Reverse time migration imaging method and device and medium

Abstract

The invention provides a reverse time migration imaging method and device and a medium, and belongs to the field of migration imaging. The method comprises the following steps: step 1, determining a check point configuration strategy, and generating a check point list; step 2, carrying out forward continuation on the shot point wave field to obtain a check point wave field; 3, reversely extending the wave field of the receiving point to reach a corresponding check point, and reading a shot point wave field of the check point; step 4, forward continuation is carried out by using shot point wave fields of two time slices before and after the read check point, and a shot point wave field of one check point is obtained and compressed and stored in a memory space; and 5, calculating to obtain a reverse time migration imaging field. According to the method, the kanzi lossless compression strategy is adopted, and the storage efficiency is remarkably improved on the premise that the data integrity is not sacrificed specially for the time slice wave field between the check points.

Description

Technical Field

[0001] This invention belongs to the field of time-shift imaging, and specifically relates to a method, apparatus and medium for time-shift imaging. Background Technology

[0002] Pre-stack reverse time migration is a two-way wave migration imaging method that uses the cross-correlation between the forward and reverse propagating wave fields to obtain the position of the reflecting interface. Reverse time migration can use complex wave field information such as gyratory waves and rhombic waves for imaging. Compared with other migration methods, it has the advantages of high accuracy, no approximation processing, and no limitations on tilt angle or drastic velocity changes, thus achieving better imaging results.

[0003] However, reverse time migration suffers from low computational efficiency, large storage requirements, and heavy reliance on the initial velocity model. In recent years, with in-depth research and improved computing power, pre-stack reverse time migration and its corresponding full waveform inversion have made significant progress. Among these advancements, new wavefield compression storage strategies have greatly reduced the requirements for computer hardware, making high-resolution imaging of 3D seismic data feasible.

[0004] Pre-stack reverse-time migration, a geophysical method based on cross-correlation, requires reconstructing the forward propagation wavefield, resulting in significant computational and storage demands. Currently, the main wavefield reconstruction approaches include: 1) Direct storage method: storing the wavefield state of all time-sampled points in memory or hard drive, and extracting the stored wavefield during imaging at a specific time point and performing cross-correlation with the reverse propagation wavefield; 2) Effective boundary method: storing the effective boundary layers around each forward propagation wavefield, and using the wavefield from the last two time-sampled points for reverse-time propagation, adding the effective boundary corresponding to each time-sampled point to the reverse propagation wavefield to reconstruct the wavefield value at that time point; 3) Wavefield reconstruction method based on random boundary conditions; 4) Reconstruction method based on checkpoint technology, during the forward propagation process... The method involves setting a checkpoint at regular intervals and storing the wavefield at that point. Starting from the checkpoint, the wavefield at any time is reconstructed through repeated recursion. It only needs to store a small number of cache points to effectively reconstruct the wavefield value. It adopts a strategy of replacing storage with computation. The wavefield is reconstructed through repeated recursion. The number of recursions increases exponentially with the increase of the number of sampling points over time, thus having a high recalculation rate. Fifth, the sampling interpolation method is used for wavefield reconstruction. Under the premise of satisfying the sampling theorem, the forward propagation wavefield is sampled and the sampled wavefield is stored through a data compression algorithm, which greatly reduces the storage amount compared with the conventional effective boundary layer reconstruction method.

[0005] There is currently no good solution for how to reasonably and effectively combine checkpoint technology and wavefield lossless compression algorithm to reduce wavefield recalculation rate while using Kanzi lossless compression algorithm to store more wavefield time slices in limited memory space, thereby improving the calculation efficiency of reverse time migration. Summary of the Invention

[0006] The purpose of this invention is to solve the problems existing in the prior art and provide a reverse time-shift imaging method, device and medium. It adopts the Kanzi lossless compression strategy and is specifically designed for the time slice wave field between check points, which significantly improves storage efficiency without sacrificing data integrity.

[0007] This invention is achieved through the following technical solution:

[0008] A first aspect of the present invention provides a reverse time-shift imaging method, comprising:

[0009] Step 1: Determine the checkpoint configuration strategy and generate a checkpoint list;

[0010] Step 2: Forward extension of the shot point wavefield to obtain the checkpoint wavefield;

[0011] Step 3: Receive the point wave field and perform reverse extension to reach the corresponding checkpoint and read the shot field of that checkpoint.

