1) the ideal source wavelet generated (Source I) at a center frequency of 4.5 kHz and a frequency band of 2–7 kHz, and (2) a source wavelet extracted (Source II) by applying an adaptive filter to the signal received from the primary reflection signal with the ideal source wavelet as a reference waveform. Subsequently, (3) the source wavelet was extracted (Source III) by applying an adaptive filter to the primary reflection signal received from two adjacent traces. These three source wavelets were extracted and applied to raw data to analyze their suitability. The optimal source wavelet was correlated with raw data via frequency spectrum analysis to utilize the result as the basic analysis data.

3. Results and Discussion

3.1. Chirp Wavelet Processing

The synthetic wave signal represents the response characteristics of the Chirp signal modified digitally according to the virtual sound source and virtual stratigraphic information. The information on the bottom layer of the seafloor was expressed as a reflectivity coefficient, which was set as +1 at 0.018 s and −0.5 at 0.027 s.

If the signal has an envelope shape, the amplitude can be easily measured regardless of the polarity of the waveform and phase characteristics. A Klauder wavelet section (Figure 3) was generated by correlating the Chirp SBP raw data (Figure 4) with the source wavelet. When the Hilbert transform is performed with the Klauder wavelet, it can be divided into real and imaginary parts. Assuming that the real part is x(t) and the imaginary part is y(t), E(t) by Hilbert transform is represented as shown in Equation (4).

E(t) = √((x(t))²+ (y(t))²)

(4)

After undergoing Hilbert transformation, an envelope-shaped section with only positive values can be obtained from the Klauder wavelet.

Figure 5 shows the result of correlating raw data from Figure 4 with a source wavelet. The noise from signals with lower correlations was attenuated more than that from correlated raw data.

As shown in Figure 6, it was possible to obtain the envelope section of acquired data by correlating the source wavelet with raw data. In general, when a Chirp SBP is used, the program displays the section shown in Figure 6, after undergoing the process shown in Figure 4 and Figure 5. Only in conjunction with the section information shown in Figure 6 could the results be used as basic analysis data in stratigraphic studies, for which Chirp SBPs have been widely used. However, if the source wavelet for deconvolution processing is extracted using raw data, an improved section can be obtained.

Figure 3b,c show the synthetic waveform signal with a reflectivity coefficient of +1 at 0.018 s and −0.5 at 0.027 s; the signal at 0.027 s represents an amplitude reduction to 0.5 and a phase reversal compared with the signal at 0.018 s.

Figure 4, Figure 5 and Figure 6 show the process of creating an acoustic wave exploration cross-sectional view from the Chirp SBP used in this study.

3.2. Chirp SBP Source Wavelet Extraction

To obtain the results from high-resolution marine seismic exploration, raw data of Chirp SBPs need to be confirmed through computer processing. The source wavelet must be acquired for data processing. Generally, only basic information for the source wavelet is disclosed in the file header, and the entire source wavelet is not given. The source wavelet used in marine seismic profiling serves a very important purpose in obtaining and processing profiling data. In the case of low-frequency sound sources, such as air-guns and water-guns, various attempts have been made to calculate transmission (source) waveforms, despite difficulties in waveform analysis due to bubble effects or mutual interference in the actual source wavelet analysis.

To extract the source wavelet from on-site sound wave data, the first method is to calculate the operator and then use it to convert the reflectivity coefficient into a waveform by comparing reflectivity coefficient log data with on-site sound wave recordings. However, to date, the program has not been put into practical use owing to the difficulty in developing an algorithm that correlates the two variables. The second method is to calculate a zero-phase source wavelet whose amplitude spectrum matches the sound wave record using the on-site sound wave records; this method is called “Statistical Wavelet Extraction” [25].

3.2.1. Ideal Source Wavelet (Source I)

Figure 7a shows a Chirp source wavelet (Source I) generated at a frequency of 2–7 kHz and pulse length of 2 ms. As shown in Figure 7b, as a result of frequency analysis, the center frequency and the frequency band were well displayed. The waveform (Figure 7c) and frequency analysis data (Figure 7d) illustrate that the correlation result was well represented with the zero-phase Klauder wavelet.

3.2.2. Source Wavelet Extraction Using the Adaptive Filter (Sources II and III)

First, the new source wavelet was extracted (Source II) using an ideal Chirp source wavelet (Source I) with a center frequency of 4.5 kHz and a frequency band of 2–7 kHz as a reference wavelet via adaptive filtering with the seabed reflection signal extracted from raw data (Figure 8). In addition, another source wavelet was extracted by applying the adaptive filter to the seabed reflection signal extracted from two adjacent traces from the raw data (Source II; Figure 9).

