Transient electromagnetic data unbiased multipoint smoothing method
A smoothing method for transient electromagnetic data, employing exponential function fitting and normalization, solves the bias problem introduced by conventional multi-point smoothing, achieving unbiased smoothing and improving data quality and the reliability of geological interpretation.
Patent Information
- Application Number
- CN202511208677.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-27
- Publication Date
- 2025-10-31
AI Technical Summary
Conventional multi-point smoothing methods for transient electromagnetic data tend to cause the smoothed response curve to rise overall due to the dominance of early high-amplitude data points, deviating from the true attenuation pattern. This is especially significant for later data, reducing data quality and affecting the accuracy of subsequent geological interpretation.
The transient electromagnetic response data is fitted using an exponential function, normalized, and then smoothed at multiple points. Unbiased smoothing is achieved by reconstructing the data from the fitted data and the smoothed normalized data.
It effectively eliminates the systematic bias introduced by conventional smoothing, ensuring that the smoothed transient electromagnetic attenuation curve retains its true shape and magnitude, thereby improving the fidelity of data processing and the scientific nature of geological interpretation.
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Figure CN120871276A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of electromagnetic detection technology, and more specifically to an unbiased multi-point smoothing method for transient electromagnetic data. Background Technology
[0002] Transient electromagnetic method (TEM), an important geophysical exploration technique, works by transmitting a bipolar pulsed current underground via an ungrounded loop. During the interval of a primary field power outage, the time-varying secondary (transient) magnetic field generated by eddy currents induced by conductive geological bodies is measured. This magnetic field response contains rich information about the underground electrical structure; its amplitude and attenuation characteristics are directly related to the conductivity and geometric distribution of the strata. The time series of the transient electromagnetic response signal is characterized by a very large dynamic range. In the early stage (shortly after the power outage), the induced electromotive force amplitude is enormous, decaying rapidly exponentially over time, while the signal amplitude may become extremely weak in the later stage. The entire attenuation process spans several or even more than ten orders of magnitude. This large dynamic range and order-of-magnitude span, on the one hand, endows it with the ability to detect geological bodies at different depths, but on the other hand, it also presents a significant challenge to the accurate processing of the data.
[0003] In transient electromagnetic data processing, smoothing is a widely adopted and effective fundamental method to suppress random noise and improve the signal-to-noise ratio. Multi-point moving average (or window averaging) is one commonly used technique. However, due to the inherent attenuation characteristics of transient electromagnetic data—strong early-stage and extremely weak late-stage attenuation—directly applying conventional multi-point smoothing (such as simple arithmetic averaging) to the original time series introduces significant systematic bias. Specifically, within the smoothing window, early high-amplitude data points have an absolute dominant weight, while late low-amplitude data points are almost ignored. This averaging operation is equivalent to adding a positive bias to the entire time series, causing the smoothed transient electromagnetic response curve to show a significant overall upward tilt from early to late stages, severely deviating from the true attenuation pattern. This problem is particularly pronounced for late-stage data or when there are many smoothing iterations. This distortion introduced by the smoothing method masks the true attenuation pattern, greatly reducing data quality. Subsequent apparent resistivity calculations, time-depth conversions, and geological interpretations are all based on distortion, potentially leading to misjudgments of underground electrical structures and reducing the reliability of exploration results.
[0004] Currently, there is no effective existing technical solution to address the problem of systematic deviations in conventional multi-point smoothing methods caused by the inherent characteristics of transient electromagnetic data. Summary of the Invention
[0005] In view of this, the present invention provides an unbiased multi-point smoothing method for transient electromagnetic data, aiming to solve the problem of overall deviation caused by multi-point smoothing of transient electromagnetic data. Because transient electromagnetic response signals have characteristics of large early amplitudes, weak late amplitudes, and a decay process spanning multiple orders of magnitude, conventional multi-point smoothing methods tend to cause the smoothed transient electromagnetic response curve to rise significantly due to the dominance of early high-amplitude data points. This deviates severely from the true decay pattern, especially for late-stage data or when smoothing multiple times, thus reducing data quality and affecting the accuracy of subsequent apparent resistivity calculations, time-depth conversions, and geological interpretations. The present invention avoids the smoothing deviation of transient electromagnetic data caused by the large magnitude of transient electromagnetic data at earlier times, ensuring that the smoothed transient electromagnetic decay curve strictly maintains its inherent decay shape and true magnitude, thereby improving the fidelity of subsequent transient electromagnetic data processing and the scientific validity and reliability of geological interpretation results.
