Enhanced seismic guided feature prediction method

Abstract

A method for predicting properties of a subsurface formation, comprising: drilling one or more boreholes in a subsurface formation at a wellsite; performing seismic exploration at the wellsite to construct a main seismic image volume, the main seismic image volume having a dataset comprising at least pressure wave velocity v p , shear wave velocity v s , and density rho encompassing a time domain and a frequency domain; performing well logging at the one or more boreholes to generate well logging information at the wellsite; generating an auxiliary seismic image volume for seismic guided property prediction at the wellsite using a Kriging method; generating a prediction operator based on the main seismic image volume, the auxiliary seismic image volume, and the well logging information; inputting the seismic image volume and the prediction operator to a property prediction engine; and generating predicted properties of the subsurface formation.

Description

Technical Field

[0001] This disclosure relates to a method for generating enhanced seismic guidance characteristic predictions, and more particularly to a method for generating auxiliary input data for seismic guidance characteristic predictions using the Kriging method. Background Technology

[0002] In the field of oil and gas exploration and development, seismic data acquisition and processing play a crucial role in delineating subsurface geological structures and characterizing reservoir properties. This processing begins with seismic data acquisition and then proceeds to generate high-resolution three-dimensional subsurface property data volumes. These data volumes may include, but are not limited to, seismic propagation velocity models, anisotropy parameters, attenuation (or absorption) coefficients, porosity distributions, and seismic reflectivity models. By integrating these geophysical property data volumes, a comprehensive and effective interpretation of subsurface structures can be achieved, thereby contributing to scientific decision-making guidance for exploration and field development activities.

[0003] Seismic data processing workflows typically involve a series of inversion and imaging steps. First, seismic inversion methods are used to construct propagation velocity models to resolve long- to medium-wave characteristics in the subsurface. These velocity models are crucial for accurate wavefield extrapolation and serve as the basis for subsequent imaging processes. After establishing the velocity models, seismic migration algorithms are applied to the recorded data to generate high-resolution seismic reflectance images, thereby capturing the short-wavelength characteristics of corresponding geological interfaces and heterogeneity. The resulting seismic reflectance images provide detailed spatial information on the location, geometry, and extent of potential hydrocarbon-bearing formations, helping to assess the storage capacity and distribution of hydrocarbon resources. This information directly guides and optimizes exploration strategies, well placement, and drilling operations.

[0004] To obtain high-fidelity seismic reflectance images with sufficient spatial resolution and accuracy, high-magnification seismic acquisition systems are required. These systems are designed to collect dense and redundant seismic measurements, thereby improving the signal-to-noise ratio and data coverage. Furthermore, the establishment of an accurate seismic velocity model—characterized by correct dynamic properties and reflecting real subsurface conditions—is a prerequisite for successful seismic migration and imaging. A high-quality velocity model ensures that subsequent migration steps produce reliable and interpretable reflectance images, which is crucial for resource assessment and risk management in oil and gas exploration.

[0005] Existing methods for seismic velocity inversion mainly include ray-based seismic tomography and full waveform inversion (FWI) techniques. Ray-based tomography relies on the approximate assumption that seismic energy propagates along discrete ray paths. It is computationally efficient and can usually generate smooth subsurface velocity models. Such models are generally sufficient to resolve geological targets with relatively simple structural features, including shallow sedimentary environments with small lateral velocity variations and a generally homogeneous subsurface.

[0006] However, the inherent limitations of ray-based tomography become particularly apparent when applied to geologically complex environments. In environments with strong lateral heterogeneity, abrupt velocity changes, or complex structural geometries—such as salt domes, subbasal structures, thrust zones, and piedmont areas—ray-based methods cannot accurately resolve the true subsurface velocity distribution. The inherent simplifications of ray theory lead to insufficient model resolution and introduce significant errors in regions dominated by wavefront distortion, multipath effects, and scattering.

[0007] To address these challenges, full waveform inversion (FWI) has become a powerful and indispensable tool for building seismic velocity models in complex geological environments. FWI utilizes complete seismic waveforms, integrating amplitude, phase, and frequency information to reconstruct high-resolution velocity models that capture subsurface features at both large and fine scales. By directly solving the seismic wave equations to iteratively minimize the discrepancies between observed and simulated seismic data, FWI considers the complete physical properties of wave propagation, including transmission, reflection, diffraction, and mode conversion phenomena. Therefore, when ray-based tomography fails, FWI can generate accurate and geologically realistic velocity models, significantly improving subsurface imaging capabilities and providing more reliable reservoir characterization.

[0008] In Full Waveform Inversion (FWI), the seismic wave equations are solved directly, and the observed seismic data are iteratively matched with synthetic data generated from the subsurface model. This method enables the construction of high-precision seismic propagation velocity models, which is particularly effective in representing complex subsurface geological structures, including those associated with salt bodies, thrust zones, and other areas with strong lateral heterogeneity or abrupt velocity changes. The velocity models obtained from FWI serve as the basis for generating accurate and high-resolution seismic reflectivity images using advanced seismic migration algorithms. These reflectivity images help to depict geological interfaces and heterogeneity in detail, thus supporting the accurate interpretation and characterization of hydrocarbon reservoirs.

