Method and device, equipment, medium for forward numerical simulation of three-dimensional drilling noise
The three-dimensional drilling noise data is simulated through the forward numerical simulation method, which solves the problem of drilling noise interference in seismic exploration, and realizes efficient and accurate noise data acquisition, supporting machine learning to remove noise.
Patent Information
- Application Number
- CN202210554035.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-05-19
- Publication Date
- 2025-05-27
- Estimated Expiration
- 2042-05-19
AI Technical Summary
During seismic exploration, drilling noise and seismic source signals interfere with each other, seriously affecting the quality of seismic exploration data. The existing denoising methods are costly and time-consuming.
Through the forward numerical simulation method, three-dimensional drilling noise data is simulated, including simulated drilling rig source and explosive source, and numerical simulation is performed in combination with the finite difference method to generate high-precision three-dimensional drilling noise data.
It realizes rapid and accurate acquisition of large amounts of three-dimensional drilling noise data, meeting the needs of machine learning to remove noise, and reducing costs and time.
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Figure CN115438530B_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the field of acoustic processing technologies, and particularly relates to a method, device, equipment, and medium for forward numerical simulation of three-dimensional drilling noise. Background Art
[0002] With the improvement of the requirements for seismic exploration accuracy, our requirements for seismic data acquisition have also gradually increased. However, during the seismic exploration acquisition process, there are often more or less drilling operations in the exploration area. As a result, the noise generated by the vibration of the drilling rig interferes with the signals generated by the seismic exploration source, seriously affecting the seismic exploration data.
[0003] Due to the continuous nature of drilling operations, if the drilling is often stopped midway, it is easy to cause situations such as stuck drill pipes and well collapses, and the coordination difficulty is great. Therefore, it is very important to remove the drilling noise from seismic exploration data. As Figure 1 shown, Figure 1 in which a represents the drilling rig noise, and b represents the amplitude spectrum of the drilling rig noise. The prior art has proposed that the drilling noise presents strong energy, hyperbolic characteristics, and a very narrow frequency band on the spectrum, approximating a single-frequency signal on the spectrum; and the superposition noise removal and model noise removal methods have been used to remove the drilling noise (for details, refer to [AN Ling-Fang, An Lingfang, ZHANG Jin, etc. Analysis of the characteristics of drilling interference and a brief analysis of noise removal methods [C] / / National Security Geophysics Series. The National Security Geophysics Professional Committee of the Chinese Geophysical Society; The Shaanxi Geophysical Society, 2014.]).
[0004] With the improvement of the computer's data processing ability and the application of machine learning in numerical signal processing, adopting machine learning methods to remove drilling noise has become a feasible method. However, for machine learning, a large number of samples are required as the training set, and the method of relying on actual measurements to obtain a large number of samples is costly and has a long time cycle. Therefore, the simulation of high-precision and effective three-dimensional drilling noise data is very important. Summary of the Invention
[0005] To solve the above technical problems, the embodiments of the present application respectively provide a method, device, equipment, and computer-readable storage medium for forward numerical simulation of three-dimensional drilling noise. Through computer simulation, a large amount of three-dimensional drilling noise data can be quickly and accurately obtained to meet the needs of machine learning.
[0006] Other features and advantages of the present application will become apparent through the following detailed description, or will be partially learned through the practice of the present application.