[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for unbiased multi-point smoothing of transient electromagnetic data, characterized by comprising the following steps: S1. Prepare transient electromagnetic response data and corresponding sampling times. The transient electromagnetic response data is a sequence containing response values of multiple time channels, and the sampling times are time sequences corresponding to each time channel. The time channel number increases with time. S2. Use an exponential function to perform curve fitting on the transient electromagnetic response data and sampling time to determine the fitting function; S3. Based on the fitting function and the sampling time, the fitting data is calculated, and the fitting data is a sequence of fitting values corresponding to each time channel; S4. The transient electromagnetic response data is normalized using the fitted data to obtain normalized transient electromagnetic data, which is a sequence of ratios between the transient electromagnetic response values and the corresponding fitted values for each time channel. S5. Perform multi-point smoothing on the normalized transient electromagnetic data to obtain smoothed normalized transient electromagnetic data. S6. Based on the smoothed normalized transient electromagnetic data and the fitted data, unbiased smoothed transient electromagnetic data is calculated. The unbiased smoothed transient electromagnetic data is a sequence of products of the smoothed normalized value and the corresponding fitted value for each time channel.
[0007] In a specific implementation scheme, in step S1, the time series of the transient electromagnetic response data covers a preset dynamic range, with the early response value having a larger amplitude, decaying exponentially over time, and the late response value having a smaller amplitude.
[0008] In one specific implementation scheme, in step S2, the exponential function is a multi-order exponential function containing multiple undetermined coefficients, and the value of each undetermined coefficient is determined by fitting the transient electromagnetic response data and the sampling time.
[0009] In one specific implementation scheme, the order of the multi-order exponential function is a positive integer, and the value of the order is determined based on the decay characteristics of the transient electromagnetic response data.
[0010] In a specific implementation scheme, in the expression of the multi-order exponential function, the independent variable is the sampling time, the dependent variable is the fitted response value, and each undetermined coefficient is determined by the least squares method or other curve fitting algorithm.
[0011] In one specific implementation scheme, in step S3, the trend of the fitted data is consistent with the decay trend of the transient electromagnetic response data, and the sequence shape of the fitted data is a smooth curve.
[0012] In one specific implementation scheme, in step S4, the normalized transient electromagnetic data shows that the normalized values of the early time channels are concentrated near a preset value, while the normalized values of the late time channels deviate from the preset value.
[0013] In one specific implementation, in step S5, the multi-point smoothing process is a moving average process, which calculates the moving average of the normalized transient electromagnetic data through a preset window.
[0014] In a specific implementation scheme, in step S5, after multi-point smoothing, the overall deviation of the smoothed normalized transient electromagnetic data is less than the overall deviation of the normalized transient electromagnetic data, and the sequence shape is smoother.
[0015] In one specific implementation, in step S6, after obtaining the unbiased smooth transient electromagnetic data, it is saved for subsequent apparent resistivity calculation, time-depth conversion, or geological interpretation.
[0016] Compared with existing technologies, the present invention provides an unbiased multi-point smoothing method for transient electromagnetic data. This method smooths transient electromagnetic response data to suppress random noise and improve the signal-to-noise ratio. It uses an exponential function to fit the decay law of the transient electromagnetic data, normalizes the data using the fitted data, performs conventional multi-point smoothing on the normalized data, and finally reconstructs the transient electromagnetic data using the fitted data and the smoothed normalized data. This achieves unbiased multi-point smoothing of transient electromagnetic data, effectively improving the quality of transient electromagnetic data processing and providing a reliable data foundation for subsequent apparent resistivity calculation, time-depth conversion, and geological interpretation. It has the following beneficial effects: 1. While retaining the advantages of multi-point smoothing technology in suppressing random noise, it achieves unbiased multi-point smoothing of transient electromagnetic data; 2. It can effectively eliminate the system uplift deviation caused by conventional smoothing, so that the smoothed transient electromagnetic attenuation curve strictly maintains its inherent attenuation shape and true magnitude. It solves the problem that multi-point smoothing of transient electromagnetic data can easily cause overall deviation, and ensures the fidelity of subsequent transient electromagnetic data processing and the scientificity and reliability of geological interpretation results. Attached Figure Description
[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0018] Figure 1 This is an overall flowchart of the transient electromagnetic data unbiased multi-point smoothing method described in this invention.
[0019] Figure 2 This is a schematic diagram of transient electromagnetic data.
[0020] Figure 3 This is a schematic diagram of transient electromagnetic data and fitted data.