[0009] Furthermore, high-fidelity velocity models generated by FWI are crucial in time-shift (4D) seismic monitoring, enabling the detection and quantification of dynamic changes within oil and gas reservoirs during production. This capability is essential for optimizing reservoir management, enhancing recovery strategies, and mitigating associated risks. Beyond their role in migration-based imaging, FWI-based models can also be directly used to generate high-resolution seismic image data volumes, commonly referred to as FWI images. These FWI images provide unprecedented detail about subsurface properties because they integrate the complete physical properties of wave propagation—capturing large-scale and fine-scale features that are typically unresolved by conventional imaging techniques. Therefore, the application of FWI has significantly advanced the research landscape in subsurface imaging and reservoir property characterization, providing a powerful and comprehensive toolset for exploration and field development activities. Summary of the Invention

[0010] According to one embodiment of this disclosure, a method for predicting subsurface formation properties is disclosed. The method includes the following steps: drilling one or more wells in the subsurface formation at a well location; and conducting seismic exploration at the well location to construct a master seismic image volume, the master seismic image volume dataset including at least pressure wave velocities v covering both the time and frequency domains. p Shear rate v s The following steps are performed: logging is conducted at one or more wells to obtain logging information at the well locations; an auxiliary seismic image volume for predicting seismic guidance characteristics at the well locations is generated using kriging; a prediction operator is generated based on the primary seismic image volume, the auxiliary seismic image volume, and the logging information at the well locations; the prediction operator and the secondary seismic image volume are used to generate the predicted properties of the subsurface strata. The secondary seismic image volume may be the same as the primary seismic image volume, or it may be obtained by seismic exploration in a region different from the region in which the primary seismic image volume is located.

[0011] According to one embodiment of this disclosure, the step of generating an auxiliary seismic image volume further includes: deriving the P-wave impedance from the main seismic image volume at the well location through seismic inversion covering both the time and frequency domains. According to another embodiment of this disclosure, the step of generating an auxiliary seismic image volume further includes: extracting the high-frequency components of the main seismic image volume in the wavelet transform domain.

[0012] According to one embodiment of this disclosure, the step of generating an auxiliary seismic image volume further includes: generating an instantaneous frequency map from the high-frequency components of the extracted main seismic image volume.

[0013] According to one embodiment of this disclosure, the step of generating an auxiliary seismic image volume further includes: convolving the main seismic image volume with a wavelet having a dominant frequency component.

[0014] According to one embodiment of this disclosure, the step of generating an auxiliary seismic image volume further includes: generating an auxiliary seismic image volume at the well that is coherent with the main seismic image volume at the well.

[0015] According to one embodiment of this disclosure, the step of conducting seismic exploration at the well location to construct a main seismic image volume further includes: establishing a well-seismic correlation. According to another embodiment of this disclosure, the step of conducting seismic exploration at the well location to construct a main seismic image volume further includes: extracting seismic attributes at the well location from the seismic image volume.

[0016] According to one embodiment of this disclosure, the high-frequency components can indicate fine-scale geological features. According to one embodiment of this disclosure, the step of conducting seismic exploration at the well location to construct a master seismic image volume further includes: resampling or interpolating the extracted seismic attributes to match the sampling interval of the well log. According to one embodiment of this disclosure, the instantaneous frequency map can capture the dominant frequency components at each spatial location. According to one embodiment of this disclosure, the step of conducting seismic exploration at the well location to construct a master seismic image volume further includes: ensuring that the seismic dataset at the well location is geologically consistent and free of artifacts or misalignments.

[0017] According to one embodiment of this disclosure, the method further includes: when the P-wave impedance is compared with (v... p , v s Establish a pseudo-linear relationship between (v, rho). According to one embodiment of this disclosure, the method further includes: establishing a pseudo-linear relationship between the dataset of the main seismic image volume and (v... p ,v s A prediction operator is established between (rho) and (rho). According to one embodiment of this disclosure, the P-wave impedance According to one embodiment of this disclosure, reflectivity , , For wavelets, According to one embodiment of this disclosure, it is assumed that: ,but According to one embodiment of this disclosure, the prediction operator is generated based on well logging information. According to another embodiment of this disclosure, the prediction operator is generated based on the main seismic image volume. Attached Figure Description

[0018] This disclosure will now be explained in more detail through exemplary embodiments and in conjunction with the accompanying drawings, wherein:

[0019] Figure 1 This is a schematic top view of a survey area containing incident points of various seismic sources according to an embodiment of the present disclosure.

[0020] Figure 2 This is a schematic cross-sectional view of an environment including the incident point of the seismic source, seismic data recording sensors, well location, wellbore, various transmission rays, and various incident angles, according to an embodiment of the present disclosure.

[0021] Figure 3 This is a schematic cross-sectional view illustrating an environment including a wellbore and a logging tool according to an embodiment of the present disclosure, the logging tool including one or more acoustic generators and one or more logging data recording sensors.

[0022] Figure 4 This is a schematic diagram illustrating a high-performance computing system according to an embodiment of the present disclosure.

[0023] Figure 5 This is a functional block diagram illustrating a kriging workflow using well information and generating attributes via seismic guidance characteristics according to an embodiment of the present disclosure.

[0024] Figure 6 This is a functional block diagram illustrating a seismic guidance characteristic prediction workflow according to an embodiment of the present disclosure.

[0025] Figure 7 This is a flowchart illustrating a method for generating auxiliary data according to an embodiment of the present disclosure.

[0026] Figure 8 The results of a conventional low-frequency model building workflow are shown in comparison with the results of a workflow for restoring real geological features according to an embodiment of the present disclosure, wherein a bullseye effect is present in the results of the conventional workflow, while no bullseye effect is present in the workflow of the present disclosure. Detailed Implementation

[0027] In subsurface reservoir characterization, the construction of accurate low-frequency models is a crucial prerequisite for achieving reliable seismic inversion and attribute prediction workflows. Traditional low-frequency model building methods often rely on sparse well data and simple interpolation schemes, which may fail to capture the inherent geological complexity and lateral variability in many formation environments. Furthermore, the lack of reliable and stable integration between well logging measurements and seismic attributes can lead to a lack of geophysical consistency in the model, thus limiting its predictive utility in reservoir delineation, lithofacies classification, and reserve estimation.

[0028] Figures 1 to 4Exemplary embodiments of methods, apparatus, and media for acquiring and storing seismic data, which, after processing, can generate one or more high-resolution geological models for high-resolution imaging of lithological identification, fluid identification, and reservoir description of complex subsurface structures in an exploration area. The exploration area can be subsurface structures beneath land or seabed. Seismic data includes, for example, seismic volumetric images, which are three-dimensional representations of the Earth's subsurface created by processing seismic reflection data. Seismic volumetric images present geological structures and strata in three dimensions, enabling interpreters to analyze spatial relationships and identify features such as faults, stratigraphic horizons, and reservoirs.