[0012] Step 4: Use the shot wavefields of the two time slices before and after the checkpoint to perform forward continuation, obtain the shot wavefield of a checkpoint, and compress and store it in memory space.

[0013] Step 5: Calculate the reverse time migration imaging field.

[0014] A further improvement of the present invention is that:

[0015] Step 1: Determine the checkpoint configuration strategy and generate a checkpoint list. Specific operations include:

[0016] Based on the inverse time offset calculation, the total duration of the finite difference calculation, sampling interval, aperture size, mesh size, etc. are determined. Combined with the available memory size, the checkpoint configuration strategy is determined, that is, a checkpoint is set every N steps, and a checkpoint list is generated.

[0017] A further improvement of the present invention is that:

[0018] Step 2: Forward continuation of the shot point wavefield to obtain the checkpoint wavefield. Specific operations include:

[0019] When calculating the reverse time offset, we start from the shot point position (the time corresponding to the bubble point position is t=0), and use the finite difference algorithm to extend the wave field outward along the positive direction of the time axis. Every N steps of extension, we reach a check point and obtain the shot point wave field of the two time slices before and after the check point. The shot point wave field is then stored on the hard disk.

[0020] Repeat the above steps until the shot point wavefields of all checkpoints in the checkpoint list generated in step 1 are obtained, and then store the shot point wavefields to the hard disk.

[0021] A further improvement of the present invention is that:

[0022] Step 3: Receive the point wavefield and perform reverse extension to reach the corresponding checkpoint and read the shot field at that checkpoint. Specific operations include:

[0023] Starting from the receiving point, the wavefield is extended backward using the finite difference algorithm. The seismic wavefield is propagated backward along the time axis. Whenever a checkpoint determined in step 1 is reached, the wavefield extension at the receiving point is paused, and the shot wavefield of the two time slices before and after the checkpoint is read from the hard disk.

[0024] A further improvement of the present invention is that:

[0025] Step 4: Using the shot wavefields of the two time slices before and after the checkpoint, perform a forward continuation to obtain the shot wavefield of a single checkpoint, and compress and store it in memory. Specific operations include:

[0026] Starting from the current checkpoint time, using the shot point wavefields of the two time slices before and after the checkpoint, the finite difference algorithm is used to extend the wavefield outward along the positive time axis. Every N steps of extension reaches a checkpoint, and the shot point wavefield at each moment of the checkpoint is obtained. The shot point wavefield at each moment is then compressed using Kanzi lossless compression and stored in the corresponding memory space.

[0027] A further improvement of the present invention is that:

[0028] Step 5: Calculate the reverse time migration imaging field. Specific operations include:

[0029] Starting from the receiving point, the wavefield is extended backward using the finite difference algorithm. The seismic wavefield is propagated backward along the time axis. Whenever a checkpoint determined in step 1 is reached, the wavefield extension at the receiving point is paused, the shot field at the corresponding time is retrieved from memory, and the retrieved shot field at the corresponding time is decompressed using the Kanzi algorithm. The decompressed wavefield is cross-correlated with the wavefield at the receiving point to obtain the reverse time migration imaging field.

[0030] A second aspect of the present invention provides a time-shift imaging apparatus, comprising:

[0031] The list generation unit is used to determine the checkpoint configuration strategy and generate a checkpoint list;

[0032] Forward extension unit, used for forward extension of the shot point wavefield to obtain the checkpoint wavefield;

[0033] The reverse extension unit is used to receive the reverse extension of the point wave field, reach the corresponding checkpoint, and read the shot point wave field of the checkpoint.

[0034] The compressed storage unit uses the shot wave field of the two time slices before and after the checkpoint to perform forward extension, obtains the shot wave field of a checkpoint, and compresses and stores it into the memory space.

[0035] The calculation unit is used to calculate the reverse time-shifted imaging field.