[0021] Figure 4 This is a schematic diagram of normalized transient electromagnetic data.
[0022] Figure 5 A schematic diagram of smoothed normalized transient electromagnetic data.
[0023] Figure 6 This is a comparison of the smoothing results of the present invention and the smoothing results of traditional algorithms. Detailed Implementation
[0024] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0025] like Figure 1 As shown, the present invention provides an unbiased multi-point smoothing method for transient electromagnetic data, applied to electromagnetic detection, comprising the following steps: S1. Prepare transient electromagnetic response data D=[ d 1, d 2, ..., d i, ..., d n ], the corresponding sampling time t=[ t 1, t 2, ..., t i , ..., t n ],in n The number of channels for sampling time. d i For the corresponding number i Time Channel t i Transient electromagnetic response value, time track number i It increases over time; S2. Curve fitting is performed using an exponential function, employing the following form of exponential function:
[0026] in y As the independent variable, x As the dependent variable, a j , b j , c j For undetermined coefficients, m To determine the order of the fitted function, we obtain the undetermined coefficients by fitting t and D, and thus determine the fitted function. y = f( x ), where f is the fitted function relationship; S3. Calculate and obtain the fitted data G=[ g 1, g 2, ..., g i , ..., g n ],in g i = f( t i ); S4. Normalize the transient electromagnetic data using the fitted data to obtain the normalized transient electromagnetic data P=[ p 1, p 2, ..., p i , ..., p n ],in p i = d i / g i ; S5. Perform conventional multi-point smoothing on the normalized transient electromagnetic data to obtain smoothed normalized transient electromagnetic data Q=[ q 1, q 2, ..., q i , ..., q n For example, conventional multi-point smoothing can be achieved using a moving average method with a window radius of 5, smoothing 3 times. S6. Obtain unbiased smooth transient electromagnetic data S=[ by fitting data and smoothing normalized transient electromagnetic data.] s 1, s 2, ..., s i , ..., s n ],in s i = q i * g i Save it for later processing.
[0027] The present invention will be further described in detail below with reference to a specific embodiment.
[0028] S1. Prepare transient electromagnetic response data D=[ d 1, d 2, ..., d i , ..., d 31 ], the corresponding sampling time t=[ t 1, t 2, ..., t i , ..., t 31 The number of sampling time channels is 31. d i For the corresponding number i Time Channel t i Transient electromagnetic response value, time track number i Increasing over time, such as Figure 2 As shown, the transient electromagnetic response data changes over time. The horizontal axis represents time, with the unit being milliseconds (ms), and the values range approximately from... arrive Between; the vertical axis represents the transient electromagnetic response value, covering a range of... arrive The curves in the figure show the decay characteristics of transient electromagnetic response data. In the early stages (when the time frame is short), the response values have larger amplitudes, but they decay exponentially over time. It can also be observed that the later data quality of this transient electromagnetic response curve is poor, with the curve exhibiting a "jumping" characteristic, reflecting potential noise interference and other issues in unprocessed transient electromagnetic data. This is precisely why smoothing is necessary. It should be noted that 31 channels represent a typical and commonly used number of channels, falling within the range of common channel configurations in practical applications. Using 31 channels as a specific case, it fully covers the entire process of method implementation (from data preparation, curve fitting to normalization, smoothing, and result reconstruction), clearly demonstrating the technical details and processing effects, sufficiently illustrating the feasibility and effectiveness of the technical solution. Other cases will not be detailed further. The timeframes corresponding to the 31 channels are as follows: [0.052,0.064,0.078,0.094,0.114,0.138,0.168,0.204,0.246,0.298,0.362,0.438,0.53,0.64,0.774,0.936,1.132,1.368,1.654,2,2.416,2.92,3.528,4.262,5.148,6.22,7.514,9.078,10.968,13.2,15.96]ms, response values are shown in the attached figure; S2. Curve fitting is performed using an exponential function, employing the following form of exponential function:
[0029] in y As the independent variable, x As the dependent variable, a j , b j , c j For undetermined coefficients, m =5 represents the order of the fitted function. The undetermined coefficients are obtained by fitting t and D, thus determining the fitted function. y = f( x ), where f is the fitted function relationship; For example, the least squares method is used for curve fitting, and the iteration termination condition is that the iteration exceeds 400 times or the relative fitting difference is less than 0.001. For example, m Based on the characteristics of transient electromagnetic response, the value is generally selected between 3 and 10. In the above example, the value is 5. The results of each undetermined coefficient are as follows: a1 = 17.37; b1 = -3.087; c1 = 2.179; a2 = -8.189; b2 = -3.211; c2 = 1.816; a3 = -0.4606; b3 = -2.393; c3 = 0.6208; a4 = 3.077; b4 = 0.2284; c4 = 1.323; a5 = 1.453; b5 = 1.632; c5 = 0.7811; S3. Calculate and obtain the fitted data G=[ g 1, g 2, ..., g i , ..., g n ],in g i = f( t i ),like Figure 3 The graph shown compares transient electromagnetic data