applications of spectral analysis in research methodology

SPECTRAL ANALYSIS

A continuous or discrete time-series, such as x = x(t) or x n = {x 0 , x 1 ,. . .}, can be analyzed in terms of time-domain descriptions and frequency-domain descriptions. The latter is also called spectral analysis and reveals some characteristics of a time-series, which cannot be easily seen from a time-domain description analysis. Spectral analysis is used for solving a wide variety of practical problems in engineering and science, for example, in the study of vibrations, interfacial waves and stability analysis.

In spectral analysis, the time-series is decomposed into sine wave components using a sum of weighted sinusoidal functions called spectral components. The weighting function in the decomposition is a density of spectral components or spectral density function.

The actual method of decomposing a time-series into a sum of weighted sinusoidal functions is to use Fourier transform which has both continuous and discrete versions corresponding to continuous time-series of type x = x(t) and discrete time-series of type x n = {x 0 , x 1 ,. . .}, respectively. Most recorded time-series data in engineering practice are of discrete type and numerical calculations of the Fourier transform are usually done using digital computers, which can only deal with discrete data and therefore use discrete Fourier transform. In view of this, the spectral analysis of only discrete time-series is described below.

Fourier Transform

We assume a discrete time-series with a finite number of samples N and a sampling time interval T s between two successive samples

According to the mathematical theory of Fourier analysis, the above time-series can be represented by the following inverse finite Fourier transform:

where m/NT s = f m is the discrete frequency and nT s = t n is the discrete time. It should be noted that the (x n – x) in Equation (1) and the G(m) in Equation (2) are equivalent measures in time and frequency domains, respectively, which are related to each other by the Fourier transform. T s does not appear in Equations (2) or (3) and is only used as a scaling factor when calculating frequencies.

Frequency Spectrum

In general, the Fourier transform G(m) is a complex-valued function and the plot of G(m) versus f m is called frequency spectrum. G(m) can be expressed in polar form as

The modulus |G(m)| and the angle G(m) are called the magnitude and the phase, respectively, of the Fourier transform. The plot of |G(m)| versus f m is called the magnitude or the amplitude spectrum and the plot of G(m) versus f m is called the phase spectrum.

Power Spectrum

The auto-correlation function for the discrete time-series given in Equation (1) is defined as (see entry for Correlation Analysis )

The Fourier transform of the auto-correlation function is given by

where P xx (m) is called the power spectral density function. The plot of P xx (m) versus fm is called the power spectrum corresponding to the time-series given in formula (1). It can be mathematically proved that the following relation exists between the power spectrum P xx (m) and the frequency spectrum G(m)

which shows that P xx (m) is a real-valued function with a zero phase. The power spectrum is an average measure of the frequency-domain properties of the time-series, which shows whether or not a strongly periodic or quasi-periodic fluctuation exists in the time-series.

Cross Spectrum

The cross-correlation function for two sets of time-series data

is defined as (see Correlation Analysis )

and its Fourier transform is given by

where P xy (m) is called the cross spectral density function or the cross spectrum which is a generally complex-valued function. The cross spectrum represents the common frequencies appearing in both the time-series x n and y n .

Coherence Function

The coherence function is defined as

which is a real-valued frequency function the value of which at a particular frequency f is a measure of similarity of the strength of components in x n and y n at that frequency. The value of K is such that 0 ≤ K ≤ 1, and the larger the K, the more strongly correlated are the x n and y n at a given frequency. Therefore, K behaves like a correlation coefficient for x n and y n components at the same frequency. All the above definitions, though given for discrete time-series, are equally applicable to continuous time signals. More details of spectral analysis can be found in the references.

• Gardner, W. A. (1988) Statistical Spectral Analysis, a Non-probabilistic Theory , Prentice-Hall, Inc., New Jersey.
• Linn, P. A. (1989) An Introduction to the Analysis and Processing of Signals, 3rd edn. , Macmillan Press Ltd., London.
• Schwartz, M. and Shaw, L. (1975) Signal Processing: Discrete Spectral Analysis, Detection and Estimation , McGraw-Hill, Inc., USA.

Related content in other products

Spectral analysis: principle and clinical applications

Affiliation.