[0036] A further improvement of the present invention is that:

[0037] The reverse extension unit is used to receive the point wavefield in reverse extension, reach the corresponding checkpoint, and read the shot point wavefield at that checkpoint. Specifically, it performs the following operations:

[0038] Starting from the receiving point, the wavefield is extended backward using the finite difference algorithm. The seismic wavefield is propagated backward along the time axis. Whenever a checkpoint is reached in the checkpoint list, the wavefield extension at the receiving point is paused, and the shot wavefield of the two time slices before and after the checkpoint is read from the hard disk.

[0039] A further improvement of the present invention is that:

[0040] The compressed storage unit is used to perform forward extrapolation of the shot wavefields of the two time slices before and after the checkpoint to obtain the shot wavefield of a checkpoint, and then compress and store it in memory space. Specifically, the following operations are performed:

[0041] Starting from the current checkpoint time, using the shot point wavefields of the two time slices before and after the checkpoint, the finite difference algorithm is used to extend the wavefield outward along the positive time axis. Every N steps of extension reaches a checkpoint, and the shot point wavefield at each moment of the checkpoint is obtained. The shot point wavefield at each moment is then compressed using Kanzi lossless compression and stored in the corresponding memory space.

[0042] A third aspect of the present invention provides a computer-readable storage medium storing at least one computer-executable program, which, when executed by the computer, causes the computer to perform the steps in the reverse time-shift imaging method.

[0043] Compared with the prior art, the beneficial effects of the present invention are:

[0044] This invention employs a Kanzi lossless compression strategy specifically targeting time-slice wavefields between checkpoints, significantly improving storage efficiency without sacrificing data integrity. With the same hardware memory configuration, this invention can significantly reduce the number of checkpoints required. This optimization not only reduces the recalculation rate of the wavefield but also greatly improves the computational efficiency of the reverse-time offset technique.

[0045] The method of this invention enables more efficient data processing under limited resource conditions, bringing revolutionary technological progress to fields such as seismic exploration. Attached Figure Description

[0046] Figure 1 This is a flowchart of a reverse time-shift imaging method according to an embodiment of the present invention;

[0047] Figure 2 This is a flowchart of the wave field extension at the shot point. Detailed Implementation

[0048] The present invention will now be described in further detail with reference to the accompanying drawings:

[0049]

Example 1

[0050] like Figure 1 As shown, this embodiment of the invention provides a reverse time offset method, which mainly includes the following steps:

[0051] Step 1: Determine the checkpoint configuration strategy and generate a checkpoint list;

[0052] Step 2: Forward extension of the shot point wavefield to obtain the checkpoint wavefield;

[0053] Step 3: Receive the point wave field and perform reverse extension to reach the corresponding checkpoint and read the shot field of that checkpoint.

[0054] Step 4: Use the shot wavefields of the two time slices before and after the checkpoint to perform forward continuation, obtain the shot wavefield of a checkpoint, and compress and store it in memory space.

[0055] Step 5: Calculate the reverse time migration imaging field.

[0056] This invention employs a Kanzi lossless compression strategy specifically targeting time-slice wavefields between checkpoints, significantly improving storage efficiency without sacrificing data integrity. With the same hardware memory configuration, this invention can significantly reduce the number of checkpoints required. This optimization not only reduces the recalculation rate of the wavefield but also greatly improves the computational efficiency of the reverse-time offset technique.

[0057] The method of this invention enables more efficient data processing under limited resource conditions, bringing revolutionary technological progress to fields such as seismic exploration.

[0058]

Example 2

[0059] Step 1: Determine the checkpoint configuration strategy and generate a checkpoint list. Specific operations include:

[0060] Based on the inverse time offset calculation, the total duration of the finite difference calculation, sampling interval, aperture size, mesh size, etc. are determined. Combined with the available memory size, the checkpoint configuration strategy is determined, that is, a checkpoint is set every N steps, and a checkpoint list is generated.

[0061] It should be understood that user parameters are calculated based on the reverse time offset, including the time domain T, sampling interval, propagation time, aperture size in the XYZ spatial direction, grid size, etc. First, the required space size A, such as hard disk and memory, is determined by the time domain T and the aperture size in the XYZ spatial direction. Then, the number of data blocks B that can be stored under the current hardware configuration is calculated by combining the hard disk size and memory size of the actual cluster hardware configuration. The number of copies of data that need to be stored, C, is calculated. Here, C = A / B, and C is the configuration of the checkpoint.