[0029] Figure 1 This is a schematic diagram showing a top-down view of a survey area containing incident points of different seismic sources according to one embodiment. More specifically, Figure 1 A seismic survey area (exploration area) 101 is shown, which is a land-based area indicated by reference numeral 102. Reference numeral 102 indicates the top strata 102 of the land-based area. Those skilled in the art will recognize that seismic survey areas can generate detailed images of the local geology to determine the location and size of potential hydrocarbon (oil and gas) reservoirs, thereby establishing well sites 103. In these survey areas, seismic waves are reflected back from the subsurface rock strata when emitted from one or more seismic sources located at different incident points 104. A blast is an example of a seismic source generated by a seismic device. The seismic waves reflected back to the surface are captured by a seismic data recording sensor 105, transmitted from the seismic data recording sensor 105 via one or more data transmission systems (typically wireless), and stored for post-processing and analysis by a high-performance computing system. While this example shows the top strata 102 of a land-based area, it should be understood that this is merely an example, and the method and system can also be applied to survey areas on the surface or bottom of the ocean.

[0030] Figure 2 This is a schematic diagram showing a cross-sectional view of an environment according to one embodiment, including the incident point of the seismic source, seismic data recording sensors, well location, wellbore, various transmission rays, and various incident angles. Figure 2 This illustrates a description according to one embodiment. Figure 1 This is a schematic diagram of a cross-sectional view of the seismic survey area 101, including the incident point of the seismic source, seismic data recording sensors (seismographs), well location, well casing, various transmission rays, and various incident angles. More specifically, in Figure 2In the figures, the cross-sectional view of the subsurface portion above the seismic survey area is indicated by reference numeral 201, and different types of strata are shown by reference numerals 102, 203, and 204. Although the seismic survey area in this example is based on land, it should be understood that this is only an example, and the system and method can also be applied to survey areas on the surface or bottom of the ocean. Figure 2 A common-center gather is shown, where seismic data is ordered according to surface geometry to simulate individual reflection points on Earth. Exploration seismic data can also be called traces, gathers, or image gathers. Figure 2 In this example, data from one or more shot points or blast points and detectors can be combined into a single image gather, or used individually depending on the type of analysis to be performed.

[0031] like Figure 2 As shown, one or more shot points or blast points represent seismic sources located on the Earth's surface, indicated by reference numeral 104, at various incident points or sites where one or more sources are activated. Seismic energy or seismic sources from multiple incident points 104 will be reflected from interfaces between different strata. These reflections will be captured by multiple seismic data recording sensors 105, each placed at a different offset distance 210 and at well site 103. Since all incident points 104 and all seismic data recording sensors 105 are placed at different offset distances 210, reconnaissance seismic data or sets (also referred to in the art as "gathers" or "image gathers") will be recorded at different incident angles 208. Incident points 104 generate downward propagating rays 205, which are captured at the surface by upward propagating reflections from the seismic data recording sensors 105. In this example, well site 103 connected to an existing drilled well 209 is shown, with multiple measurements taken along well 209 using techniques known in the art. The wellbore 209 is used to acquire logging data, which may include P-wave velocity, S-wave velocity, density, etc. (Not in...) Figure 2 Other sensors shown can be placed within the survey area to capture seismic data. Seismic data can be used to examine the dependence of amplitude, signal-to-noise ratio, time difference, frequency content, phase, and other seismic properties on the incident angle 208°, offset 210°, azimuth, and other geometric properties that are crucial for data processing and imaging in the seismic survey area.

[0032] Figure 3This is a schematic diagram showing a cross-sectional view of a wellbore and logging tool according to one embodiment, wherein the logging tool includes one or more acoustic generators and one or more logging data recording sensors. The acoustic generator is an example of a device that generates one or more acoustic waves (acoustic waves). The acoustic generator can be referred to as a sound source because it generates or produces one or more acoustic waves (acoustic waves), which are also called seismic waves. The one or more logging data recording sensors are examples of one or more seismic data recording sensors (seismic detectors or seismic data recorders), and are the same seismic data recording sensor as seismic data recording sensor 105. In embodiments of the invention, oil and / or gas production is suspended in order to generate seismic waves and record seismic data, including reflections of seismic waves as they move through one or more subsurface strata in a seismically surveyed area.

[0033] Figure 3 An oil drilling system 300 on land 305 is shown, including a drilling rig 310. The drilling rig 310 supports the insertion of a logging tool 315 into a wellbore 320. The logging tool 315 includes one or more acoustic generators (sound sources) for generating one or more acoustic waves, which are transmitted to one or more formations to generate reflected or reflected waves in the formations. Although this example shows one or more formations in a land-based exploration area, it should be understood that this is only an example, and the method and system can also be applied to exploration areas on the surface or bottom of the ocean. The logging tool 315 also includes one or more logging data recording sensors. These sensors receive and record logging data, including reflected data received by the sensors in response to acoustic waves emitted by the acoustic generators into the formations. The logging data is an example of seismic data. The logging data includes compressive wave velocity or P-wave velocity (Vp), S-wave velocity (Vs), and density (Rho) as an indicator of porosity. This logging process used to record logging data can also be called sonic logging. The logging vehicle 325 can be coupled to the logging tool 315 to assist in its lowering and raising, and to communicate with the logging tool 315 to obtain logging data. Alternatively, in methods and systems targeting exploration areas on the surface or bottom of water bodies (such as oceans), other equipment or systems can be used to assist in the lowering and raising of the logging tool 315 and to communicate with the logging tool 315 to obtain logging data.