• 1 Department of Medical Physics and Engineering, Division of Medical Technology and Science, Course of Health Science, Graduate School of Medicine, Osaka University, Suita, Japan. [email protected]
• PMID: 14575374
• DOI: 10.1007/BF03006429

This review article describes the principle and clinical applications of spectral analysis. Spectral analysis provides a spectrum of the kinetic components which are involved in the regional uptake and partitioning of tracer from the blood to the tissue. This technique allows the tissue impulse response function to be derived with minimal modeling assumptions. Spectral analysis makes no a priori assumptions regarding the number of compartments or components required to describe the time course of tracer in the tissue. Spectral analysis can be applied to various dynamic data acquired by planar scintigraphy, single photon emission computed tomography (SPECT) or positron emission tomography (PET) as an alternative approach to compartment analysis. This analysis appears to be clinically useful, because it not only facilitates the interpretation of dynamic scintigraphic, SPECT or PET data, but also simplifies comparisons between regions and between subjects.

Publication types

• Research Support, Non-U.S. Gov't
• Algorithms*
• Diagnosis, Computer-Assisted / methods*
• Liver Diseases / diagnostic imaging*
• Liver Diseases / metabolism
• Models, Biological*
• Radioisotope Dilution Technique*
• Radioisotopes / blood
• Radioisotopes / pharmacokinetics*
• Radiopharmaceuticals / blood
• Radiopharmaceuticals / pharmacokinetics
• Tomography, Emission-Computed / methods*
• Tomography, Emission-Computed, Single-Photon / methods
• Radioisotopes
• Radiopharmaceuticals

New metrology tool for grating quality control utilises artificial neural network

Spectral scatterometry is a technique that allows rapid measurements of diffraction efficiencies of diffractive optical elements (DOEs). The method is fast but does not measure the parameters of the sample directly. Hence, the analysis of such diffraction efficiencies has traditionally been laborious and time consuming. However, machine learning can be employed to aid in the analysis of measured diffraction efficiencies. VTT MIKES has developed a novel instrument for providing measurements of multiple measurands rapidly and concurrently using a custom spectral scatterometer and an artificial neural network (ANN). The instrument is suitable for inline quality control in the manufacture of diffractive optical elements.

Spectral scatterometer

The scatterometer hardware and a schematic of the components are show in figure 1. The scatterometer uses a fibre-coupled white LED light source. The light is collimated using a condenser lens ( A ) and directed through a pair of apertures to an adjustable polarizer ( B ). Then the polarized light passes through a beam splitter ( C ), to a microscope objective ( D ), which focuses the beam to the sample ( E ), where it is reflected back through the objective ( F ) into a fibre coupler and a fibre to a spectrometer. The design of the scatterometer allows it to be used also for transmitted beam measurements ( G ). The measurements are automatically performed employing a custom Python program.       

Artificial neural network for spectrum analysis

In our method an artificial neural network is used to analyse the spectrum instead of time consuming inverse calculation. The model is constructed offline in two phases. In the first phase the multi-layer perceptron model is created and trained using the simulated data. The second phase includes the transfer learning where the model will be fine-tuned using experimental data.

In the preliminary training phase, an array of training data is generated by first randomly selecting a simulated spectrum. Then a small amount of random noise will be added to it, so the spectrum would better match the real-world data. Finally, the spectrum is added to the training data set. This will be repeated until the set contain e.g., 1 000 000 spectra.  

Applications of the scatterometer

This instrument is capable to provide results for several important measurands needed in industrial quality control of manufacturing photonics components such as gratings, waveguide couplers and diffractive optical elements. The most important measurands are height, pitch, duty cycle and side wall angles of manufactured samples. Thus, the instrument meets the requirements for a new, more accurate inline characterisation method, especially for DOE manufacturing and for the development of virtual and augmented reality glasses.

For customers, we offer customized instrument for quality control and development of ANN data analysis.

If you are interested in this tool or need more information, please feel free to contact us!

Watch our brand new video on spectral scattering!

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• Open access
• Published: 18 May 2024

Research on trajectory control technology for L-shaped horizontal exploration wells in coalbed methane

• Xiugang Liu 1 , 2 , 3 ,
• Zaibing Jiang 1 , 2 , 3 ,
• Yi Wang 3 ,
• Haitao Mo 3 ,
• Haozhe Li 3 &
• Jianlei Guo 3  

Scientific Reports volume  14 , Article number:  11343 ( 2024 ) Cite this article