To examine the characteristics of the source wavelet, Source II and III waveforms were represented as Klauder wavelets, and the frequency spectrum was analyzed. The data in Figure 8e,f, which represent the results of Source II data, are a source wavelet with a center frequency of 4.5 kHz and a frequency band of 2–7 kHz and are better than the data in Figure 9, which represent the results of Source III data.

To determine the optimal source wavelet, three source wavelets—Sources I, II, and III—were applied to the Chirp SBP traces and sections acquired at the actual site. As a result, the sound wave traces correlated with the application of the Source II wavelet, which are shown in Figure 10c and Figure 11c, showed higher amplitude seabed signals. The amplitude of the reflection signal from the lower strata was also higher than that from other data (red boxes in Figure 10 and Figure 11).

By correlating the signals and the entire section and representing the result as an envelope section, the images in locations (a), (b), and (c) show that the section acquired using Source II data (Figure 12) had a higher resolution and better continuity of the strata than the sections obtained using Source I (Figure 13) and Source III (Figure 14). Location (a) is a depression, and because Figure 13 and Figure 14 show relatively higher amplitudes, the result appears in a blurred form, whereas Figure 12 displays the shape in detail.

As for Location (b), Figure 12 shows an abnormal signal, which is not visible in Figure 13 and Figure 14. Location (c) is a reflection signal from a buried object near the surface. The reflection signal continuing from the object’s surface to the bottom of the seabed can be observed in Figure 12.

These results show that the source wavelet extracted by applying adaptive filters to the reflective signal of the Chirp SBP, which contains the characteristics of the actual source wavelet, exhibited a higher resolution and continuity of strata compared with the artificially created ideal source wavelet. Thus, it is possible to extract source wavelets using the adaptive filters of machine learning. This technique can be applied to many similar data types, such as seismic land and marine low-frequency data, in addition to Chirp SBP data processing.

To confirm the optimal source wavelet, three source wavelets designated as Sources I, II, and III were applied to the Chirp SBP trace acquired in the field and the cross-section. By applying the Source II wavelet (i.e., data from Figure 10c and Figure 11c), it was confirmed that the correlated seismic trace revealed the relatively high amplitude of the submarine signal, and that the amplitude of the lower reflected signal was relatively high compared with that of other data (red boxes in Figure 10 and Figure 11). As a result of confirming not only the signal, but also the envelope cross-section after correlating the entire cross-section, the figure obtained using Source II was compared with the cross-section obtained using Source I (Figure 12) and the cross-section obtained using Source III (Figure 14). Using the images of Locations (a), (b), and (c), it was possible to confirm that the cross-section in Figure 14 had a relatively high resolution and continuity of strata. Location (a) appears in a depression-shaped position; in Figure 12 and Figure 14, and this location appears compressed owing to the relatively high amplitude, while Figure 13 presents a detailed view of the depression shape. Additionally, in Figure 12 and Figure 14, abnormal signals that are not easily distinguished are apparent at Location (b). This was confirmed in Figure 14. Location (a) depicts a signal that was reflected from an object buried in the surface layer and illustrates a reflection signal extending from the surface layer to the bottom of the seafloor. This was confirmed in Figure 13. Location (c) is a reflective signal from a buried object sunk in the surface layer. Reflective signals from the surface layer to the bottom of the seafloor can be clearly identified in Figure 14.

This study has some limitations. In general, the Chirp SBP is displayed on the screen as a signal in the form of an envelope having only a positive value. Because only positive values result in high-resolution images, images were displayed using only these values in the form of an envelope and used for data processing. Therefore, while some manufacturers allow for the acquisition of raw data, equipment manufacturers only allow for the acquisition of data that have undergone computer processing processes such as matching filters. As a result, Chirp SBP cannot be used for other computer processes.

4. Conclusions

In this study, we extracted three source wavelets of a Chirp SBP using a MATLAB-based GUI tool for computational processing. Extraction was performed by applying an adaptive machine learning filter to the ideal 2–7 kHz of the Chirp wavelet and the seafloor reflective signal, exploiting the fact that reflective SBP signals also contain the characteristics of the source wavelet.

For data processing of Chirp SBP, a correlation cross-section in the form of a Klauder wavelet can be created and applied by determining the optimal source wavelet. Therefore, in this study, it was possible to extract the source wavelet by using the adaptive filter.

The source wavelet extracted from Source II (applying an adaptive filter to the signal received from the primary reflection signal with the ideal source wavelet as a reference waveform) was confirmed to be the optimal source wavelet. This method can be used to produce high-resolution sub-seafloor strata sections and to detect buried objects.

The Chirp SBP is displayed on the screen as a signal in the form of an envelope having only a positive value (only positive values provide a high-resolution image), and is used for data processing. Importantly, certain manufacturers allow the acquisition of raw data, whereas equipment manufacturers often only allow for the acquisition of data that have undergone processing using computer processes such as matching filters, but not raw data. Hence, the use of Chirp SBP is limited by the fact that it cannot be used for other computer processes.