# A new method for high resolution well-control processing of post-stack seismic data

### Concept and research of high resolution

Seismic resolution includes vertical resolution and lateral resolution. The former is referred to in this paper.

Usually, the concept of resolution is discussed by analyzing (1) whether the reflection waves at the top and bottom of thin layers can be separated, (2) the amplitude response–tuning thickness of the wedge model, or (3) the convolution model of the Ricker wavelet in time domain.

The third analysis method above involves the Ricker wavelet, and the Rayleigh criterion and the Ricker criterion are formed depending on the wavelet parameters (e.g. width or period, frequency). The Rayleigh criterion, which is commonly used, takes 1/2 of the dominant period as the resolution limit to obtain a thickness resolution limit of 1/4 wavelength.

When the seismic data contain noise, resolution is calculated mainly according to the definition of Widess [[1], [2], [3]]. Let the resolution without noise be P0, P with noise, and the signal to noise ratio (SNR) be R, we get,

According to Equation (1), the higher the SNR, the closer the resolution is to the resolution without noise; conversely, the resolution is reduced.

Therefore, in addition to narrow wavelet and wide band signals, the SNR should also be considered to improve resolution.

Resolution can be improved from the prospective of acquisition, prestack processing and poststack processing. In this paper, only a high-resolution processing technology of poststack seismic data (including stack migration data and migration stack data) is presented.

A number of poststack data high-resolution processing methods are available [[4], [5], [6]], but they are not sufficient enough, fundamentally due to the (high-frequency) noise of seismic data.

The high-resolution processing methods emerged since the 1990s are generally based on deconvolution algorithm, and need to meet three prerequisites [[7], [8], [9]]:(1) seismic data are minimal phase and non-time/space-variant; (2) seismic reflection coefficient is white noise; and(3) noise interference is zero or very small, and in a random and stationary sequence. However, these conditions are difficult to meet, especially at a certain frequency height, the noise is extremely complex and strong, making it hard to achieve a significant increase in resolution.

The key to improving resolution is denoising, while the key to denoising is to figure out the law of noise distribution. However, for high-frequency noise, which is usually complex with wide band and unclear or no regularity, the common denoising methods are not effective, thereby hindering the improvement of resolution.

Since 2000, other high-resolution processing methods have been developed, including the well-control high-resolution processing method based on neural network algorithm. These methods extract wavelets before deconvolution, or use the log spectrum to expand the seismic spectrum, or directly perform high-resolution physical property inversion [[10], [11], [12], [13], [14]]. The former two denoise before expanding frequency, which cannot significantly improve the resolution; the latter does not directly improve the seismic resolution characterized by seismic waveform, which is not a high resolution in common sense.

Obviously, the methods by denoising before frequency expanding cannot substantially improve the resolution. This paper presents a new method combining the log synthetic record and the seismogram, which are similar and regular in high-frequency effective signals. The new method can release the high-frequency effective signals to improve the resolution while automatically denoising.

### Overview of high-resolution processing method

Usually, seismic data have a dominant frequency ranging from 10 to 70 Hz and a primary frequency from 20 to 40 Hz. However, the high-frequency effective signals of real data are distributed above 120 Hz, or even as high as 200 Hz. If such high-frequency seismic signals are completely released, the resolution will undoubtedly be greatly improved, so reservoir geological problems related to resolution can be solved effectively. In this paper, high-frequency effective information is obtained by using a well-control method.

### Basic algorithm

High-resolution processing is complex. It requires specific algorithms. Neural network algorithm is a typical one.

Neural network algorithm is well-structured and mature, represented by BP algorithm. As to the BP algorithm, i.e., the error back propagation algorithm, fundamentally, the input signal is brought into the network to react with the network function; the result formed is compared with the sample data to get the error, which is back-propagated to the input end and then assigned to the input layer and the middle layer before being propagated to the output end. Reiterate the process until the expected minimum error is obtained, that is, the network weight value or the model is obtained. In the extrapolation stage, the model is applied to the unknown data, and after certain processing, the output result is got.

In the well-control high-resolution processing method proposed herein, the input end is the actual seismogram, and the output end is the log synthetic record.

### Methodology

### Modeling using the “three properties”

Synthetic record and seismogram are characterized by similar effective signal and dissimilar noise, regular effective signal and irregular noise, and similar adjacent frequency. According to these characteristics, the final model can be established more readily and accurately by progressive mapping from low frequency to high frequency, and ultimately the relationship between the lowest frequency and the highest frequency is determined. This method, not noise-oriented, can strengthen effective signals and weaken noise. It improves resolution and removes noise at the same time, different from traditional methods which expand frequency after denoising.

### Adaptive extrapolation

First of all, a high-resolution adaptive extrapolation network structure is designed [11,12]. Fig. 1 shows an adaptive extrapolation network, which connects two common BP networks. The front and rear input ends are all seismograms, while the middle layer is used as the output layer to output high-resolution results (equivalent to synthetic record, or called pseudo-synthetic record). Unknown samples can be input in the extrapolation process for adaptability training of the network.