[0034] Figure 4 This is a schematic diagram illustrating a high-performance computing system according to one embodiment, which receives (typically wirelessly) data from... Figure 1 and Figure 2 Earthquake data recording sensor 105 and / or Figure 3 Earthquake data recording sensors (in) Figure 3 Seismic data of seismic waves (also known as well logging data recording sensors). Figure 4 A high-performance computer system stores the seismic data in at least one memory for post-processing and analysis via a computer-implemented method and apparatus according to one or more embodiments. The analyzed or processed seismic data can be accessed via a personal computer system. More specifically, Figure 4 A data transmission system 400 is shown for wirelessly transmitting seismic data from a seismic data recording sensor to a system computer 405 coupled to one or more storage devices 410 for storing the seismic data in a database. The data transmission system can also wirelessly transmit seismic data directly from the seismic data recording sensor 405 to one or more storage devices 410 for storing the seismic data in a database, which can be accessed by the system computer 405. Wireless transmission is indicated by reference numeral 402. The one or more storage devices 410 may also store other computer software instructions or programs to implement the apparatus and methods described in the embodiments. The system computer 405 may be coupled (e.g., wirelessly) to one or more output storage devices 420, which can receive the results of computer-implemented processes or methods executed by the system computer 405. A personal computer system 425 may be coupled (e.g., wirelessly) to one or more output storage devices 420 and / or the system computer 405 so that a user can use the user interface of the personal computer system 425 to input information or obtain the results of computer-implemented processor methods executed by the system computer 405. One or more storage devices 420 may also store other computer software instructions or programs to implement the apparatus and methods described in the embodiments.

[0035] The user interface of the personal computer system 425 may include, for example, one or more of the following: a keyboard, mouse, joystick, button, switch, electronic pen or stylus, gesture recognition sensor (e.g., for recognizing gestures of the user including body part movements), input sound device or voice recognition sensor (e.g., microphone for receiving voice commands), output sound device (e.g., speaker), trackball, remote control, portable (e.g., cellular or smartphone) phone, tablet computer, pedal or foot switch, virtual reality device, etc. The user interface may also include a haptic device to provide haptic feedback to the user. The user interface may also include, for example, a touchscreen. Furthermore, the personal computer system 425 may be a desktop computer, laptop computer, tablet computer, mobile phone, or any other personal computing system.

[0036] The processes, functions, methods, and / or computer software instructions or programs in the apparatus and methods described in the embodiments herein may be recorded, stored, or fixed in one or more non-transitory computer-readable media (computer-readable storage (recording) media) including program instructions (computer-readable instructions) executable by a computer to cause one or more processors to execute (implement or implement) the program instructions. The media may also be included alone or in combination with program instructions, data files, data structures, etc. The media and program instructions may be specially designed and constructed, or may be well-known and usable by those skilled in the art of computer software. Examples of non-transitory computer-readable media include magnetic media, such as hard disks, floppy disks, and magnetic tapes; optical media, such as CD-ROMs and DVDs; magneto-optical media, such as optical discs; and hardware devices specifically configured for storing and executing program instructions, such as read-only memory (ROM), random access memory (RAM), flash memory, etc. Examples of program instructions include machine code (e.g., generated by a compiler) and files containing higher-level code that can be executed by a computer using an interpreter. The program instructions may be executed by one or more processors. The described hardware device can be configured as one or more software modules that are recorded, stored, or embedded in one or more non-transitory computer-readable media to perform the above-described operations and methods, and vice versa. Furthermore, the non-transitory computer-readable media can be distributed among computer systems connected via a network, and program instructions can be stored and executed in a distributed manner. In addition, the computer-readable media can also be embodied in at least one application-specific integrated circuit (ASIC) or field-programmable logic array (FPGA).

[0037] One or more databases may include a collection of data and supporting data structures that can be stored, for example, in one or more storage devices 410 and 420. For example, one or more storage devices 410 and 420 may be embodied as one or more non-transitory computer-readable storage media, such as non-volatile memory devices, such as read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), and flash memory, USB drives, volatile memory devices (e.g., random access memory (RAM)), hard disks, floppy disks, Blu-ray discs, or optical media (e.g., CD-ROMs and DVDs), or combinations thereof. However, examples of storage devices 410 and 420 are not limited to those described above, and the storage can be implemented by a variety of other devices and structures understood by those skilled in the art.

[0038] Recent advances in seismic processing and machine learning have led to more accurate methods for attribute prediction, particularly those guided by seismic attributes. These techniques offer the potential to improve the fidelity of low-frequency models by integrating spatially continuous information derived from seismic data, while also taking into account the vertical resolution and surface realism provided by well logging data. However, the core challenge remains developing a unified workflow to systematically integrate these diverse data sources (well information and seismically guided predictions) into a geologically plausible and inversion-adaptive collaborative modeling framework.

[0039] This disclosure addresses this need by introducing a novel low-frequency model building workflow that combines well information with seismic guidance characteristic predictions. The disclosed method generates low-frequency models that are geologically consistent, spatially continuous, and can be optimized for subsequent inversion processes. By integrating the correlation between constraints derived from the well and seismic properties, this workflow helps improve elastic properties (e.g., P-wave velocity v). p S-wave velocity v s The method enhances the resolution and reliability of subsurface interpretation by estimating the density (rho). This integrated approach represents a significant advance in geophysical modeling, offering improved accuracy, reduced uncertainty, and greater applicability to diverse reservoir environments.

[0040] Low-frequency model construction is a crucial step in the full-waveform inversion of reservoir properties. This low-frequency model must conform to the trends of the true properties to ensure that the inversion process converges to the true solution. Currently, low-frequency models are typically constructed using the Kriging method with well information and other attribute information, such as pressure velocities (i.e., P-wave velocities v) obtained during imaging. p ).