[0062]

Example 3

[0063] Step 2: Forward extrapolation of the shot point wavefield to obtain the checkpoint wavefield, such as... Figure 2 As shown, the specific operations include:

[0064] When calculating the reverse time offset, we start from the shot point position (the time corresponding to the bubble point position is t=0), and use the finite difference algorithm to extend the wave field outward along the positive direction of the time axis. Every N steps of extension, we reach a check point and obtain the shot point wave field of the two time slices before and after the check point. The shot point wave field is then stored on the hard disk.

[0065] Repeat the above steps until the shot point wavefields of all checkpoints in the checkpoint list generated in step 1 are obtained, and then store the shot point wavefields to the hard disk.

[0066]

Example 4

[0067] Step 3: Receive the point wavefield and perform reverse extension to reach the corresponding checkpoint and read the shot field at that checkpoint. Specific operations include:

[0068] Starting from the receiving point, the wavefield is extended backward using the finite difference algorithm. The seismic wavefield is propagated backward along the time axis. Whenever a checkpoint determined in step 1 is reached, the wavefield extension at the receiving point is paused, and the shot wavefield of the two time slices before and after the checkpoint is read from the hard disk.

[0069]

Example 5

[0070] Step 4: Using the shot wavefields of the two time slices before and after the checkpoint, perform a forward continuation to obtain the shot wavefield of a single checkpoint, and compress and store it in memory. Specific operations include:

[0071] Starting from the current checkpoint time, using the shot point wavefields of the two time slices before and after the checkpoint, the finite difference algorithm is used to extend the wavefield outward along the positive time axis. Every N steps of extension reaches a checkpoint, and the shot point wavefield at each moment of the checkpoint is obtained. The shot point wavefield at each moment is then compressed using Kanzi lossless compression and stored in the corresponding memory space.

[0072] In this embodiment of the invention, kanzi lossless compression is an existing compression method, and will not be described in detail here.

[0073]

Example 6

[0074] Step 5: Calculate the reverse time migration imaging field. Specific operations include:

[0075] Starting from the receiving point, the wavefield is extended backward using the finite difference algorithm. The seismic wavefield is propagated backward along the time axis. Whenever a checkpoint determined in step 1 is reached, the wavefield extension at the receiving point is paused, the shot field at the corresponding time is retrieved from memory, and the retrieved shot field at the corresponding time is decompressed using the Kanzi algorithm. The decompressed wavefield is cross-correlated with the corresponding receiving point wavefield to obtain the reverse time migration imaging field.

[0076] Repeat steps 3 through 5 until all checkpoints in the checkpoint list generated in step 1 have been traversed.

[0077]

Example 7

[0078] This invention provides a time-lapse imaging device, comprising:

[0079] The list generation unit is used to determine the checkpoint configuration strategy and generate a checkpoint list; specifically, it performs the following operations:

[0080] Based on the inverse time offset calculation, the total duration of the finite difference calculation, sampling interval, aperture size, mesh size, etc. are determined. Combined with the available memory size, the checkpoint configuration strategy is determined, that is, a checkpoint is set every N steps, and a checkpoint list is generated.

[0081] It should be understood that user parameters are calculated based on the reverse time offset, including the time domain T, sampling interval, propagation time, aperture size in the XYZ spatial direction, grid size, etc. First, the required space size A, such as hard disk and memory, is determined by the time domain T and the aperture size in the XYZ spatial direction. Then, the number of data blocks B that can be stored under the current hardware configuration is calculated by combining the hard disk size and memory size of the actual cluster hardware configuration. The number of copies of data that need to be stored, C, is calculated. Here, C = A / B, and C is the configuration of the checkpoint.

[0082] Forward extension unit, used for forward extension of the shot point wavefield to obtain the check point wavefield, specifically performs the following operations:

[0083] When calculating the reverse time offset, we start from the shot point position (the time corresponding to the bubble point position is t=0), and use the finite difference algorithm to extend the wave field outward along the positive direction of the time axis. Every N steps of extension, we reach a check point and obtain the shot point wave field of the two time slices before and after the check point. The shot point wave field is then stored on the hard disk.