Secondly, an efficient adaptive training method is proposed. Affected by the limitation of logging data (non-dense distribution, non-uniform distribution, non-facies belt distribution, data error, etc.) and the lateral phase variation, structural relief and wavelet difference of seismic data, the established model may not be well adapted to the whole block. Therefore, corresponding measures are considered in the extrapolation stage, including trace by trace [10] and radial adjustment models, that is, the network structure obtained from the current seismic trace is taken as the initial weight of next trace or in a certain range around it to perform stepwise adjustment. In order to improve the computational efficiency, it is necessary to use the ways like phase control and structural control to adjust the model, that is, seismic data extracted in different facies belts and structural positions of the whole block serve as input data to adjust the model adaptively, and then the model is applied to all unknown data.

### Model tests

A theoretical model was designed to verify the validity and correctness of the method. The frequency recovery, energy recovery, phase correction, removal of random noise and regular noise were tested, and finally the convolution model was used for verification.

### Model design

The designed geological model is shown in Fig. 2. It is a velocity model combining several horizontal layers and wedge-shaped layers, where the upper part (Layer 4) contains a thin layer of 2 m in thickness. In the model, three wells, w1, w3, and w2, are designed from left to right, at 200 m, 500 m and 800 m, respectively. A synthetic seismic profile (zero phase) with primary frequency of 80 Hz is generated according to the geological model, and it is used to identify the designed geological horizons.

In the test, the synthetic records at wells w1 and w2 were used as the known curves, while the synthetic record at w3 was used as the verification curve. In the profile, the well curves are all simulated synthetic records, and formed by convolution of reflection coefficient and wavelet converted from formation velocity at wellhead.

### Frequency recovery tests

Based on the same frequency mapping, the seismic trace (broad band, noise-free) and the synthetic record with the same primary frequency of 80 Hz are correlated and processed to obtain a profile (Fig. 3). The purpose is to verify whether the algorithm destroys or recovers the existing signal. The comparison of the recovered profile (Fig. 3) with the original synthetic profile (Fig. 2) shows that almost all the frequency components are completely recovered, only resulting in some weak noises.

### Energy recovery tests

Fig. 4 is a simulation of the common stacked profile, i.e., the primary frequency is low, and the high frequency exists with very weak energy. The purpose of the test is to recover the potential effective components of high frequency with weak energy by calculation and improve the resolution. The frequency spectrum was formed by attenuating the medium and high frequency energy above 50 Hz in the 80 Hz primary frequency profile to 20% of the original frequency. At this time, the primary frequency is 40 Hz, the effective bandwidth is the same as the profile of 80 Hz primary frequency (5–150 Hz), but the energy is strong in low frequency band and high in high frequency band, which is similar to the actual seismic profile. The test basically recovers all the frequency components, and the whole profile is close to the profile of 80 Hz primary frequency, only resulting in a few noises. The test result shows that as long as the profile contains effective components of high frequency, they can be recovered, although the energy is weak.

### Phase correction test

Fig. 5 shows a test of phase correction, which is made to observe whether the phase of the original profile should be considered at the time of high-resolution processing. The synthetic seismic profile of the minimum phase (30 Hz primary frequency, Fig. 5-a) was designed. The relationship between this profile and the synthetic record of zero phase was established, and then processed to obtain the zero phase profile (Fig. 5-b), which is close to the original zero phase profile (Fig. 5-c). The test result shows that the method has the function of phase correction, and the zero-phase wavelet can be used to improve the resolution, regardless of the phase of the seismic record. This method does not need to consider the wavelet phase, so it is very convenient to improve resolution and greatly improves the efficiency of data utilization.

### High-frequency strong random noise removing

Fig. 6-a shows an original noise-free profile of 40 Hz primary frequency, Fig. 6-b shows the profile obtained by adding 50–70% random noise after attenuation of high frequency above 40 Hz, and Fig. 6-c shows the processed high–resolution profile. Fig. 6-d, e and f show the high frequency corresponding to Fig. 6-a, b and c, and the primary frequency is 110 Hz. The event of effective signal in the high frequency of noise-free profile is clear; the effective signal in the high frequency of original noise profile is disordered, and the event is almost completely submerged in the noise; and the effective signal in the high frequency of high–resolution profile is significantly enhanced compared with that in the high frequency of original noise profile, closer to that in the high frequency of noise-free profile. Obviously, the high-frequency strong noise is better suppressed in the high–resolution profile than in the original noise profile.

### High-frequency regular noise removing

Fig. 7 shows a randomly selected external actual seismic profile, which is significantly different from the model profile; especially, the strongly inclined event in the upper part is largely different from the horizontal event in the model profile. The medium and high frequency (50–90 Hz, Fig. 7-b) filtered from the external profile was added as the regular noise of the model to the noise-free profile of 40 Hz primary frequency, forming a regular noise profile, with noise content of about 50%.