and its fitted data. The horizontal axis represents time (unit: ms), and the range is from... arrive The vertical axis represents the transient electromagnetic response (unit: nT / s), ranging from... arrive The solid line represents "transient electromagnetic data," and the dashed line represents "fitted data." Both show a decreasing trend over time; the fit is better in the early stages, but decreases in later stages (e.g., when time is close to the desired value). (At ms) Because the original data may be affected by noise, etc., there will be some deviation, reflecting the fitting's extraction of data patterns and its correlation with the original data; S4. Normalize the transient electromagnetic data using the fitted data to obtain the normalized transient electromagnetic data P=[ p 1, p 2, ..., p i , ..., p n ], n The value is 31 as mentioned above, where p i = d i / g i ,like Figure 4The line graph shown represents the normalized transient electromagnetic data over time, with the horizontal axis representing time in milliseconds (ms), and the range from... arrive The vertical axis represents normalized transient electromagnetic data, with values ranging from 0.7 to 1.2. The graph shows that the broken line represents the trend of the normalized data, exhibiting overall fluctuations, particularly in the earlier periods (e.g., time). - The price fluctuated slightly between 0.9 and 1.1 (around ms), and later (closer to) The transient electromagnetic data exhibits dramatic fluctuations (within milliseconds), showing distinct peaks and troughs. This reflects the complex changes in the normalized transient electromagnetic data over time and can be used to analyze data noise, abnormal responses, and other issues. Figure 4 The early normalized data were all around the value of 1, while the later data deviated significantly from the value of 1, with the maximum deviation being about 28%. S5. Perform conventional multi-point smoothing on the normalized transient electromagnetic data to obtain smoothed normalized transient electromagnetic data Q=[ q 1, q 2, ..., q i , ..., q n The result is as follows Figure 5 As shown, the line graph depicts the normalized transient electromagnetic data over time, illustrating the characteristics of the processed transient electromagnetic data. The horizontal axis represents time, with units in milliseconds (ms), and the scale covers... The values are distributed logarithmically; the vertical axis represents normalized transient electromagnetic data, with a range of approximately [value missing]. This reflects the relative size of the data; The line represents the change of normalized data over time, and there are overall fluctuations. As can be seen in the graph, in the early stage (e.g., until...), the change is more pronounced. Data in the ms interval Slight fluctuations nearby; later (closer) A significant peak appears at ms, followed by a rapid decline, reflecting the complex changes in normalized transient electromagnetic data over time. This can be used to analyze the effects of data smoothing, noise suppression, and other processing methods. Figure 5 The smoothed and normalized data in the dataset all converge to a value of 1, resulting in a smoother overall performance, with a maximum deviation of approximately 16%. S6. Obtain unbiased smooth transient electromagnetic data S=[ by fitting data and smoothing normalized transient electromagnetic data.] s 1, s 2, ..., s i , ..., s n ],in s i = q i* g i The calculation results are as follows Figure 6 The comparison chart shows the smoothing process of transient electromagnetic data. Figure 6 This tool is used to display how data changes under different processing methods. The horizontal axis represents time, in milliseconds (ms), and the range is from... arrive The vertical axis represents the transient electromagnetic response, with units of nT / s, ranging from... arrive The graph is presented on a logarithmic scale. The solid line represents the "raw transient electromagnetic data," showing a trend of exponential decay in response values over time, with high values in the early stages and gradually decreasing in the later stages. The dashed line represents the "smoothed transient electromagnetic data," with an overall trend consistent with the raw data, but the curve is smoother, reflecting the effect of smoothing on suppressing data noise. Scatter points... Representing the "smoothing results of traditional algorithms," the data is distributed between the original data and the smoothed data, and can be used to compare the differences between traditional algorithms and smoothing in data optimization. Through the presentation of three types of data, the effects of smoothing on noise reduction and pattern extraction of transient electromagnetic data are intuitively demonstrated, as well as the comparison with the smoothing results of traditional algorithms, which helps to illustrate the effectiveness of the new smoothing method. Figure 6 As can be seen, although the smoothing result using the traditional algorithm is relatively smooth, the value deviates significantly from the original transient electromagnetic data. It is lower than the original data in the early stage and significantly higher than the original data in the later stage. The smoothing result using the present solution is also relatively smooth, and the value is consistent with the trend of the original transient electromagnetic data. This shows that the smoothing method of the present invention effectively preserves the trend of transient electromagnetic data and achieves unbiased smoothing.