[0084] Repeat the above steps until the shot point wavefields of all checkpoints in the checkpoint list generated in step 1 are obtained, and then store the shot point wavefields to the hard disk.

[0085] The reverse extension unit is used to receive the point wavefield in reverse extension, reach the corresponding checkpoint, and read the shot point wavefield at that checkpoint. Specifically, it performs the following operations:

[0086] Starting from the receiving point, the wavefield is extended backward using the finite difference algorithm. The seismic wavefield is propagated backward along the time axis. Whenever a checkpoint is reached in the checkpoint list, the wavefield extension at the receiving point is paused, and the shot wavefield of the two time slices before and after the checkpoint is read from the hard disk.

[0087] The compressed storage unit performs forward extrapolation of the shot wavefields from two time slices before and after the checkpoint to obtain the shot wavefield of a checkpoint, and then compresses and stores it in memory. Specifically, the following operations are performed:

[0088] Starting from the current checkpoint time, using the shot point wavefields of the two time slices before and after the checkpoint, the finite difference algorithm is used to extend the wavefield outward along the positive time axis. Every N steps of extension reaches a checkpoint, and the shot point wavefield at each moment of the checkpoint is obtained. The shot point wavefield at each moment is then compressed using Kanzi lossless compression and stored in the corresponding memory space.

[0089] The calculation unit is used to calculate the reverse time-lapse imaging field, and specifically performs the following operations:

[0090] Starting from the receiving point, the wavefield is extended backward using the finite difference algorithm. The seismic wavefield is propagated backward along the time axis. Whenever a checkpoint determined in step 1 is reached, the wavefield extension at the receiving point is paused, the shot field at the corresponding time is retrieved from memory, and the retrieved shot field at the corresponding time is decompressed using the Kanzi algorithm. The decompressed wavefield is cross-correlated with the corresponding receiving point wavefield to obtain the reverse time migration imaging field.

[0091] Repeat steps 3 through 5 until all checkpoints in the checkpoint list generated in step 1 have been traversed.

[0092] This invention employs a Kanzi lossless compression strategy specifically for time-slice wavefields between checkpoints, significantly improving storage efficiency without sacrificing data integrity. With the same hardware memory configuration, this invention can significantly reduce the number of required checkpoints. This optimization not only reduces the recalculation rate of the wavefield but also greatly improves the computational efficiency of the reverse-time offset technique.

[0093]

Example 8

[0094] This invention provides a computer-readable storage medium storing at least one computer-executable program, which, when executed by the computer, causes the computer to perform the steps in the reverse time-shift imaging method.

[0095] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0096] The above technical solution is only one embodiment of the present invention. For those skilled in the art, based on the principles disclosed in the present invention, it is easy to make various types of improvements or modifications, and not limited to the technical solutions described in the specific embodiments of the present invention. Therefore, the foregoing description is only a preferred option and is not restrictive.

Claims

1. A reverse time migration imaging method, characterized in that, include: Step 1: Determine the checkpoint configuration strategy and generate a checkpoint list; Step 2: Forward extension of the shot point wavefield to obtain the checkpoint wavefield; Step 3: Receive the point wave field and perform reverse extension to reach the corresponding checkpoint and read the shot field of that checkpoint. Step 4: Use the shot wavefields of the two time slices before and after the checkpoint to perform forward continuation, obtain the shot wavefield of a checkpoint, and compress and store it in memory space. Step 5: Calculate the reverse time migration imaging field.

2. The method according to claim 1, characterized in that, Step 1: Determine the checkpoint configuration strategy and generate a checkpoint list. Specific operations include: Based on the inverse time offset calculation, the total duration of the finite difference calculation, sampling interval, aperture size, mesh size, etc. are determined. Combined with the available memory size, the checkpoint configuration strategy is determined, that is, a checkpoint is set every N steps, and a checkpoint list is generated.

