A method for analyzing relative sea level change based on imaging logging

Abstract

The application discloses a relative sea level change analysis method based on imaging logging, which comprises the following steps: acquiring imaging logging image data of a target well section, and accurately identifying a sedimentary stratum interface based on high-resolution images; dividing the geological well section into multiple sedimentary sublayers according to the picked interface and calculating the thickness of the sublayers; calculating the cumulative deviation of the thickness of each sublayer and the average thickness of all the sublayers to generate a cumulative deviation curve; determining the positive or negative correlation between the cumulative deviation curve and the relative sea level change by using a preset identification chart according to the specific sedimentary environment type, and converting the cumulative deviation curve according to the correlation, and finally generating a relative sea level change curve. The application uses high-resolution imaging logging data, and establishes an analysis model for different sedimentary environments, thereby significantly improving the accuracy and reliability of the analysis result and having stronger geological applicability.

Description

Technical Field

[0001] This invention relates to the fields of sedimentology and oil and gas exploration information technology, and in particular to a method for analyzing relative sea-level changes based on imaging logging. Background Technology

[0002] Relative sea-level change is a key parameter for reconstructing the evolution of sedimentary basins during geological history, playing a crucial role in sequence stratigraphy research and oil and gas exploration and development. Accurate reconstruction of the relative sea-level change history can effectively establish a regional sequence stratigraphic framework, thereby predicting the spatial distribution of high-quality source rock reservoirs. Currently, methods for reconstructing paleosea-level changes based on borehole data have made some progress, with mainstream techniques relying primarily on conventional logging curves, such as natural gamma (GR) curves. Specific methods include using spectral analysis techniques such as INPEFA, wavelet transform, or Fourier transform to identify periodic signals in the depth domain of logging curves to reveal different levels of sequence cycles, indirectly reflecting periodic fluctuations in sea level. In addition, the Fischer plot method is also widely used. This method generates a curve that accommodates spatial changes by calculating the cumulative deviation of sedimentary sublayer thickness relative to the average thickness, thus characterizing the trend of relative sea-level rise and fall.

[0003] However, the aforementioned existing technologies have inherent limitations in their theoretical foundation and data accuracy, restricting the reliability and universality of their analytical results. First, these methods generally rely on a core assumption: that finer sediment grain size or increased formation thickness indicates sea-level rise. This assumption is not universally applicable in geological practice. In complex sedimentary environments such as tidal flats and undercompensated shelves, sedimentary patterns may be completely opposite, leading to systematic biases or even errors in analytical conclusions based on this assumption. Second, existing technologies typically use conventional well logging data with low resolution and large sampling intervals, making it difficult to accurately identify and delineate thin sedimentary units, thus affecting the accuracy of thickness statistics and cyclic analysis. More critically, conventional well logging curves are one-dimensional scalar curves, lacking intuitive representation and making it difficult to effectively identify unconformities representing sedimentary discontinuities or erosion events. If unconformities exist in the formation but are not identified, the sedimentary record will be incomplete, resulting in severe distortion of the reconstructed relative sea-level change curve. Therefore, a relative sea-level change analysis method that can overcome theoretical limitations and improve data accuracy is urgently needed. Summary of the Invention

[0004] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0005] In view of the aforementioned existing problems, this invention is proposed. Therefore, this invention provides a method for analyzing relative sea-level changes based on imaging logging to solve the problems mentioned in the background art.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a method for analyzing relative sea level changes based on imaging logging, comprising: Acquire imaging logging image data of the target geological well section, and based on the imaging logging image data, identify and pick multiple sedimentary stratigraphic interfaces, and obtain the depth data of each sedimentary stratigraphic interface; Based on the depth data of the multiple sedimentary stratigraphic interfaces, the target geological well section is divided into multiple sedimentary sub-layers, and the thickness value of each sedimentary sub-layer is calculated. The average thickness of the plurality of depositional sublayers is calculated, and based on the deviation between the thickness value of each depositional sublayer and the average thickness, the cumulative deviation value corresponding to each depositional sublayer is calculated, and a cumulative deviation curve is generated; Based on the sedimentary environment type of the target geological well section, a preset correlation between the cumulative deviation curve and the relative sea level change is determined, and the cumulative deviation curve is transformed according to the preset correlation to generate the relative sea level change curve of the target geological well section.