[0041] Kriging is a sophisticated geostatistical technique that interpolates discrete spatially distributed data points into a continuous surface by explicitly considering spatial correlations. This method is particularly valuable when the underlying variables exhibit spatial dependence, enabling more accurate predictions and quantifying uncertainty. The kriging process comprises several systematic stages, beginning with exploratory data analysis to identify spatial patterns and correlations. This initial stage typically involves constructing a differential function, which characterizes how the variance between data points varies as a function of distance, thus revealing the spatial structure of the dataset.

[0042] Following data exploration, the next step involves variogram modeling, which involves fitting an empirical variogram using mathematical functions. This model encapsulates key parameters such as kernel functions, baseline values, and ranges, which collectively describe the degree and scale of spatial autocorrelation. Once the spatial model is established, it is used to calculate the weights of neighboring data points, thereby estimating the values ​​at unsampled locations. These weights are derived not only from proximity but also from the spatial configuration and correlation structure defined by the variogram, ensuring that the interpolation process conforms to the spatial continuity of the data.

[0043] A key feature of the Kriging method is its ability to generate not only interpolation surfaces but also corresponding surfaces representing the predicted uncertainties. This variance plot provides crucial insights into the reliability of cross-spatial-domain estimations, offering scientific decision-making guidance in applications requiring uncertainty quantification.

[0044] To adapt to different assumptions and data characteristics, various variations of kriging have been developed. Traditional kriging is implemented under the assumption of local constants but unknown means, suitable for stationary datasets. General kriging relaxes this assumption by introducing a deterministic trend component, allowing surfaces to exhibit non-stationary behavior. Block kriging extends the method to evaluate the mean of spatial blocks rather than single-point locations, resulting in smoother surfaces and facilitating regional analysis. Co-kriging further enhances predictive power by integrating secondary variables spatially correlated with the main variable, thereby utilizing additional information to improve interpolation.

[0045] Kriging is widely used in disciplines such as soil science, geology, hydrology, and environmental monitoring, where spatial relationships play a crucial role in understanding and managing natural phenomena. This method is often used to estimate variables such as altitude, temperature, water content, and pollutant concentrations, providing a rigorous framework for spatial prediction and uncertainty assessment in the study and operation of environments.

[0046] Compared to another commonly used inverse distance interpolation method, kriging produces more natural interpolation results. Co-kriging allows for the inclusion of background models (such as v...) p This is integrated into the interpolation. However, v during the imaging process... p It typically lacks good local fidelity and often leads to bullseye effect in kriging.

[0047] As described above, a seismic image volume is a three-dimensional representation of the Earth's subsurface created by processing seismic reflection data. It visualizes geological structures and strata in three dimensions, enabling interpreters to analyze spatial relationships and identify features such as faults, stratigraphic horizons, and reservoirs. In this disclosure, a seismic image volume is also referred to as a seismic image, seismic body, seismic image data, or seismic dataset.

[0048] In exploration geophysics, a seismic image volume is the final product of processing and imaging seismic data obtained from 3D seismic surveys. During acquisition, seismic waves are generated at the Earth's surface and their reflections from subsurface strata are recorded by sensor arrays (detectors or hydrophones). Subsequently, sophisticated algorithms (e.g., migration or full waveform inversion (FWI)) are used to process this raw data to reconstruct a spatially coherent image of the subsurface.

[0049] The generated seismic image volume is constructed as a three-dimensional voxel mesh, where each voxel contains a seismic attribute (typically amplitude) that reflects the contrast in acoustic impedance between geological strata. The three axes of this image volume correspond to:

[0050] 1. The main survey line is usually aligned with the data acquisition direction.

[0051] 2. The connecting line is perpendicular to the main survey line, and...

[0052] 3. Time or depth, vertical axis, representing two-way travel time or converted depth.

[0053] This monolithic dataset allows interpreters to extract 2D slices (e.g., time slices, depth slices, or arbitrary cross-sections) or generate 3D visualizations for analyzing subsurface features. It is a fundamental tool for oil and gas exploration, reservoir characterization, and geological hazard assessment.

[0054] Advanced seismic image volumes (e.g., those derived from FWI) incorporate the full physical properties of seismic wave propagation and can resolve large-scale structures and fine-scale inhomogeneities with high fidelity. These high-resolution volumes are increasingly used not only for structural interpretation but also as input to quantitative workflows such as seismic inversion, property analysis, and machine learning-based property prediction.

[0055] As will be discussed in detail below, the auxiliary seismic image volume is generated by applying specific wavelet operations to the main seismic image volume or the original seismic image volume.

[0056] Figure 5 A functional block diagram illustrating a kriging workflow utilizing well information and generating attributes via seismic guided characteristics, according to an embodiment of this disclosure, is shown. In this workflow, the input consists of two parts: well logging information and attributes mapped from the seismic domain, which serves as the background model for the co-kriging interpolation process.

[0057] The illustrated workflow aims to generate a spatially continuous subsurface property model by integrating direct measurement data and geophysical inferred properties. The input data used in this process comprises two distinct parts. The first part includes well logging information 5100, which provides high-resolution local measurements of rock physical properties such as acoustic impedance, porosity, or density. The second part 5200 is a property volume generated using seismic guided characteristic prediction techniques, which use inversion, machine learning, or other predictive algorithms to infer subsurface characteristics from seismic data. The third part is kriging interpolation 5300. This derived seismic property volume serves as a spatially extended background model to inform the co-kriging interpolation procedure. By integrating the local accuracy of well data and the broader spatial continuity of seismic predictions, the co-kriging framework enables robust estimation of subsurface properties at unsampled locations while maintaining geological consistency and conforming to spatial correlation structures. The output 5400 is generated using the kriging method.

[0058] Based on the establishment of the Kriging-based interpolation workflow described above, Figure 5 The process illustrated can be further characterized as a hybrid geostatistical modeling framework that synergistically integrates high-resolution well logging measurements with spatially extended seismically derived attribute volumes to produce a geologically consistent subsurface model. This integration is achieved through co-kriging, which leverages the spatial correlation between primary variables (typically rock physical properties measured at the well site) and secondary variables inferred from seismic data to improve the predictive fidelity of the interpolated surfaces.