Metrics details

• Energy science and technology
• Engineering

Horizontal wells have significant advantages in coal bed methane exploration and development blocks. However, its application in new exploration and development blocks could be challenging. Limited geological data, uncertain geological conditions, and the emergence of micro-faults in pre-drilled target coal seams make it hard to accurately control the well trajectory. The well trajectory prior to drilling needs to be optimized to ensure that the drilling trajectory is within the target coal seam and to prevent any reduction in drilling ratio (defined here as the percentage of the drilling trajectory in the entire horizontal section of the well located in the target coal seam) caused by faults. In this study, the well trajectory optimization is achieved by implementing the following process to drill pilot hole, acquire 2D resonance, and azimuthal gamma logging while drilling. The pilot hole drilling can obtain the characteristic parameters of the target coal seam and the top and bottom rock layers in advance, which can provide judgment values for the landing site design and real-time monitoring of whether the wellbore trajectory extends along the target coal seam; 2D resonance exploration can obtain the construction of set orientation before drilling and the development of small faults and formation fluctuations in the horizontal section, which can optimize the well trajectory in advance; the azimuth gamma logging while drilling technology can monitor the layers drilled by the current drill bit in real time, and can provide timely and accurate well trajectory adjustment methods.The horizontal well-Q in the Block-W of the Qinshui Basin was taken as a case study and underwent technical mechanism research and applicability analysis. The implementation of this new innovative process resulted in a successful drilling of a 711 m horizontal section, with a target coal seam drilling rate of 80%. Compared to previous L-type wells, the drilling rate increased by about 20%, and the drilling cycle shortened by 25%. The technical experience gained from this successful case provides valuable insight for low-cost exploration and development of new coalbed methane blocks.

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Introduction.

Coal Bed Methane (CBM) is found in many parts of the world, and is considered as a clean and abundant source of energy 1 , 2 , 3 . In general, CBM wells mainly include three types; vertical, cluster and horizontal wells. The cluster and horizontal wells belong to directional wells. Moreover, horizontal wells could be further classified into; V-, U- and L-shaped wells. Which in turn could also be divided according to their radius, and branches. Figure  1 below provide an illustration for some of these wells.

Illustration of well types; ( a ) Vertical well, ( b ) Cluster well, ( c ) Horizontal Well, and ( d ) Horizontal L-Shaped well with a vertical well forming a U-Shaped well.

In the development of CBM wells, L-shaped, U-shaped and multi-branch horizontal wells are usually used for new exploration and development blocks (defined here as new fields or area blocks in the oil and gas industry) 4 , 5 , 6 . However, complex formation structure, and small faults development have made it an extremely challenging task to achieve high output from newly developed CBM wells 7 . For instance, U-shaped wells (a well type in which a vertical well and a horizontal well are connected in the same target layer) face huge difficulties in accurate docking along the coal seam and have limited benefits in the presence of multiple faults in the horizontal Section 8 . Similarly, the applicability of multi-branch horizontal wells is poor, especially in complex stratigraphic structures and fault development of the block 9 .

On the other hand, L‑shaped horizontal wells are often adopted as the main type of wells for exploring and developing CBM in new blocks. The L-shaped horizontal wells exhibit uncomplicated drilling prerequisites, demonstrate a low probability of wellbore collapse or obstruction, and facilitate subsequent access for maintenance of the initial wellbore 10 . However, the drilling process of these wells are not free of challenges. L-shaped wells have a high requirement for wellbore trajectory control, and they are usually difficult to achieve one-time “soft landing” and ultra-long horizontal segment footage 10 . In addition, drainage equipment and method are another key restriction for the promotion and application of this type of well 11 . For example, reported completion data from several exploration wells indicated that the drilling ratio along the coal seam of the actual trajectory is less than 60%. The drilling cycle is nearly two months, and gas production is low 11 . Table 1 illustrates a tabulated analysis of the applicability and challenges associated with different well types in exploration blocks characterized by complex geological formations and the presence of micro-faults.

Various methods have been used to improve the drilling ratio, by improving the trajectory control. These methods, shown in Table 2 , include: geological guidance technology of adjacent well data, electromagnetic waves, natural gamma measurement, and three-dimensional seismic exploration technology. However, each method has its own limitations, such as high costs, difficulty in obtaining gamma values in specific directions, and signal loss when applied to drilling in complex formations 12 , 13 .

This study delves into trajectory control methods for Horizontal wells within Coalbed Methane (CBM) exploration and development blocks. The approach involves the utilization of pilot holes to determine the characteristics of the target coal seam and the surrounding upper and lower rock layers based on the magnitude of gamma values. This information serves as a predictive identification of marker layers, allowing real-time control and adjustment of the drilling trajectory within the target coal seam. This methodology enables the identification of whether the drilling trajectory is presently positioned within the target coal seam, the roof rock layer, or the floor rock layer. Additionally, a two-dimensional resonance exploration technology is employed for geological structure and fault detection prior to drilling, enabling pre-drilling trajectory optimization. Furthermore, azimuth gamma logging technology is utilized for real-time monitoring and correction of the drilling trajectory's horizontal positioning during the drilling process. Using L-shaped Short-Radius Well-Q in Block-W of the Qinshui Basin as a case study, a comprehensive assessment of the combined effectiveness of these three methods is conducted. Simultaneously, the research delves into the technical mechanisms and applicability analysis. This exploration of the technical mechanisms aims to enhance the understanding of the functions of these methods, their application conditions, and the analysis and utilization of their technical effects.