[0030] The key technical points of this invention are: the introduction of an exponential function fitting and normalization mechanism to eliminate the influence of the large dynamic range of TEM data and its intrinsic characteristics of strong early signals and weak late signals on the multi-point smoothing effect; the accurate normalization of transient electromagnetic data is achieved through curve fitting; the overall data offset is effectively avoided through multi-point smoothing of normalized data; the transient electromagnetic data is effectively reconstructed through fitted data and normalized smoothed data; and finally, unbiased multi-point smoothing of transient electromagnetic data is achieved.
[0031] The various embodiments described in this specification are presented in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for unbiased multi-point smoothing of transient electromagnetic data, characterized in that, Includes the following steps: S1. Prepare transient electromagnetic response data and corresponding sampling times. The transient electromagnetic response data is a sequence containing response values of multiple time channels, and the sampling times are time sequences corresponding to each time channel. The time channel number increases with time. S2. Use an exponential function to perform curve fitting on the transient electromagnetic response data and sampling time to determine the fitting function; S3. Based on the fitting function and the sampling time, the fitting data is calculated, and the fitting data is a sequence of fitting values corresponding to each time channel; S4. The transient electromagnetic response data is normalized using the fitted data to obtain normalized transient electromagnetic data, which is a sequence of ratios between the transient electromagnetic response values and the corresponding fitted values for each time channel. S5. Perform multi-point smoothing on the normalized transient electromagnetic data to obtain smoothed normalized transient electromagnetic data. S6. Based on the smoothed normalized transient electromagnetic data and the fitted data, unbiased smoothed transient electromagnetic data is calculated. The unbiased smoothed transient electromagnetic data is a sequence of products of the smoothed normalized value and the corresponding fitted value for each time channel.
2. The method for unbiased multi-point smoothing of transient electromagnetic data according to claim 1, characterized in that, In step S1, the time series of the transient electromagnetic response data covers a preset dynamic range, with large amplitudes in the early response values, which decay exponentially over time, and small amplitudes in the late response values.
3. The method for unbiased multi-point smoothing of transient electromagnetic data according to claim 1, characterized in that, In step S2, the exponential function is a multi-order exponential function containing multiple undetermined coefficients. The values of each undetermined coefficient are determined by fitting the transient electromagnetic response data and the sampling time.
4. The method for unbiased multi-point smoothing of transient electromagnetic data according to claim 3, characterized in that, The order of the multi-order exponential function is a positive integer, and the value of the order is determined based on the decay characteristics of the transient electromagnetic response data.
5. The method for unbiased multi-point smoothing of transient electromagnetic data according to claim 3, characterized in that, In the expression of the multi-order exponential function, the independent variable is the sampling time, the dependent variable is the fitted response value, and each undetermined coefficient is determined by the least squares method or other curve fitting algorithms.
6. The method for unbiased multi-point smoothing of transient electromagnetic data according to claim 1, characterized in that, In step S3, the trend of the fitted data is consistent with the decay trend of the transient electromagnetic response data, and the sequence shape of the fitted data is a smooth curve.
7. The method for unbiased multi-point smoothing of transient electromagnetic data according to claim 1, characterized in that, In step S4, the normalized transient electromagnetic data shows that the normalized values of the early time channels are concentrated near the preset value, while the normalized values of the late time channels deviate from the preset value.
8. The method for unbiased multi-point smoothing of transient electromagnetic data according to claim 1, characterized in that, In step S5, the multi-point smoothing process is a moving average process, which calculates the moving average of the normalized transient electromagnetic data through a preset window.
9. The method for unbiased multi-point smoothing of transient electromagnetic data according to claim 1, characterized in that, In step S5, after multi-point smoothing, the overall deviation of the smoothed normalized transient electromagnetic data is less than that of the normalized transient electromagnetic data, and the sequence shape is smoother.
10. The method for unbiased multi-point smoothing of transient electromagnetic data according to claim 1, characterized in that, In step S6, after obtaining the unbiased smooth transient electromagnetic data, it is saved for subsequent apparent resistivity calculation, time-depth conversion, or geological interpretation.