The middle figures in Fig. 8 show the high–resolution profiles and high frequency after 500 times and 5000 times of iteration, respectively. Obviously, with the increase of iterations, the regular noise is gradually weakened, the effective signal of high frequency is gradually recovered, and the obtained high–resolution profile and its high frequency are gradually close to the noise-free profile and its high frequency. The variation of the inclined event in the ellipses can clearly reflect the effect of the method, showing that the effective signal of high frequency is gradually recovered and approaches the noise-free profile.

The above tests comprehensively reflect the key role of this method in improving resolution: it can effectively recover the effective signal of weak-energy high frequency, remove regular and random noises and correct phases.

### Selection and determination of key parameters

Two key parameters should be carefully selected in practical application.

### Frequency range

Nowadays, the low frequency of poststack seismic data is generally below 10 Hz, and the effective signal of high frequency usually exceeds 120 Hz, or even reaches 200 Hz [15,16]. The frequency range can be determined by frequency division narrow band scanning. The event of effective signal of high frequency is nearly parallel to the event of primary frequency profile, while the random noise of high frequency is disordered, and the event of regular noise of high frequency is generally not parallel to the event of primary frequency. Therefore, observation is made in the direction of high frequency until the event parallel to that of primary frequency cannot be seen; thus, the frequency can act as a high cutoff frequency, and the high frequency can be lower but not higher than the high cutoff frequency (Fig. 9). The low cutoff frequency can maintain the low cutoff frequency of the original profile.

Sample data

A large number of practical applications show that the correlation coefficient between synthetic record and seismogram used in modeling usually exceeds 0.8 – the higher, the better. Optimal samples must be selected, that is, the samples are taken from the well section with a high correlation coefficient. In addition, the distribution of wells should be considered, namely, the samples are taken from different facies belts and structural positions if possible, in order to enhance the adaptability of the model.

### Real data processing

### High-frequency strong noise removing

Fig. 10, Fig. 11 show a seismic profile of the Sichuan Basin, with a primary frequency of only 20 Hz. The high frequency noise is serious in the original profile, but the effective signal of high frequency exceeds 125 Hz (event parallel to the red horizon line in the profile). The effective signal of high frequency in the high–resolution profile is significantly enhanced, and the noise is effectively suppressed. The frequency spectrogram shows that the primary frequency increases from 20 Hz to 60 Hz, the bandwidth expands from 5–50 Hz to 5–125 Hz, and the resolution is improved by 2–3 times.

### Frequency expanding effectiveness

Fig. 12 shows the original stacked seismic profile and high–resolution profile of shale gas reservoir in a structure of the Sichuan Basin. The primary frequency of the original profile is 35 Hz, the frequency band range is between 10 Hz and 70 Hz, and the resolution is low. The resolution of high–resolution profile is significantly improved, the primary frequency reaches 80 Hz, and the frequency band range is between 5 Hz and 120 Hz. Before frequency expanding, the high-frequency signal is disturbed by noise, and the event is disordered (e.g. 110 Hz), which is obviously inconsistent with the synthetic record (vertical red curve in the middle part of the figure); after frequency expanding, the effective signal of high frequency in the high–resolution profile is significantly enhanced, which is consistent with the strength and the phase of synthetic record, and the event is effectively recovered. In addition, the effective signal in the medium and low frequency range (e.g. 30 Hz) has not changed significantly and is well protected.

The above two examples show that this method can greatly improve resolution, can recover the effective signal in the high frequency strong noise, and does not cause damage to the medium and low frequency components. Numerous practices show that the method can be applied in different types of reservoirs.

### Conclusions

1) This paper presents a new method of improving resolution by using the “three properties” to establish the relationship between seismogram and synthetic record for extracting the effective information of medium and high frequency in seismogram while suppressing the noise. Unlike traditional methods that expand frequency after denoising, the new method realizes frequency expanding while denoising, in combination with innovative modeling and extrapolation algorithm.

2) Theoretical modeling and actual applications show that the new method can improve the seismic resolution significantly and effectively, and the results are correct.

3) The proposed method can be phase-corrected, indicating that it is not limited by phase, making it more practicable.

4) The proposed method can release the effective information of high frequency in a stacked profile, so it is believed that the more the effective information of high frequency in the original profile is, the better. Therefore, a more effective method should be adopted in prestack processing to protect the effective components of high frequency. For example, the frequency division dynamic correction method [17] was adopted to achieve the in-phase superposition of high frequency, which can significantly increase the effective information of high frequency, thereby creating more favorable conditions for this method to improve resolution to a greater extent.

5) The high-resolution processing results of this method have been applied in the description of various reservoirs, with satisfactory precision and accuracy.

Authors: Dakui Wu, Zongwei Wu, Yijia Wu