3. The method according to claim 1, characterized in that, Step 2: Forward continuation of the shot point wavefield to obtain the checkpoint wavefield. Specific operations include: When calculating the reverse time offset, we first start from the shot point position and use the finite difference algorithm to extend the wave field outward along the positive time axis. Every N steps of extension, we reach a checkpoint and obtain the shot point wave field of the two time slices before and after the checkpoint. The shot point wave field is then stored on the hard disk. Repeat the above steps until the shot point wavefields of all checkpoints in the checkpoint list generated in step 1 are obtained, and then store the shot point wavefields to the hard disk.

4. The method according to claim 3, characterized in that, Step 3: Receive the point wavefield and perform reverse extension to reach the corresponding checkpoint and read the shot field at that checkpoint. Specific operations include: Starting from the receiving point, the wavefield is extended backward using the finite difference algorithm. The seismic wavefield is propagated backward along the time axis. Whenever a checkpoint determined in step 1 is reached, the wavefield extension at the receiving point is paused, and the shot wavefield of the two time slices before and after the checkpoint is read from the hard disk.

5. The method according to claim 4, characterized in that, Step 4: Using the shot wavefields of the two time slices before and after the checkpoint, perform a forward continuation to obtain the shot wavefield of a single checkpoint, and compress and store it in memory. Specific operations include: Starting from the current checkpoint time, using the shot point wavefields of the two time slices before and after the checkpoint, the finite difference algorithm is used to extend the wavefield outward along the positive time axis. Every N steps of extension reaches a checkpoint, and the shot point wavefield at each moment of the checkpoint is obtained. The shot point wavefield at each moment is then compressed using Kanzi lossless compression and stored in the corresponding memory space.

6. The method according to claim 5, characterized in that, Step 5: Calculate the reverse time migration imaging field. Specific operations include: Starting from the receiving point, the wavefield is extended backward using the finite difference algorithm. The seismic wavefield is propagated backward along the time axis. Whenever a checkpoint determined in step 1 is reached, the wavefield extension at the receiving point is paused, the shot field at the corresponding time is retrieved from memory, and the retrieved shot field at the corresponding time is decompressed using the Kanzi algorithm. The decompressed wavefield is cross-correlated with the wavefield at the receiving point to obtain the reverse time migration imaging field.

7. A reverse time-shift imaging device, characterized in that, include: The list generation unit is used to determine the checkpoint configuration strategy and generate a checkpoint list; Forward extension unit, used for forward extension of the shot point wavefield to obtain the checkpoint wavefield; The reverse extension unit is used to receive the reverse extension of the point wave field, reach the corresponding checkpoint, and read the shot point wave field of the checkpoint. The compressed storage unit uses the shot wave field of the two time slices before and after the checkpoint to perform forward extension, obtains the shot wave field of a checkpoint, and compresses and stores it into the memory space. The calculation unit is used to calculate the reverse time-shifted imaging field.

8. The apparatus according to claim 7, characterized in that, The reverse extension unit is used to receive the reverse extension of the point wave field, reach the corresponding check point, and read the shot point wave field at that check point. Specifically, it performs the following operations: Starting from the receiving point, the wavefield is extended backward using the finite difference algorithm. The seismic wavefield is propagated backward along the time axis. Whenever a checkpoint is reached in the checkpoint list, the wavefield extension at the receiving point is paused, and the shot wavefield of the two time slices before and after the checkpoint is read from the hard disk.

9. The apparatus according to claim 8, characterized in that, The compressed storage unit is used to perform forward extrapolation of the shot wavefields of the two time slices before and after the checkpoint to obtain the shot wavefield of a checkpoint, and then compress and store it in memory space. Specifically, the following operations are performed: Starting from the current checkpoint time, using the shot point wavefields of the two time slices before and after the checkpoint, the finite difference algorithm is used to extend the wavefield outward along the positive time axis. Every N steps of extension reaches a checkpoint, and the shot point wavefield at each moment of the checkpoint is obtained. The shot point wavefield at each moment is then compressed using Kanzi lossless compression and stored in the corresponding memory space.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores at least one computer-executable program, which, when executed by the computer, causes the computer to perform the steps in the reverse time-shift imaging method as described in any one of claims 1-6.

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