[0007] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. Utilizing the high-resolution characteristics of imaging logging (sampling rate up to 0.00254 meters), it is possible to precisely identify thin sedimentary units and unconformities that are difficult to distinguish with conventional logging (sampling rate typically 0.125 meters). Accurate acquisition of formation interfaces through intuitive wellbore images significantly improves the accuracy of sedimentary sublayer thickness calculations.

[0008] 2. An identification chart covering various sedimentary systems, including gentle-slope carbonate platforms, shelf carbonate platforms, and barrier-free clastic shores, has been established. It can determine the positive / negative correlation between the cumulative deviation curve and the relative sea level change based on the actual sedimentary environment. This effectively overcomes the systematic bias caused by the traditional method's reliance on the non-universal assumption that "increased thickness equals sea level rise," and is applicable to more complex sedimentary backgrounds.

[0009] 3. By combining high-precision data sources with a more universally applicable analytical model, the relative sea-level change curve generated by this invention can more realistically reflect the sea-level fluctuation patterns during geological history, and has a higher degree of consistency with actual geological understanding. This not only improves the accuracy of sequence stratigraphy, but also provides a more accurate decision-making basis for the prediction of reservoirs, caprocks, and source rocks in oil and gas exploration. Attached Figure Description

[0010] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a flowchart illustrating the overall process of a relative sea level change analysis method based on imaging logging according to an embodiment of the present invention. Figure 2 This is a schematic diagram illustrating the principle of obtaining formation attitude using imaging logging in a relative sea level change analysis method according to an embodiment of the present invention. Figure 3 This is a graph showing the relationship between Fischer values ​​and sea-level changes in different sedimentary environments using the imaging logging-based relative sea-level change analysis method described in one embodiment of the present invention. Figure 4 This is an application example diagram of a well in a basin using the relative sea level change analysis method based on imaging logging as described in an embodiment of the present invention. Detailed Implementation

[0011] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0012] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0013] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0014] This invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of this invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not adhering to the usual scale. Furthermore, the schematic diagrams are merely examples and should not be construed as limiting the scope of protection of this invention. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0015] Furthermore, in the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0016] Unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" in this invention should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; similarly, they can refer to mechanical connections, electrical connections, or direct connections, or indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances. Example 1

[0017] Reference Figures 1 to 3 This is the first embodiment of the present invention, which provides a method for analyzing relative sea level changes based on imaging logging, including: S1. Acquire imaging logging image data of the target geological well section and process it into static and dynamic images.

[0018] Furthermore, raw microresistivity scanning imaging or acoustic imaging data at the target depth are acquired and loaded into well logging interpretation software (such as Techlog, Ciflog, etc.). During the upward pulling process, the electrical imaging instrument continuously records the resistivity measurement value of each button electrode at extremely high vertical resolution (typically 0.1 inches). The measurement value of each depth point and each electrode can be considered as a pixel, its color or grayscale determined by the resistivity value at that point. These pixels are arranged sequentially according to the electrode azimuth and measurement depth to form a unfolded map covering 360° of the wellbore. The imaging well logging interpretation module in the software is used to process and generate raw data images, static images, and dynamic images. The static images use a uniform color / grayscale scale across the entire well section to highlight macroscopic overall resistivity changes; the dynamic images undergo independent contrast enhancement within a short depth window (e.g., 0.5 meters to several meters), displaying a full range of black to white to enhance the visual effect of the formation's fine structure.

[0019] S2. Based on static and dynamic images, identify and pick multiple sedimentary stratigraphic interfaces and obtain depth data for each sedimentary stratigraphic interface.

[0020] Furthermore, using the formation and fracture interpretation modules of the logging software, based on static and dynamic images, formation interfaces are identified by detecting abrupt changes in grayscale values. It should be noted that in the wellbore unfolded diagram, formation interfaces are typically displayed as a series of sinusoidal curves with different initial phases. According to the sinusoidal curves, the azimuth corresponding to the maximum trough is the formation azimuth angle; the depth difference between the maximum peak and the maximum trough... The ratio of the wellbore diameter d to the formation dip angle is the tangent of the dip angle. The dip angle DIP is obtained using inverse trigonometric functions; the formation interface depth is the average of the maximum crest depth and the maximum trough depth, referring to... Figure 2 .