Trajectory control methodology

Pilot hole drilling, construction background and reasons.

The area formation structure and faults nature could be obtained by two-dimensional seismic data. Seismic surveys and exploratory drilling in the area could provide a good indication on the coal seam actual depth, coal seam distribution, layers, belts and interbeds. For the geological conditions of developing new blocks, such as less drilling data, less seismic exploration data, complex formation structure and micro-fault development, etc., before drilling, it is imperative to obtain the key parameters of the target coal seam, including its lithology, gas-bearing capacity, gamma value, etc., along with those of the rock layers above and below it. This will allow for the determination of the precise horizon of the coal seam and provide technical support for real-time monitoring and well trajectory control along the target coal seam. To achieve this, it is necessary to design and implement a pilot hole drilling program to obtain the characteristic parameters of the target coal seam and the surrounding strata 14 , 15 .

Pilot hole construction design

Once the goal of layer identification is achieved, the next step is to backfill and sidetrack the pilot hole to open branches and land according to the actual occurrence of the coal seam. To ensure the effectiveness of the pilot hole guidance in subsequent construction, it is advisable to minimize the distance between the coal-seem top point (the point where the drilling trajectory first drills into the target coal seam) and the landing point by increasing the well angle of inclination. Conversely, in order to enhance the construction efficiency of the pilot hole, it is preferable to keep the depth of the pilot hole to a minimum, which is indicated by a small well angle of inclination (70 degrees). Figure  2 illustrates this concept.

Optimization of pilot hole scheme.

Taking into account the underlying reasons and background for constructing a pilot hole, as well as the difficulty of side-tracking and the efficiency of construction, a comprehensive plan has been developed. The plan involves drilling the pilot hole at a steady angle of approximately 70° until the bottom of the target coal seam is reached.

• Two-dimensional resonance exploration

Resonance exploration mechanism

The seismic wave frequency resonance exploration technology is a novel geophysical exploration method that utilizes the frequency resonance principle prevalent in nature to investigate underground geological formations 16 , 17 , 18 , 19 . This technique enables the acquisition of geometric attributes of subsurface structures, such as fractures and faults. Figure  3 illustrates a typical resonance diagram of a seismic wave.

( a ) Typical resonance curve of seismic wave ( b ) self-excite resonance to vibration.

Resonance exploration technology boasts numerous advantages, including high sensitivity to density changes, exceptional vertical and horizontal resolution, and an exploration depth of up to 5000 m. Additionally, this technology can be acquired and processed passively, making it an economical and straightforward exploration method 20 .

Analysis of technical applicability

At this stage, the analysis of the existing two-dimensional seismic data in the exploration block would indicate the geological structure of the target coal seam in the block. In addition, it will reveal fault’s locations beside faults development status. The pilot hole drilling can accurately obtain the actual depth of the target coal seam and the characteristic parameter values of the target layer, as well as the roof and floor, but conventional means cannot predict structural conditions such as the development of micro faults in the horizontal section of the drilling along the designated direction. This increases the difficulty of well trajectory control and makes it challenging to ensure the coal seam drilling ratio. However, the two-dimensional resonance exploration technology can be used to infer the development of small faults in the horizontal section drilled along the specified direction by interpreting the resonance image. This enables the optimization of the well trajectory in advance to control the actual drilling trajectory and improve the drilling rate of the target coal seam.

Azimuth gamma control technology

Working principle of azimuth gamma.

The azimuth gamma logging tool is utilized to measure the width of gamma ray energy level 21 , 22 , 23 . The scintillation counter captures gamma rays from the stratum, and azimuth gamma logging while drilling offers unique advantages 24 , 25 . Firstly, it enables real-time calculation of the strata's apparent dip angle. It is convenient to calculate the apparent dip angle of the strata by utilizing the azimuth gamma data. The apparent dip angle at the current position can be obtained as long as it is required to cross an interface. The formula for calculating the apparent dip angle using the azimuth gamma 26 is as follows:

where α is the apparent strata dip; D is the well diameter; Δd is the distance between the upper and lower gamma value change points; β is the well deviation angle.