[0007] According to one aspect of the embodiments of the present application, a method for forward numerical simulation of three-dimensional drilling noise is provided. The method includes: determining a simulated drilling rig source as shown in the following formula (1) according to the characteristics of the drilling rig source:
[0008] A i (AX i ,AY i ,AZ i ,t) = a*sin(2πft c t) (1)
[0009] Wherein, A i (AX i ,AY i ,AZ i ,t) is the simulated drill source at the i-th simulated drill; (AX i ,AY i ,AZ i ) represents the position of the i-th simulated drill, f c is the mechanical vibration frequency of the simulated drill; a is the amplitude of the simulated drill source;
[0010] Estimate the delay time t of the simulated explosive source through the following formula (2) D :
[0011]
[0012] Wherein, (RX i ,RY i ,RZ i ) is the coordinate of the receiving point farthest from (AX i ,AY i ,AZ i );v i is the average velocity between (AX i ,AY i ,AZ i ) and (RX i ,RY i ,RZ i );
[0013] Based on the delay time t of the simulated explosive source D ,determine the simulated explosive source as shown in the following formula (3):
[0014]
[0015] Wherein, S(SX, SY, SZ, t) is the simulated explosive source, (SX, SY, SZ) is the position of the simulated explosive source, f m is the main frequency of the Ricker wave;
[0016] Add the simulated explosive source S(SX, SY, SZ, t) and the simulated drill source A i (AX i ,AY i, AZ i , after t), the equation shown in the following formula (4) is obtained:
[0017]
[0018] In the formula, P is the wave field value; V is the wave propagation speed in the medium; N is the number of drilling rigs;
[0019] The equation in formula (4) is numerically simulated by the finite difference method.
[0020] According to one aspect of the embodiments of the present application, a device for forward numerical simulation of three-dimensional drilling noise is provided, including: a simulated drilling rig source determination module configured to determine a simulated drilling rig source shown in the following formula (1) according to the characteristics of the drilling rig source:
[0021] A i (AX i , AY i , AZ i , t) = a * sin(2πf c t) (1)
[0022] In the formula, A i (AX i , AY i , AZ i , t) is the simulated drilling rig source at the i-th simulated drilling rig; (AX i , AY i , AZ i ) represents the position of the i-th simulated drilling rig, f c is the mechanical vibration frequency of the simulated drilling rig; a is the amplitude of the simulated drilling rig source;
[0023] A simulated explosive source delay time estimation module configured to estimate the simulated explosive source delay time t through the following formula (2) D :
[0024]
[0025] In the formula, (RX i , RY i , RZ i ) is the coordinate of the receiving point farthest from (AX i , AY i , AZ i ); v i is the average speed between (AX i , AY i , AZ i ) and (RX i , RY i , RZ i );
[0026] The simulated explosive source determination module is configured to determine the simulated explosive source based on the simulated explosive source delay time t D , and determine the simulated explosive source as shown in the following formula (3):
[0027]
[0028] In the formula, S(SX, SY, SZ, t) is the simulated explosive source, (SX, SY, SZ) is the position of the simulated explosive source, and f m is the main frequency of the Ricker wavelet;
[0029] The first calculation module is configured to add the simulated explosive source S(SX, SY, SZ, t) and the simulated drill source A i (AX i , AY i , AZ i , t) to the wave equation to obtain the equation shown in the following formula (4):
[0030]
[0031] In the formula, P is the wave field value; V is the propagation speed of the wave in the medium; N is the number of drills;
[0032] The numerical simulation module is configured to perform numerical simulation on the equation in formula (4) by the finite difference method.
[0033] According to one aspect of the embodiments of the present application, an electronic device is provided, including: a controller; a memory for storing one or more programs, and when the one or more programs are executed by the controller, the controller implements the method for forward numerical simulation of three-dimensional drilling noise described above.
[0034] According to one aspect of the embodiments of the present application, a computer-readable storage medium is further provided, on which computer-readable instructions are stored. When the computer-readable instructions are executed by a processor of a computer, the computer executes the method for forward numerical simulation of three-dimensional drilling noise described above.
[0035] According to one aspect of the embodiments of the present application, a computer program product or a computer program is further provided. The computer program product or the computer program includes computer instructions, and the computer instructions are stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device executes the method for forward numerical simulation of three-dimensional drilling noise described above.
[0036] In the technical solution provided by the embodiments of the present application, in a three-dimensional space, an explosive source is placed on the shallow surface, and a drilling rig source is placed at different positions. By simulating the superposition of explosive excitation and the simultaneous operation vibration of the drilling rig, and receiving on the surface, a large number of numerical simulation seismic records with drilling rig noise can be obtained, providing a reliable training set for subsequent machine learning to remove drilling noise.