[0059] The workflow begins with the acquisition and preprocessing of well logging data, which serves as anchor points for local attribute measurements. While this data is typically sparse, it still possesses high vertical resolution, capturing fine-scale variations in subsurface features. Simultaneously, the seismic guided property generation module estimates the data volumes of identical or related attributes over a broader survey area. Seismic derivatives are generated using inversion algorithms, statistical learning models, or other predictive techniques to translate seismic attributes into petrophysical estimates. Although less accurate than well data, seismic volumes provide continuous spatial coverage, making them ideal for minor variables in co-kriging.

[0060] Once both datasets are ready, the workflow proceeds to spatial analysis and differential function modeling. This step involves quantifying the spatial autocorrelation and cross-correlation of each variable, typically using empirical differential functions and cross-differential functions. These statistical models capture the degree to which attribute values ​​at different locations are correlated as a function of distance and orientation. The resulting differential function structure is then used to calculate the optimal interpolation weights for each unsampled location, thus balancing the influence of near-wellbore measurements with the seismic background model.

[0061] Co-kriging algorithms utilize these weights to generate continuous attribute surfaces, thus conforming to the local accuracy of well data and the spatial continuity of seismic predictions. Importantly, the method also generates corresponding uncertainty surfaces that quantify the confidence level of each interpolated value. This dual-output characteristic (estimated attributes and associated uncertainties) provides a solid foundation for downstream applications such as reservoir characterization, geomechanical modeling, and drilling risk assessment.

[0062] In summary, Figure 5 The described workflow illustrates a data fusion strategy that leverages the complementary strengths of well and seismic data within a rigorous geostatistical framework. By implementing co-kriging, this method enhances the spatial predictability of subsurface properties while maintaining geological rationality and quantifiable uncertainty, thereby providing more comprehensive scientific decision-making for subsurface exploration and development.

[0063] Figure 6 This is a functional block diagram illustrating a seismic guidance characteristic prediction workflow according to an embodiment of the present disclosure. The generated prediction operator is then input into the attribute prediction engine along with the seismic volume to obtain the predicted attribute volume.

[0064] This workflow 6000 aims to generate data volume estimates of subsurface properties by utilizing well logging data and seismic information, thereby enabling spatially continuous prediction of rock physical properties across the entire exploration area.

[0065] Further as Figure 6 As shown, workflow 6000 begins with generating a prediction operator 6400. The inputs to this operator generation module include three main data sources: (i) well logging information generated in step 6200, which provides high-resolution ground-measured values ​​of target attributes at discrete well locations; (ii) the main seismic image volume at the well location acquired in step 6100; and (iii) the auxiliary seismic image volume generated in step 6300 based on the main seismic image volume. These inputs—the main seismic image volume at the well location acquired in step 6100, the well logging information acquired in step 6200, and the auxiliary seismic image volume generated in step 6300—are jointly analyzed to establish a statistical or machine learning-based relationship between seismic features and the corresponding well logging responses. Finally, the prediction operator is generated in step 6400.

[0066] The resulting prediction operator 6400 encapsulates this learned relationship and is subsequently applied to the complete main seismic image volume. Specifically, this prediction operator, along with the main seismic image volume 6500, is input into the attribute prediction engine 6600, which performs transformations across the entire seismic domain. The seismic image volume obtained in step 6500 can be the main seismic image volume or a seismic image volume at a different location from the well site, i.e., an auxiliary seismic image volume obtained by seismic surveying different areas obtained from the main seismic image volume. The output of this process is the predicted attribute volume 6700—a spatially continuous three-dimensional representation of the target subsurface attributes (e.g., acoustic impedance, porosity, or lithofacies probability).

[0067] This seismic guided characteristic prediction workflow 6000 can extrapolate sparse well logging data to areas without direct sampling, while preserving geological trends and conforming to the spatial variability captured by seismic data. The resulting attribute volume 6700 can be used as an independent interpretation result or as input to subsequent geostatistical modeling workflows (e.g., co-kriging or stochastic simulation), thereby improving the resolution and reliability of subsurface features.

[0068] Figure 7 This is a flowchart illustrating a method for generating an auxiliary seismic image volume according to an embodiment of the present disclosure. According to one embodiment of the present disclosure, a workflow is proposed that uses a primary seismic image volume to assist in constructing a reliable pressure wave velocity (V)... p ), shear rate (v) s Low-frequency models of seismic properties (v) and density (rho) are used. Seismic image volumes provide regional structural information and can be viewed as bridges connecting local wells. A key step involves creating operators to map from the main seismic image volume domain to seismic properties (v). p , v s , rho) domain.

[0069] In the description of earthquake guidance characteristic prediction, P-wave impedance refers to longitudinal wave impedance, also known as acoustic impedance. It is a fundamental geophysical parameter characterizing how earthquake P-waves (main waves or compression waves) propagate in underground geological structures.

[0070] P-wave impedance controls the intensity of seismic wave reflections at geological boundaries. Variations in P-wave impedance between adjacent layers cause seismic reflections, which are recorded during seismic surveys. Using seismic inversion techniques, P-wave impedance volumes can be estimated from seismic data and used to infer subsurface properties (e.g., lithology, porosity, and fluid content). P-wave impedance is obtained from seismic data through a process known as seismic inversion, which converts seismic reflection data into quantitative estimates of rock properties.

[0071] In Kriging-assisted seismic guided prediction workflows, P-wave impedance is typically used as the primary input attribute. P-wave impedance possesses spatial continuity and is derived from the seismic image volume, making it suitable for co-kriging with sparse well logging measurements. This integration improves the accuracy and geological consistency of the interpolated attribute models, such as porosity or saturation distributions.