Second, measuring the natural gamma value in a specific direction. By transmitting up and down gamma data in real-time, it becomes possible to accurately determine the positions of different formation interfaces 27 , 28 . This information can then be used to ensure that the trajectory of the control well is precisely aligned with the target coal seam after drilling is complete. The specific process involved is illustrated in Fig.  4 .

Trajectory control based on azimuth-while-drilling gamma logging. ( a ) Coal seam drilled out from the roof. ( b ) Coal seam drilled out from the floor.

The drilling process in the horizontal section along the coal seam is susceptible to deviate from the target due to increased drilling pressure or the impact of the formation structure. The strata above and below the coal seam are usually mudstone or carbonaceous mudstone. When using azimuth gamma logging during drilling, the upper gamma value first increases, followed by the lower gamma value, indicating that the drilling has exited the coal seam roof at point C in Fig.  4 a. When the upper and lower gamma values become similar, it suggests that the drilling has left the layer, as shown at point D in Fig.  4 a. To correct the inclined drilling control track deviation, the trajectory correction process is initiated when drilling to point C using azimuth gamma measurement, as demonstrated at point E in Fig.  4 a. Similarly, when the lower gamma value increases first and the upper gamma value increases later, it indicates that the drilling trajectory is exiting the coal seam floor at point C1 in Fig.  4 b. When the upper and lower gamma values become similar, the drilling has left the layer, as shown at point D1 in Fig.  4 b. To correct the incremental drilling control track deviation, the trajectory correction process is initiated when drilling to point C1, as illustrated at point E1 in Fig.  4 b.

In terms of technical applicability, conventional natural single gamma logging technology cannot accurately determine the bit's position once it leaves the coal seam, making it challenging to provide precise corrective measures. This issue is particularly problematic wherever the geological structure of the target coal seam is complex, micro faults are developed, and the coal seam is thin. To ensure the penetration ratio of the target coal seam and ensure the safety of underground construction, azimuth gamma logging while drilling technology can be utilized. This technology allows for the real-time monitoring of the current drilling horizon and provides effective guidance during construction. As a result, the drill bit can efficiently drill into the coal seam, maximizing the penetration ratio of the target coal seam.

Technical applicability analysis

In the second drilling operation, if the targeted coal seam is complex due to its thinness or the presence of micro-faults, it will be very challenging to accurately determine the position of the drilling bit after it exits the coal seam. Therefore, it will be necessary to use azimuth gamma logging while drilling. This technology enables the real-time monitoring of the drilling bit's current horizon, guiding the construction process and ensuring that the bit drills to the maximum extent possible within the coal seam.

Trajectory control technology and case study

Geological setting.

In this study, the short radius, well-Q in Block-W of the Qinshui Basin is taken as an example. Based on the most recent exploration wells drilled in Block-W of Qinshui Basin, the geological horizons have been revealed. The strata in the block, from bottom to top, consist of Paleozoic Ordovician, Carboniferous, Permian, Mesozoic Triassic, Jurassic, and Cenozoic Quaternary. The stratum near Well-Q has a general inclination from northeast to northwest, and Coal Seam no.15 is the development target stratum. The coal seam is located in the lower part of the Taiyuan Formation and has a simple structure. It is a thick coal seam that is stable and easy to drill throughout the area and generally contains 0–2 layers of dirt shale. The effective thickness of the coal seam ranges from 0 to 5.30 m, with an average of 3.39 m. It is thicker in the east and thinner in the west. However, there is one exploration well in the block that did not drill into Coal Seam no.15, possibly due to fault interference resulting in the loss of the coal seam. The coal seam deposit depth ranges from 728 to 2002 m, with an average of 1479 m. The depth is shallow in the southeast of the block and gradually deepens towards the northwest. Due to the influence of the stratum tendency (Stratum dip), the depth of the coal seam reaches over 1500 m in the west 14 . The roof lithology of the coal seam mostly consists of sandy mudstone, mudstone, siltstone, and fine sandstone, while the floor is mostly sandy mudstone, mudstone, and siltstone.

Wellbore structure

Designing an optimized wellbore structure can greatly improve drilling efficiency and safety by reducing annular pressure loss and back pressure (the drilling tool back pressure phenomenon), especially for long well sections. In the case of Well-Q, the wellbore structure was designed with a three-opening sections to ensure gas production of the coal seam during subsequent fracturing development. The first section seals the formation prone to collapse and leakage in the upper part of the primary casing, creating a safe drilling environment for the second well section. The second section seals sandstone, mudstone, and sandy mudstone intervals at the upper part of the coal seam, with the second well section casing obliquely drilled to a depth of no less than 3 m from the target coal seam no.15.