[0021] Furthermore, due to the complexity of actual geological conditions, such as cross-bedding, faults, and unconformities, non-ideal sine curves are often generated. Therefore, segment-by-segment identification and investigation are necessary. The judgment criteria are as follows: Depositional layers generally exhibit relatively continuous and gradually changing layered characteristics; fractures often have high dip angles and extremely high resistivity (closed cemented fractures) or extremely low resistivity (open fractures); induced fractures usually appear as two vertical fractures with an azimuth angle difference of 180°.

[0022] Specifically, once the stratigraphic interface is confirmed, the relevant parameters are output as a table in the form of three columns: depth, azimuth, and dip.

[0023] S3. Divide the target geological well section into multiple sedimentary sub-layers and calculate the thickness of each sedimentary sub-layer.

[0024] Specifically, a sedimentary sublayer is defined by using two adjacent layers as constraints. If there are n+1 layers in total, then n sedimentary sublayers can be divided, and they are numbered in depth order. The top and bottom depths of each sedimentary sublayer are read sequentially, and the median depth of each sedimentary sublayer is calculated. (i.e., the arithmetic mean of the top depth and bottom depth) and thickness (That is, the difference between the top depth and the bottom depth).

[0025] S4. Calculate the average thickness and cumulative deviation of the depositional layer, and generate the cumulative deviation curve.

[0026] Furthermore, the arithmetic mean of the thicknesses of all sublayers is calculated. And calculate the thickness deviation of each sublayer from the average value. The formula is as follows: Furthermore, the cumulative deviation value is calculated for each sub-layer. This involves adding the thickness deviation of the current sedimentary layer to the cumulative deviation of the previous sedimentary layer arranged in depth order. The formula is as follows: Furthermore, and then will be obtained One-dimensional data; loaded onto a wellbore histogram to obtain the Fischer curve.

[0027] S5. Based on the sedimentary environment type of the target geological well section, determine the preset correlation between the cumulative deviation curve and the relative sea level change, and convert it to generate the relative sea level change curve.

[0028] It should be noted that the Fischer curve, also known as the sediment accumulation deviation curve, is a curve plotted over a complete sedimentary sequence, with the sedimentary layer number on the horizontal axis and the trend of formation thickness variation on the vertical axis. Formation thickness is jointly controlled by water energy, sediment supply rate, and relative sea-level change rate. In regions with high water energy and high sediment supply rate, the Fischer curve is positively correlated with relative sea-level change; while in regions with low water energy and low sediment supply rate, the two are negatively correlated. Figure 3 The Fischer curve response patterns are presented under nine typical conditions in three sedimentary systems applicable to this invention. The specific geological mechanisms are as follows: In the sedimentary system of gentle-slope carbonate platforms, the tidal flat-inner shoal inter-sedimentary zone is characterized by high water energy and high sediment supply rate, and the Fischer curve is positively correlated with the relative sea level change (①); while other sedimentary facies areas (such as areas with lower water energy and lower carbonate rock formation rate) show a negative correlation (②, ③).

[0029] In barrier-free wave-controlled coastal systems, high water energy and high sediment supply rates are typically observed, and the Fischer curve is positively correlated with relative sea level changes (④~⑥).

[0030] In the shelf carbonate platform sedimentary system, the nearshore tidal flat-intraplatform alternating sedimentary zone and the open platform facies zone are characterized by high water energy and high sediment supply rate. The Fischer curve is positively correlated with the relative sea level change (⑦, ⑧). However, the basin facies zone is characterized by deep sedimentary water and low water energy, and is a still water sedimentary environment. The relative sea level change has little impact on water energy and sediment supply rate. The sediments are mainly thin-layered argillaceous carbonate rocks. Therefore, the relationship between the Fischer curve and the relative sea level change is not significant (⑨).