[0037] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present application. BRIEF DESCRIPTION OF THE DRAWINGS
[0038] The drawings herein are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with the present application, and are used together with the specification to explain the principles of the present application. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts. In the drawings:
[0039] Figure 1 is a schematic diagram of a kind of drilling rig noise related to the present application;
[0040] Figure 2 is a schematic diagram of a three-dimensional inverse inference model shown in an exemplary embodiment of the present application;
[0041] Figure 3 is a schematic diagram of the distribution of the source positions shown in an exemplary embodiment of the present application;
[0042] Figure 4 is a single-shot analysis diagram of the simulation results shown in another exemplary embodiment of the present application.
[0043] Figure 5 is a schematic diagram of the structure of a forward numerical simulation three-dimensional drilling noise device shown in an exemplary embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0044] Here, the exemplary embodiments will be described in detail, and the examples are shown in the drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. On the contrary, they are only examples of devices and methods consistent with some aspects of the present application as detailed in the appended claims.
[0045] The block diagrams shown in the drawings are only functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices.
[0046] The flowcharts shown in the drawings are only illustrative and do not necessarily include all the contents and operations / steps, nor are they necessarily executed in the described order. For example, some operations / steps can be decomposed, while some operations / steps can be combined or partially combined, so the actual execution order may change according to the actual situation.
[0047] As used in this application, "a plurality of" means two or more. "And / or" describes the association relationship of associated objects and indicates that three relationships can exist. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone. The character " / " generally represents an "or" relationship between the associated objects before and after.
[0048] An embodiment of this application provides a method for forward numerical simulation of three-dimensional drilling noise, and the method includes:
[0049] Step S100, according to the characteristics of the drill rig source, determine the simulated drill rig source as shown in the following formula (1):
[0050] A i (AX i ,AY i ,AZ i ,t)=a*sin(2πf c t) (1)
[0051] In the formula, A i (AX i ,AY i ,AZ i ,t) is the simulated drill rig source at the i-th simulated drill rig; (AX i ,AY i ,AZ i ) represents the position of the i-th simulated drill rig, f c is the mechanical vibration frequency of the simulated drill rig; a is the amplitude of the simulated drill rig source.
[0052] It should be noted that the characteristics of the drill rig source usually manifest as a continuously vibrating sine signal. Therefore, as in the embodiment of this application, the simulated drill rig source is designed as a continuously vibrating sine signal as shown in formula (1) to obtain a high-precision simulated drill rig source. The mechanical vibration frequency of the simulated drill rig and the amplitude of the simulated drill rig source can be referred to Figure 1The b-rig noise amplitude spectrogram in, the simulated rig mechanical vibration frequency is Figure 1 The frequency corresponding to the spectral peak in b of
[0053] Step S200, estimate the simulated explosive source delay time t through the following formula (2) D :
[0054]
[0055] In the formula, (RX i , RY i , RZ i ) are the coordinates of the receiving point farthest from (AX i , AY i , AZ i ); v i is the average velocity between (AX i , AY i , AZ i ) and (RX i , RY i , RZ i ).
[0056] In step S200, the embodiment of the present application uses a Ricker wavelet to replace the explosive source. The inventor considered that in actual data, when the explosive source is excited, the vibration signal generated by the rig source has already reached the surface and continues to vibrate. Therefore, when performing numerical simulation, it is equivalent to simulating the delayed excitation of the explosive source. Therefore, it is necessary to consider the simulated explosive source delay time, and this delay time is estimated through the above formula (2).
[0057] Step S300, based on the simulated explosive source delay time t D , determine the simulated explosive source as shown in the following formula (3):
[0058]
[0059] In the formula, S(SX, SY, SZ, t) is the simulated explosive source, (SX, SY, SZ) is the simulated explosive source position, f m is the main frequency of the Ricker wavelet.