The third section extends along coal seam no.15 and runs casing to form a stable gas production channel to prevent coal seam collapse in the horizontal section due to the influence of multiple factors such as fracturing in the later stage. Prior to drilling the second well section of the main borehole, pilot hole drilling was carried out to obtain relevant geological parameter information of the target coal seam and the adjacent marker bed. Specific design parameters and requirements are as follows:

In the first well section, a ø 346.1 mm drill bit was used to drill into the stable bedrock for 30 m. J55 grade steel ø 273.1 mm surface casing was then lowered and cementing cement slurry returned to the surface.

In the second well section, a ø 241.3 mm drill bit was used to drill to the roof of the target no.15 coal seam and then the drilling was stopped. The landing point was determined based on the lithology of the roof of the coal seam and the actual drilling process. N80 grade steel ø 193.7 mm technical casing was run to 3–5 m above the roof of the coal seam. Through variable density cementing process, high-density cement slurry was used to return to 300 m above the roof of Coal Seam no.15, while low-density cement slurry returned to the surface.

The third well section was drilled with a ø 171.5 mm drill bit. After entering the target coal seam no.15, the drilling followed the coal seam. Upon reaching the designed well depth, P110 grade steel ø 139.7 mm production casing was run, and the well was completed without cementing.

The pilot hole was drilled with a ø215.9 mm bit, and the inclination angle stabilizing drilling crossed the floor of the target coal seam for tens of meters. Subsequently, the bit was backfilled with pure cement slurry to the side drilling depth of the second well section. The specific wellbore structure is shown in Fig.  5 .

Well structure.

Case study: well-Q design optimization

Using Well-Q as a case study, the pilot hole trajectory design included the following: straight well section, kicking-off section, and stabilizing section. The stabilizing drilling passes through the floor of Coal Seam no.15 for approximately 30 m at an inclination angle of 70° to ensure accurate measurement of the gamma value, gas measurement value, and other characteristic parameters of the target coal seam bottom and floor using a simple gesturing instrument. The pilot hole is sealed by backfilling it with 42.5 grade Portland cement up to the well section with an inclination of about 25°, and the cement slurry has a specific gravity of 1.6–1.7 g/cm3. As the well deviation angle increases, the azimuth angle of directional and composite drilling becomes more stable, particularly when the well deviation angle exceeds 25°, resulting in a smaller azimuth drift 29 . This stability is beneficial for the subsequent inclined side-tracking in the main wellbore's second well section. The pilot hole and main borehole design trajectories are shown in Fig.  6 .

Design trajectory of pilot hole and main hole.

Significant data has been obtained through the pilot hole design and the actual drilling of Well-Q. This dataset is pivotal for precise trajectory control in Coalbed Methane (CBM) exploration. The acquisition process relies on several methods, including real-time drilling natural gamma logging for gamma values of marker layers, and downhole gas logging for coal seam gas characteristics. The examination of cuttings recorded in real-time during drilling operations further aids in the identification and differentiation of these marker layers.

The critical information gleaned encompasses the identification of the K2 marker bed, the longitudinal stratification of the target no.15 coal seam, as well as the lithological composition, gamma values, and gas-bearing attributes of the upper and lower rock layers. These specific parameters are thoughtfully presented in Fig.  7 , establishing a robust foundation for the meticulous control of trajectory and the rational design of the landing point within the target coal seam. This dataset also serves as a valuable point of reference, ensuring the seamless execution of the horizontal drilling phase within the coal seam. Consequently, these findings play a pivotal role in enhancing drilling efficiency, ultimately culminating in the realization of efficient drilling objectives.

Characteristic parameters and lithology map of the marker layer, target, top, bottom layer.

The effect of two-dimensional resonance method

The horizontal section's overall drilling azimuth in the target coal seam is 200°. To identify minor faults in the coal seam azimuth direction, measurement points are arranged every 10 m from the landing point A to the final target point B along the 200° azimuth direction. Additionally, one exploration point is set every 20 m across the azimuth line perpendicular to the landing point A and 200° azimuth direction. Furthermore, exploration points are arranged 300 m along both sides of the landing point. Figure  8 shows the specific layout of the exploration points, where Line (L1) represents the 711 m long horizontal well section of the target coal seam in the 200° azimuth direction. Meanwhile, Line (L2) represents the 600 m long vertical section between the landing point A and L1. The obtained data from these exploration points are crucial in detecting potential faults and ensuring smooth drilling of the horizontal section of the coal seam. ultimately leading to improved drilling ratios and more efficient drilling.