[0072] According to one embodiment of this disclosure, a physical link between P-wave impedance and seismic image volume integration is proposed. In most cases, it is reasonable to assume that P-wave impedance is related to (v... p , v s There exists a quasi-linear relationship between the main seismic image volume and (v, rho), where rho is the density. This disclosure establishes a quasi-linear relationship between the main seismic image volume and (v, rho) based on physical principles and reasonable assumptions. p , v s The mapping operator between (rho) and (rho). Assume the time-domain v at the well. p , v s rho and seismic data are denoted as rho and rho respectively. ,but:

[0073] P-wave impedance (1);

[0074] reflectivity (2);

[0075] , For wavelet (3);

[0076] thus: (4);

[0077] Assumption: ;

[0078] but: (5).

[0079] The limitation of seismic wavelet bandwidth restricts the resolution of predicted properties. To improve prediction resolution, an auxiliary seismic image volume (i.e., an auxiliary dataset) needs to be generated. Figure 6 As shown and described in the corresponding paragraphs above, the inputs to the prediction operator generation module include three main data sources: (i) well logging information acquired in step 6200, which provides high-resolution ground-measured values ​​of target attributes at discrete wellbore locations; (ii) the main seismic image volume acquired in step 6100; and the auxiliary seismic image volume acquired in step 6300. These inputs will be jointly analyzed to establish statistical or machine learning-based relationships between seismic features and corresponding well logging responses.

[0080] According to one embodiment of this disclosure, a prediction operator 6400 generated at the well location aims to minimize the difference between the prediction and the well information in a least-squares sense. This operator is then applied to the entire main seismic image volume to generate the desired attributes at each location. At least one well is required in the region of interest.

[0081] In mathematical form, the prediction operator estimation can be formulated as follows:

[0082] (6);

[0083] In the formula, It is formed by integrating seismic data from the corresponding well locations, and includes a main seismic image volume and auxiliary seismic image volumes. This indicates the logging data at that well.

[0084] Once the prediction operator 6400 was determined, it was then applied to seismic image volumes located far from the well site:

[0085] (7).

[0086] In the aforementioned workflow, it was initially assumed that a single, spatially uniform prediction operator could be effectively applied to attribute estimation across the entire seismic survey area. However, this assumption may no longer hold when the geological environment of a well differs significantly from that of other wells in the region of interest. Indiscriminately using a uniform operator can lead to inaccuracies in attribute predictions due to the inability to adequately capture local geological variations.

[0087] To overcome this limitation, this disclosure introduces a geostatistical interpolation technique called co-kriging, in which the predicted attribute volume (derived from applying prediction operators to a seismic dataset) serves as a spatially continuous background model. Co-kriging facilitates the combination of discrete well logging data with continuous property estimates provided by the seismically derived background model, thereby generating a final attribute volume that is locally consistent with the well data and globally coherent with seismic trends.

[0088] Specifically, co-kriging employs a dual-constraint approach: it utilizes high-resolution real-world surface logging measurements at the wellbore location while simultaneously leveraging the broader spatial coverage of the background attribute model to interpolate at unsampled locations. This approach ensures that the resulting attribute estimates achieve not only high local fidelity for the well data but also maintain smooth spatial variations and geological continuity across the entire model domain. This method is particularly advantageous in complex geological environments because it systematically considers spatial nonstationarity and heterogeneity, thereby improving the accuracy and reliability of subsurface attribute predictions for reservoir characterization, geological modeling, and related applications.

[0089] Figure 7 This is a flowchart illustrating a method for generating an auxiliary seismic image volume according to an embodiment of the present disclosure. The method generates an auxiliary seismic image volume 7000, which is as described above. Figure 6 The implementation of step 6300 includes a structured sequence of four computational steps, each designed to enhance the fidelity and interpretability of seismic-derived features using a downstream geostatistical modeling workflow (such as co-kriging). This method utilizes primary and secondary seismic image volume properties to extract high-resolution spatial information, supplementing well logging data in subsurface property prediction.

[0090] A seismic volume dataset at the well location is obtained by aligning and sampling the seismic volume at spatial coordinates corresponding to the wellbore trajectory. This begins with well-seismic correlation, where a synthetic seismic record is generated using well logging data (typically sonic and density logging) and known or estimated seismic wavelets. The synthetic seismic trace is then correlated with the actual seismic trace at the well location to establish a time-depth relationship. This alignment ensures an accurate correspondence between depth-based well logging measurements and time-based seismic volume data.

[0091] To facilitate integration with well logging data, the extracted seismic image volume is resampled or interpolated to match the well logging sampling interval. This resizing enables the construction of feature vectors for each time or depth sample, which are then used as input to train prediction operators. The resulting seismic feature matrix is ​​used to establish a statistical or machine learning-based relationship between seismic features and well logging responses.

[0092] Finally, a quality control process was applied to ensure that the seismic image volume at the well location was geologically consistent and free of artifacts or misalignments. This local seismic image volume dataset became the basis for training prediction operators, which were then applied to the entire seismic volume to estimate subsurface properties in areas lacking direct well measurements.

[0093] In the first step 7100, a comprehensive analysis of the main seismic image volume is performed to obtain the P-wave impedance.

[0094] Step 7200 involves using wavelet transform domain methods to extract high-frequency components from the main seismic image volume. Unlike traditional Fourier-based methods, wavelet transform enables multi-resolution analysis by decomposing the main seismic image volume into local frequency bands across time and space. This decomposition helps isolate high-frequency components that indicate fine-scale geological features such as thin layers, fractures, or abrupt lithological transitions. Wavelet-based extraction preserves spatial localization, which is crucial for maintaining geological plausibility in the resulting auxiliary data.

[0095] In step 7300, an instantaneous frequency map is generated from the master seismic image volume after wavelet transform. This instantaneous frequency map captures the master frequency information at each spatial location, reflecting subtle variations in subsurface composition and structure. Instantaneous frequency properties are particularly valuable for identifying stratigraphic boundaries and detecting lithological changes because they are sensitive to impedance contrast and signal attenuation effects.