[0031] Furthermore, refer to Figure 3The positive and negative correlations between the Fischer curve and relative sea level changes were determined based on the sedimentary environment of the studied well section.

[0032] Specifically, define a This parameter itself has no actual physical meaning; it is only used to achieve a unified expression for numerical conversion under positive and negative correlation conditions. (Relative to sea level) Defined as the relative sea level height during the nth depositional layer, its value is: A moving average is a multi-point moving average. Moving averages typically use an odd number of data points, such as 3, 5, or 7 points. The number of points should not be too large to avoid filtering out information about small-scale sea level fluctuations. The specific number of points can be determined based on the researcher's visual requirements for the smoothness of the curve.

[0033] Furthermore, in this embodiment, the positive correlation applies to: tidal flat-intraplatform alternating sedimentary zones within the gentle-slope carbonate platform sedimentary system (corresponding to...). Figure 3 ①); barrier-free clastic coastal sedimentary system (corresponding to Figure 3 (4~6); Nearshore tidal flat-intraplatform shoal interleaved sedimentary zone and open platform facies zone in the shelf carbonate platform sedimentary system (corresponding to) Figure 3 (⑦, ⑧). At this point, intermediate conversion values ​​are defined. .

[0034] Specifically, a multi-point moving average (e.g., 3-point or 5-point) is applied to the intermediate transformation value sequence to obtain the relative sea level height. : or It should be noted that the positive correlation formed as described above... The data column, when plotted as a curve, becomes the curve representing the relative sea level change.

[0035] Furthermore, in this embodiment, the negative correlation applies to: facies regions with lower water energy and lower formation rates in gently sloping carbonate platform sedimentary systems (corresponding to...). Figure 3 (②, ③), such as the outer gentle slope-slope transition facies zone. In this case, intermediate transformation values ​​are defined. The formula is the same as above: or It should be noted that, similarly, based on the aforementioned negative correlation... The data column, when plotted as a curve, becomes the curve representing the relative sea level change. Example 2

[0036] Reference Figure 4 This is the second embodiment of the present invention, which provides a method for analyzing relative sea-level changes based on imaging logging. This embodiment uses a practical application case of a well section from 4750m to 4782m in a basin to illustrate the technical solution of the present invention in detail. The lithology of this section is mainly composed of interbedded argillaceous limestone and calcareous mudstone.

[0037] Specifically, firstly, imaging logging data for the target well section was acquired, imported into the Ciflog logging interpretation platform, and processed into static and dynamic images respectively. Then, the sedimentary formation interpretation module automatically divided the sedimentary sublayers, supplemented by manual adjustments, to obtain formation attitude data. A total of 121 sedimentary interfaces were accurately identified within this well section, and the depth, dip, and dip angle of each sublayer were recorded. Using these 121 identified interfaces as constraints, 120 consecutive sedimentary sublayers were formed. The mid-depth of each sublayer was calculated sequentially. With deposition thickness The average thickness of this stratum is calculated. The thickness is 0.264 meters. Calculate the deviation of each sublayer thickness from the average thickness of 0.264 meters. and cumulative deviation ,generate Data sequence, plotted Figure 4 The Fischer curve in the figure. Combined with sedimentary facies analysis, the studied section was determined to belong to the transitional facies zone between the outer gentle slope and shelf of a marine gentle slope carbonate platform. Refer to Example 1 for the original... Figure 3 The sedimentary environment identification chart was used to determine that the response pattern matched location ③ on the chart, i.e., the Fischer curve was negatively correlated with relative sea-level change. Therefore, the formula was used for numerical conversion. And a 5-point moving average was calculated to obtain Value. Finally, the drawing is produced. Figure 4 The rightmost curve shows the relative sea level change (RSL). From... Figure 4 The experimental results show that the relative sea level change curves generated by this algorithm have extremely high geological consistency: the thin layer segment corresponds precisely to the high sea level period, while the thick layer segment corresponds to the low sea level period, which is completely consistent with the sedimentary model of the outer gentle slope-slope facies deep-water carbonate rocks, verifying the high reliability of the method of this invention.