Two-dimensional resonance exploration layout points.

Figure  9 shows the seismic frequency resonance inversion profile. The trajectory of the designed horizontal section coincides with the ground position of L1, with the no.4700 measuring point located at the ground projection position of the A target point, and the no.4000 measuring point located at the ground projection position of the B target point. Based on the interpretation of seismic frequency resonance line L1 profile, it is observed that the burial depth of the coal seam on the horizontal well section from target A to target B of the no.15 coal seam in the direction of 200° azimuth is shallow in the northeast and deep in the southwest. The overall trend of the burial depth of the coal seam indicates a shallow-to-deep trend. Furthermore, three small faults are expected to be encountered while drilling along this azimuth direction, located at no.4700, no.4280 and no.4096 measuring points, respectively, with a fault distance of approximately 5–10 m.

Design of horizontal section trajectory resonance exploration inversion profile.

The contour map of fault points found in the horizontal section is displayed in Fig.  10 . This map serves as a useful tool in guiding the vertical depth control of the horizontal section track.

Contour map of fault points in the horizontal section.

To ensure that the drilling trajectory is within the target coal seam and to prevent any reduction in drilling ratio caused by the faults, it is necessary to optimize the well trajectory prior to drilling. Each fault point must be considered as a target point and their relative coordinate positions are presented in Table 3 .

Resonance exploration data is utilized to adjust the trajectory parameters every 10 to 20 m during the actual drilling process. This is before exploring the coal seam behind the fault following reasonable adjustment of the parameters. This method is simple and minimizes the length of the non-coal section during the coal chasing process after drilling through the fault. Based on the coordinate position of each target point, the design of the directional trajectory for the third well section is optimized, as shown in Fig.  11 .

optimized well trajectory for drilling reservoir section. ( a ) vertical section, ( b ) horizontal projection section.

The optimized design trajectory should be followed during actual drilling, ensuring that the dogleg degree ≤ 4°/30 m required by the management method for safe operations. Across the fault points F1, F2, and F3, the length of the non-coal section for coal tracking drilling was 56 m, 53 m, and 35 m, respectively. The total non-coal section for actual drilling was approximately 144 m, while achieving a drilling ratio of 80% for the target coal seam with an average thickness of 2.06 m. The entire drilling cycle takes approximately 45 days.

Azimuth gamma application

By analyzing the azimuth gamma data obtained during the drilling of the pilot hole and using the basic parameters of the pilot hole and formula ( 1 ), the apparent dip angle of the stratum near the designed landing point is determined to be α = 6.5°. The parameters of the landing point are shown in Fig.  12 , and the deviation angle of the actual main borehole trajectory of the second well section at the landing point β should be controlled at around 83.5° to ensure that the drilling ratio along the coal seam of the third well section is achieved and to reduce the frequency of directional trajectory adjustment.

Parameters of the landing site.

During the drilling of the third horizontal section of Well-Q, a combination of Two-dimensional resonance exploration results and azimuth gamma logging while drilling technology was used to guide rapid coal tracking during the drilling of three faults. The process for each fault was as follows:

F1 Fault: The logging curve in Fig.  13 indicates that the F1 fault caused the drilling track of the 1920–1976 m well section to be drilled out from the coal seam roof. Geological logging revealed that the rock debris returning out of the hole bottom contained a large amount of mudstone. Based on the Two-dimensional resonance exploration inversion (Fig.  9 ) and fault contour (Fig.  10 ), the coal seam was traced by drilling with deviation correction through the lowering of well deviation. The actual drilling track during the pursuit of coal process is shown in Fig.  14 .

Non-coal seam section azimuth gamma logging curve crossing fault F 1 .

Actual drilling trajectory of fault F 1 in pursuit coal.

F2 Fault: The logging curve in Fig.  15 shows that the F2 fault caused the drilling trajectory of the 2130–2183 m well section to be drilled out from the coal seam roof. Geological logging revealed that the rock debris returning out of the hole bottom contained a large amount of mudstone. Based on the Two-dimensional resonance exploration inversion (Fig.  9 ), the back fault block of F2 fault in the direction of drilling trajectory of F2 fault shows a tendency of coal seam incline, so directly using lowering deviation correction drilling to trace the coal seam is not feasible and increases the length of the non-coal seam section. Therefore, the coal seam was pursued by increasing well deviation and rectifying drilling. The actual drilling track during the pursuit of coal process is shown in Fig.  16 .