[0060] Step S400, add the simulated explosive source S(SX, SY, SZ, t) and the simulated rig source A i (AX i , AY i , AZ i , t) to the wave equation to obtain the equation shown in the following formula (4):
[0061]
[0062] In the formula, P is the wave field value; V is the velocity of wave propagation in the medium; N is the number of drilling rigs.
[0063] It should be noted that the "wave equation" described in this article, also known as the wave equation, is a set of differential equations derived from Maxwell's equations and used to describe the wave characteristics of electromagnetic fields. It is an important partial differential equation that mainly describes various wave phenomena in nature, including transverse waves and longitudinal waves, such as sound waves, light waves, and water waves. The wave equation is abstracted from fields such as acoustics, electromagnetics, and fluid mechanics. The "wave equation" described in this article is applied to acoustics and includes one-dimensional wave equations, two-dimensional wave equations, and three-dimensional wave equations. The embodiments of this application mainly use the three-dimensional wave equation. That is, a simulated explosive source S (SX, SY, SZ, t) and a simulated drilling rig source A i (AX i AY i AZ i t) are added to the three-dimensional wave equation to obtain the equation shown in formula (4).
[0064] Finally, in step S400, the equation in formula (4) is numerically simulated by the finite difference method. The finite difference method is a method for obtaining numerical solutions to the definite solution problems of partial differential (or ordinary differential) equations and systems of equations. That is, in this step, the partial differential equation in formula (4) is solved, and finally, simulated three-dimensional drilling noise is obtained. In the simulated three-dimensional drilling noise, the embodiments of this application fully consider the vibration noise of the drilling rigs and explosives, and combine the positions of each vibration noise, which is more in line with the measured data, obtaining high-precision noise data and providing a reliable training set for subsequent machine learning to remove drilling noise. Only as an example, the equation in formula (4) is numerically simulated by the finite difference method proposed by [Yang L, 2017; Miao Z and Zhang J, 2020; Wang W, 2020].
[0065] Next, the embodiments of this application will further illustrate the feasibility and progressiveness of this application in combination with specific experimental data.
[0066] As Figure 2 shown, it is a schematic diagram of a three-dimensional inverse inference model shown in an exemplary embodiment of this application. For the three-dimensional inverse inference model, a forward numerical simulation with drilling noise is performed. The corresponding sources (i.e., the drilling rig source and the explosive source) are added to the three-dimensional inverse inference model, and the schematic diagram of the obtained source position distribution is as Figure 3 shown. In the case of the source position distribution as Figure 3 shown, a forward numerical simulation of three-dimensional drilling noise is performed through steps S100 to S400 described above. The obtained result is asFigure 4 As shown, it is the single-shot record of three receiving lines at different distances from the drill rig, as well as the corresponding amplitude spectrum diagram at the position of the dashed box.