[0038] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0039] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0040] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0041] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0042] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0043] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for analyzing relative sea-level change based on imaging logging, characterized in that, include: Acquire imaging logging image data of the target geological well section, and based on the imaging logging image data, identify and pick multiple sedimentary stratigraphic interfaces, and obtain the depth data of each sedimentary stratigraphic interface; Based on the depth data of the multiple sedimentary stratigraphic interfaces, the target geological well section is divided into multiple sedimentary sub-layers, and the thickness value of each sedimentary sub-layer is calculated. The average thickness of the plurality of depositional sublayers is calculated, and based on the deviation between the thickness value of each depositional sublayer and the average thickness, the cumulative deviation value corresponding to each depositional sublayer is calculated, and a cumulative deviation curve is generated; Based on the sedimentary environment type of the target geological well section, a preset correlation between the cumulative deviation curve and the relative sea level change is determined, and the cumulative deviation curve is transformed according to the preset correlation to generate the relative sea level change curve of the target geological well section.

2. The method for analyzing relative sea level changes based on imaging logging as described in claim 1, characterized in that, Acquiring the imaging logging image data includes: Acquire raw data of microresistivity scanning imaging or acoustic imaging of the target geological well section, and process them to generate static and dynamic images; The identification and picking of the sedimentary stratigraphic interfaces are based on the static images and the dynamic images.

3. The method for analyzing relative sea level changes based on imaging logging as described in claim 1, characterized in that, The identification and picking of multiple sedimentary stratigraphic interfaces includes: By combining automatic acquisition with manual correction, the sinusoidal curve corresponding to the sedimentary strata interface on the wellbore unfolding diagram is determined, and the depth of each sedimentary strata interface is determined based on the position of the peak and trough of the sinusoidal curve.

4. The method for analyzing relative sea level changes based on imaging logging as described in claim 1, characterized in that, The target geological well section is divided into multiple sedimentary sub-layers, including: The interface between two adjacent sedimentary strata is defined as a sedimentary sublayer, and the depth difference between the top and bottom interfaces of the sedimentary strata is calculated as the thickness value of the sedimentary sublayer.

5. The method for analyzing relative sea level changes based on imaging logging as described in claim 1, characterized in that, The calculation yields the cumulative deviation value corresponding to each depositional layer, including: The thickness deviation value is obtained by calculating the difference between the thickness value of each deposition layer and the average thickness. The cumulative deviation value of the current sedimentary layer is obtained by adding the thickness deviation value of the current sedimentary layer to the cumulative deviation value of the previous sedimentary layer arranged in depth order.

6. The method for analyzing relative sea level changes based on imaging logging as described in claim 1, characterized in that, Determining the preset correlation includes: The sedimentary environment type of the target geological well section is divided into one of the preset sedimentary facies zones, and based on the sedimentary facies zone, it is determined whether the cumulative deviation curve and the relative sea level change are positively or negatively correlated.

7. The method for analyzing relative sea level changes based on imaging logging as described in claim 6, characterized in that, The cumulative deviation curve is transformed according to the preset correlation, including: If a positive correlation is determined, the cumulative deviation value of each sedimentary sublayer is used as an intermediate conversion value; If a negative correlation is determined, the inverse of the cumulative deviation value of each sedimentary sublayer is used as the intermediate conversion value; The relative sea level change curve is obtained by performing a multi-point moving average process on the intermediate conversion value sequence arranged in depth order.

8. The method for analyzing relative sea level changes based on imaging logging as described in claim 6, characterized in that, When the sedimentary facies region is a tidal flat-inner shoal alternating sedimentary region in a gentle-slope carbonate platform sedimentary system, the positive correlation is determined.

9. The method for analyzing relative sea level changes based on imaging logging as described in claim 6, characterized in that, When the sedimentary facies region is a barrierless clastic coastal sedimentary system, or a nearshore tidal flat-inland shoal alternating sedimentary region and an open platform facies region in a shelf carbonate platform sedimentary system, the positive correlation is determined.

10. The method for analyzing relative sea level changes based on imaging logging as described in claim 6, characterized in that, When the sedimentary facies region is the outer gentle slope-shelf transitional facies region in the gentle slope carbonate platform sedimentary system, it is determined to be the negative correlation.

Images