Non-coal seam section azimuth gamma logging curve crossing fault F 2 .

Actual drilling trajectory of fault F 2 in pursuit coal.

F3 Fault: The logging curve in Fig.  17 shows that the F3 fault caused the drilling trajectory of the 2315–2350 m well section to be drilled out from the coal seam roof floor. Geological logging revealed that the rock debris returning out of the hole bottom contained a large amount of carbonaceous mudstone. Using formula ( 1 ), the coal point well inclination angle was calculated as 96°. Based on the Two-dimensional resonance exploration inversion (Fig.  9 ) and fault contour (Fig.  10 ), the coal seam was pursued by slowly lowering the well inclination and correcting the deviation. The actual drilling track during the pursuit of coal process is shown in Fig.  18 . The well inclination angle was 91° upon returning back to the coal seam, after which drilling along the coal seam was continued normally.

Non-coal seam section azimuth gamma logging curve crossing fault F 3 .

Actual drilling trajectory of fault F 3 in pursuit coal.

In conclusion, for the exploration block of CBM, the combined use of pilot hole drilling, two-dimensional resonance exploration technology, and azimuth gamma logging technology has proven effective in controlling the drilling of short-radius horizontal sections along the seam and ensuring the coal seam drilling ratio. Two major points can be drawn from this:

The two-dimensional resonance exploration technology detected the development of micro faults in the horizontal section of the drilling, enabling trajectory optimization before drilling. The azimuth gamma logging while drilling technology monitored the current drill bit drilling horizon in real-time, ensuring timely and accurate well trajectory adjustment.

The comprehensive use of these technologies has led to a 20% improvement in the coal seam drilling ratio and a 25% reduction in drilling cycle time in tested short-radius wells in the new exploration and development block-W in Qinshui Basin. This provides technical experience for low-cost exploration and development of CBM in new blocks.

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The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

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Acknowledgements

The financial support by the Found of the National Key Research and Development Program and Key Special Fund Project (No.2018YFC0808202) are gratefully acknowledged.

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X.L. conceived the study and, together with Z.J., Y.W., and H.M. did the literature search, selected the studies. X.L. and H.L. extracted the relevant information. X.L. synthesised the data. J.G. drawed pictures. X.L.and Z.J.wrote the first drafts of the paper.Y.W.and H.M.critically revised successive drafs of the paper. All authors approved the final drafts of the manuscript. X.L. is the guarantor of the study.

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Composite spectral spatial pixel CNN for land-use hyperspectral image classification with hybrid activation function

• Published: 15 May 2024

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• Anasua Banerjee 1 ,
• Satyajit Swain 2 ,
• Minakhi Rout 1 &
• Mainak Bandyopadhyay 1  

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Deep learning methods have played a prominent role in the development of computer visualization in recent years. Hyperspectral imaging (HSI) is a popular analytical technique based on spectroscopy and visible imaging which examines the pattern of light in a target and recognizes objects based on varying spectral properties. However, in remote sensing, detecting surface material via HSI analysis is a critical and difficult task. The performance of spectral-spatial data exploitation is well established to outperform typical spectral pixel-wise techniques. Because of its great feature extraction ability, convolutional neural networks (CNN) have emerged as a potent deep learning approach. CNN translates the input features of an image into an equivalent CNN feature map, in addition to naturally combining spectral and spatial information. However, spectral-spatial properties when combined with pixel-wise extraction can learn more minute details of objects present on the earth’s terrain. In this paper, a noble Composite Spectral Spatial Pixel CNN model for the classification of hyperspectral data is presented which is an amalgamation of 3D-2D-1D CNN. While the 3D and 2D CNN exploit the spectral-spatial features effectively, 1D CNN works on pixel-wise feature extraction. Further, to optimize the classification performance of the proposed model, a new hybrid activation function Flatten-T Swish is also used which is the combination of ReLU and Swish function. The proposed model is compared with other state-of-the-art models based on three popular HSI datasets, and it is found that the proposed model performs better among others in terms of classification and computation time, giving 98.87% accuracy for Indian Pines, 99.92% accuracy for Pavia University, and 99.99% accuracy for Salinas Valley dataset.

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Banerjee, A., Swain, S., Rout, M. et al. Composite spectral spatial pixel CNN for land-use hyperspectral image classification with hybrid activation function. Multimed Tools Appl (2024). https://doi.org/10.1007/s11042-024-19327-0

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Received : 23 August 2023

Revised : 04 March 2024

Accepted : 30 April 2024

Published : 15 May 2024

DOI : https://doi.org/10.1007/s11042-024-19327-0

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