[0067] Another embodiment of the present application further provides a device for forward numerical simulation of three-dimensional drilling noise, as Figure 5 shown, Figure 5 is a schematic structural diagram of a device for forward numerical simulation of three-dimensional drilling noise shown in an exemplary embodiment of the present application. Among them, the device 500 for forward numerical simulation of three-dimensional drilling noise includes:
[0068] A simulated drill rig source determination module 501, configured to determine a simulated drill rig source as shown in the following formula (1) according to the characteristics of the drill rig source:
[0069] A i (AX i , AY i , AZ i , t) = a * sin(2πf c t) (1)
[0070] In the formula, A i (AX i , AY i , AZ i , t) is the simulated drill rig source at the i-th simulated drill rig; (AX i , AY i , AZ i ) represents the position of the i-th simulated drill rig, f c is the mechanical vibration frequency of the simulated drill rig; a is the amplitude of the simulated drill rig source;
[0071] A simulated explosive source delay time estimation module 502, configured to estimate the simulated explosive source delay time t through the following formula (2) D :
[0072]
[0073] In the formula, (RX i , RY i , RZ i ) is the coordinate of the receiving point farthest from (AX i , AY i , AZ i ); v i is the average velocity between (AX i , AY i , AZ i ) and (RX i , RY i , RZ i );
[0074] The simulated explosive source determination module 503 is configured to determine the simulated explosive source based on the simulated explosive source delay time t D , and determine the simulated explosive source as shown in the following formula (3):
[0075]
[0076] In the formula, S(SX, SY, SZ, t) is the simulated explosive source, (SX, SY, SZ) is the position of the simulated explosive source, and f m is the main frequency of the Ricker wavelet;
[0077] The first calculation module 504 is configured to add the simulated explosive source S(SX, SY, SZ, t) and the simulated drill source A i (AX i , AY i , AZ i , t) to the wave equation to obtain the equation shown in the following formula (4):
[0078]
[0079] In the formula, P is the wave field value; V is the propagation speed of the wave in the medium; N is the number of drills;
[0080] The numerical simulation module 505 is configured to perform numerical simulation on the equation in formula (4) by the finite difference method.
[0081] Each module involved in the embodiments described in this application can be implemented in software or in hardware, and the described modules can also be set in the processor. Among them, the names of these modules do not constitute a limitation to the unit itself in some cases.
[0082] It should be noted that the forward numerical simulation three-dimensional drilling noise device provided in the above embodiments and the forward numerical simulation three-dimensional drilling noise method provided in the foregoing embodiments belong to the same concept. The specific ways in which each module and unit perform operations have been described in detail in the method embodiments, and will not be repeated here.
[0083] Another embodiment of this application further provides an electronic device, including: a controller; a memory for storing one or more programs, which when executed by the controller, are used to execute the forward numerical simulation three-dimensional drilling noise method in the above embodiments.
[0084] According to one aspect of the embodiments of this application, there is also provided a computer-readable storage medium, on which computer-readable instructions are stored. When the computer-readable instructions are executed by the processor of the computer, the computer is made to execute the above forward numerical simulation three-dimensional drilling noise method.
[0085] It should be noted that the computer-readable medium shown in the embodiments of the present application may be a computer-readable signal medium, a computer-readable storage medium, or any combination of the two. A computer-readable storage medium may, for example, be an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples of the computer-readable storage medium may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), a flash memory, an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, a computer-readable storage medium may be any tangible medium that contains or stores a program, which can be used by or in conjunction with an instruction execution system, apparatus, or device. In the present application, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, which carries a computer-readable computer program. Such a propagated data signal may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device. The computer program contained on the computer-readable medium may be transmitted by any appropriate medium, including but not limited to: wireless, wired, etc., or any suitable combination of the above.
[0086] Another embodiment of the present application also provides a computer program product or a computer program, which includes computer instructions stored in a computer-readable storage medium. The processor of the computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device executes the method for forward numerical simulation of three-dimensional drilling noise provided in the above various embodiments.
[0087] Another embodiment of the present application also provides a computer system, including a Central Processing Unit (CPU), which can perform various appropriate actions and processes according to programs stored in a Read-Only Memory (ROM) or programs loaded from a storage section into a Random Access Memory (RAM), such as executing the methods in the above embodiments. In the RAM, various programs and data required for system operations are also stored. The CPU, ROM, and RAM are connected to each other via a bus. An Input / Output (I / O) interface is also connected to the bus.
[0088] The following components are connected to the I / O interface: an input section including a keyboard, a mouse, etc.; an output section including a Cathode Ray Tube (CRT), a Liquid Crystal Display (LCD), etc. and a speaker, etc.; a storage section including a hard disk, etc.; and a communication section including a network interface card such as a Local Area Network (LAN) card, a modem, etc. The communication section performs communication processing via a network such as the Internet. A drive is also connected to the I / O interface as required. A removable medium, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive as required, so that a computer program read from it can be installed into the storage section as required.