[0096] Step 4 (7400) involves convolving the main seismic image volume with a wavelet that matches the dominant frequencies identified in the main seismic image volume. This convolution process improves the signal-to-noise ratio and enhances the most representative frequency features of the subsurface geology. By aligning the wavelet filter with the dominant frequencies, this method ensures that the resulting auxiliary dataset remains coherent with the main seismic image volume while highlighting geologically relevant features.

[0097] High-frequency component extraction using the wavelet transform domain offers significant advantages over traditional Fourier domain techniques. Specifically, the wavelet method introduces an additional decomposition dimension—time-frequency localization—which enables more accurate and context-aware feature isolation. This results in high-quality auxiliary seismic image volumes characterized by improved spatial resolution and interpretability, thus supporting more accurate and geologically consistent attribute predictions within an integrated geostatistical framework.

[0098] Figure 8 The results of the conventional low-frequency model building workflow are shown in comparison with the results of the workflow for restoring true geological features disclosed in this disclosure. The conventional workflow results in a bullseye effect (left figure), while the workflow of this disclosure does not show a bullseye effect (right figure).

[0099] In traditional low-frequency model (LFM) construction workflows, the generated background attribute models often fail to accurately represent real subsurface geological structures. Specifically, these models typically lack fidelity to actual subsurface structures (such as river channels) and exhibit poor local consistency with actual surface well logging measurements. This deficiency manifests as artificial artifacts, often referred to as the "bullseye effect," such as... Figure 8As shown in the left figure, the model prediction exhibits spurious circular or elliptical artifacts centered on the well location. These artifacts indicate that the model does not conform to geological continuity or local well data, thus reducing its reliability in reservoir characterization and other subsurface prediction tasks.

[0100] In contrast, the workflow of the present invention described herein maps a background attribute model from a seismic domain in a manner that systematically conforms to real geological structures and local well measurements. For example, in the case of a river channel, the proposed method ensures that the background model accurately depicts the channel geometry and maintains local consistency with well data. Therefore, bullseye artifacts are effectively eliminated, and the final attribute estimates exhibit geological plausibility and high local fidelity, such as... Figure 8 As shown in the right figure.

[0101] This improvement is achieved by integrating advanced seismic attribute analysis and wavelet-based feature extraction, thereby providing high-resolution auxiliary data that enhances the interpretability and accuracy of the geostatistical modeling framework.

Claims

1. A method for predicting the properties of subsurface strata, comprising: Drill one or more wells in the underground strata at the well location; Seismic exploration is conducted at the well site to construct a master seismic image volume, wherein the dataset of the master seismic image volume includes at least pressure wave velocity v covering both the time and frequency domains. p Shear rate v s and density rho; Logs are performed at one or more wellbores to obtain logging information at the well locations; Kriging was used to generate an auxiliary seismic image volume at the well location for predicting seismic guidance characteristics. A prediction operator is generated based on the main seismic image volume, the auxiliary seismic image volume, and the well logging information at the well location; The predicted properties of the subsurface strata are generated using the predicted operators and secondary seismic image volumes.

2. The method according to claim 1, wherein, The steps for generating auxiliary seismic image volumes also include: The P-wave impedance is derived from the main seismic image volume at the well location by seismic inversion covering both the time and frequency domains.

3. The method according to claim 1, wherein, The steps for generating auxiliary seismic image volumes also include: The high-frequency components of the main seismic image volume are extracted in the wavelet transform domain.

4. The method according to claim 1, wherein, The steps for generating auxiliary seismic images also include: Instantaneous frequency maps are generated from the high-frequency components of the extracted main seismic image volume.

5. The method according to claim 1, wherein, The steps for generating auxiliary seismic images also include: The main seismic image volume is convolved with a wavelet having the dominant frequency component.

6. The method according to claim 1, wherein, The steps for generating auxiliary seismic images also include: At the well location, an auxiliary seismic image volume coherent with the primary seismic image volume at the well location is generated.

7. The method according to claim 1, wherein, The step of conducting seismic exploration at the well location to construct the main seismic image volume also includes: establishing well-seismic correlation.

8. The method according to claim 1, wherein, The step of conducting seismic exploration at the well location to construct a master seismic image volume further includes: extracting seismic attributes at the well location from the master seismic image volume.

9. The method according to claim 1, wherein, The high-frequency components are indicators of fine-scale geological features.

10. The method according to claim 1, wherein, The step of conducting seismic exploration at the well location to construct the main seismic image volume further includes: resampling or interpolating the extracted seismic attributes to match the sampling interval of the well logging information.

11. The method according to claim 1, wherein, The instantaneous frequency map captures the dominant frequency component at each spatial location.

12. The method according to claim 1, wherein, The steps of conducting seismic exploration at the well location to construct the main seismic image volume also include: Ensure that the seismic dataset at the well location is geologically consistent and free of artifacts or misalignments.

13. The method according to claim 1, wherein, The method further includes: Establish P-wave impedance and (v p ,v s A pseudo-linear relationship exists between v and rho, where v p The velocity of the pressure wave, v s rho represents the shear rate, and rho represents the density.

14. The method according to claim 1, wherein, The method further includes: The dataset of the main seismic image volume and (v p ,v s Construct prediction operators between rho and rho.

15. The method according to claim 1, wherein, The P-wave impedance is Where: I(t) represents the P-wave impedance in the time domain, v p rho(t) represents the pressure wave velocity in the time domain, and rho(t) represents the density in the time domain.

16. The method according to claim 1, wherein, Reflectance , , For wavelets, 。 17. The method according to claim 1, wherein, Assumption: , Then there is .

18. The method according to claim 1, wherein, The secondary seismic image volume is the same as the primary seismic image volume.

19. The method according to claim 1, wherein, The secondary seismic image volume is obtained from a region different from the region where the well is located.

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