[0089] The above content is only a preferred exemplary embodiment of the present application and is not used to limit the implementation of the present application. Those of ordinary skill in the art can make corresponding adaptations or modifications very conveniently according to the main concept and spirit of the present application. Therefore, the protection scope of the present application should be subject to the protection scope required by the claims.
Claims
1. A method for forward numerical simulation of three-dimensional drilling noise, characterized in that, the method includes: determining a simulated drill rig source as shown in formula (1) below according to the characteristics of the drill rig source: A i (AX i ,AY i ,AZ i ,t) = a * sin(2πf c t) (1) where A i (AX i , AY i , AZ i , t) is the simulated drill rig source at the i-th simulated drill rig; (AX i , AY i , AZ i ) represents the position of the i-th simulated drill rig, f c is the mechanical vibration frequency of the simulated drill rig; a is the amplitude of the simulated drill rig source; Estimate the simulated explosive source delay time t through the following formula (2) D : Wherein, (RX i , RY i , RZ i ) are the coordinates of the receiving point farthest from (AX i , AY i , AZ i ); v i is the average velocity between (AX i , AY i , AZ i ) and (RX i , RY i , RZ i ). Based on the simulated explosive source delay time t D , the simulated explosive source is determined as shown in the following formula (3): where S(SX, SY, SZ, t) is the simulated explosive source, (SX, SY, SZ) is the position of the simulated explosive source, and f m is the dominant frequency of the Ricker wavelet; Add the simulated explosive source S(SX, SY, SZ, t) and the simulated drill source A to the wave equation i (AX i , AY i , AZ i , t) to obtain the equation shown in the following formula (4): wherein, P is the wave field value; V is the velocity of wave propagation in the medium; N is the number of drill rigs; performing numerical simulation on the equation in formula (4) by the finite difference method.
2. An apparatus for forward numerical simulation of three-dimensional drilling noise, characterized in that, it includes: a simulated drill rig source determination module configured to determine a simulated drill rig source as shown in formula (1) below according to the characteristics of the drill rig source: A i (AX i ,AY i ,AZ i ,t) = a * sin(2πf c t) (1) Where, A i (AX i , AY i , AZ i , t) is the simulated drill rig source at the i-th simulated drill rig; (AX i , AY i , AZ i ) represents the position of the i-th simulated drill rig, f c is the mechanical vibration frequency of the simulated drill rig; a is the amplitude of the simulated drill rig source; The simulated explosive source delay time estimation module is configured to estimate the simulated explosive source delay time t by the following formula (2) D :[[-END]] Wherein, (RX i , RY i , RZ i ) are the coordinates of the receiving point farthest from (AX i , AY i , AZ i ); v i is the average speed between (AX i , AY i , AZ i ) and (RX i , RY i , RZ i ). The simulated explosive source determination module is configured to determine the simulated explosive source as shown in the following formula (3) based on the delay time t of the simulated explosive source D , where the simulated explosive source is determined as follows: In the formula, S(SX, SY, SZ, t) is the simulated explosive source, (SX, SY, SZ) is the position of the simulated explosive source, and f m is the dominant frequency of the Ricker wavelet; The first calculation module is configured to add a simulated explosive source S(SX, SY, SZ, t) and a simulated drill source A to the wave equation i (AX i , AY i , AZ i , t) to obtain the equation shown in the following formula (4): wherein, P is the wave field value; V is the velocity of wave propagation in the medium; N is the number of drill rigs; a numerical simulation module configured to perform numerical simulation on the equation in formula (4) by the finite difference method.
3. An electronic device, including: a controller; a memory for storing one or more programs, which when executed by the controller, cause the controller to implement the method for forward numerical simulation of three-dimensional drilling noise as claimed in claim 1.
4. A computer-readable storage medium, characterized in that, it stores computer-readable instructions which, when executed by a processor of a computer, cause the computer to execute the method for forward numerical simulation of three-dimensional drilling noise as claimed in claim 1.
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