CN110954947B - Time domain linear low-frequency fusion method and system - Google Patents
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Abstract
A time domain linear low frequency fusion method and system are disclosed. The method can comprise the following steps: obtaining relative wave impedance, removing low frequency of the relative wave impedance, and obtaining medium-high frequency components of the relative wave impedance; normalizing the medium-high frequency components of the relative wave impedance to obtain normalized medium-high frequency components; calculating a low-frequency fusion coefficient according to the normalized medium-high frequency components, the normalized wave impedance curve in the well and the normalized low-frequency model; and calculating absolute wave impedance according to the normalized medium-high frequency components, the normalized low-frequency model and the normalized low-frequency fusion coefficient. According to the invention, through low frequency removal, normalization and linear embedded low frequency fusion, the influence of the initial value and recursion of the wave impedance on the relative wave impedance is eliminated, and the obtained absolute wave impedance can keep better energy consistency with the impedance in the well.
Description
Technical Field
The invention relates to the field of geophysical exploration, in particular to a time domain linear low-frequency fusion method and a time domain linear low-frequency fusion system.
Background
The seismic inversion is a core technology of seismic exploration, and the seismic inversion fully utilizes rich information such as structure, horizon, lithology and the like provided by logging, drilling and geological data to deduce information such as wave impedance, density, speed, porosity and the like of the underground stratum from a conventional seismic profile.
Seismic inversion can be divided into post-stack inversion and pre-stack inversion from the seismic data being utilized; the implementation method can be divided into direct inversion, inversion based on a model and seismic attribute inversion, and the low-frequency model established according to prior information can be used in post-stack inversion, pre-stack inversion or direct inversion, model-based inversion and seismic attribute inversion. The inversion based on the model starts from a low-frequency model, an iterative perturbation algorithm is optimized by the model, the model is continuously modified and updated, the forward modeling synthetic seismic data is optimally matched with the actual seismic data, and the final model data is the inversion result; the seismic attribute inversion is to continuously modify an input model through multiple attribute inversion on the basis of the prior model until the reservoir realization condition is approached; both types of inversion low-frequency models are directly involved in the inversion process as initial values. The trace integral is to calculate the stratum relative wave impedance by using the post-stack seismic data, and the recursion inversion is to calculate the stratum relative wave impedance based on the recursion of the reflection coefficient (the problem of initial value of the wave impedance is involved in the recursion process, if the initial value is not accurate, the obtained relative wave impedance is not in accordance with the actual situation, meanwhile, the recursion is a continuous multiplication operation, and the error is amplified continuously). The colored inversion does not need wavelets and a filtering process is used by a model to obtain the relative wave impedance of the stratum, and the like, the results obtained by the inversion are the relative wave impedance, and low-frequency information missing from the earthquake needs to be compensated for when the absolute wave impedance is obtained. The traditional method is to use a wave impedance curve in a well to perform difference to obtain a low-frequency trend of wave impedance, and determine the low frequency and band limit of the low frequency and relative wave impedance in a frequency domain through interaction, such as the channel merging function of Jason software. This implementation can compensate for the low frequency component of the seismic event missing, but does not ensure that the absolute wave impedance results obtained can be energetically consistent with the wave impedance in the well; if the energy can not be kept consistent, certain errors can be caused when the favorable reservoir range is extracted by using the result of the early-stage rock physical analysis, and the accuracy of reservoir prediction is reduced. Therefore, it is necessary to develop a time domain linear low frequency fusion method and system.
The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
Disclosure of Invention
The invention provides a time domain linear low-frequency fusion method and a time domain linear low-frequency fusion system, which can eliminate the influence of wave impedance initial value and recursion on relative wave impedance through low-frequency removal, normalization and linear embedded low-frequency fusion, and the obtained absolute wave impedance can keep better energy consistency with the impedance in a well.
According to an aspect of the present invention, a time domain linear low frequency fusion method is provided. The method may include: obtaining relative wave impedance, removing low frequency of the relative wave impedance, and obtaining medium-high frequency components of the relative wave impedance; normalizing the medium-high frequency components of the relative wave impedance to obtain normalized medium-high frequency components; calculating a low-frequency fusion coefficient according to the normalized medium-high frequency components, the normalized wave impedance curve in the well and the normalized low-frequency model; and calculating absolute wave impedance according to the normalized medium-high frequency component, the normalized low-frequency model and the normalized low-frequency fusion coefficient.
Preferably, the medium-high frequency component of the relative wave impedance is obtained by equation (1):
IMPmh(t)＝IMPrelative(t)-Trend(t) (1)
wherein, IMPrelative(t) is the relative wave impedance, and Trend (t) is the low frequency trend of the relative wave impedance.
Preferably, the normalizing the medium-high frequency component of the relative wave impedance to obtain the normalized medium-high frequency component includes: calculating the average value of the medium-high frequency components of the relative wave impedance; subtracting the average value from each value of the medium-high frequency components of the relative wave impedance to obtain an impedance difference value corresponding to the medium-high frequency components of the relative wave impedance; and searching the absolute maximum value of the impedance difference value, and calculating the normalized medium-high frequency component according to the absolute maximum value and the impedance difference value.
Preferably, the normalized medium-high frequency component is calculated by formula (2):
NORM(t)＝TMPmh(t)/TMPmax (2)
wherein NORM (t) is normalized medium-high frequency component TMPmh(t) is the difference in impedance, TMPmaxIs the absolute maximum.
Preferably, the calculation parameter sigma of formula (3) is used as the low-frequency fusion coefficient:
wherein J represents an objective function, IMPwell(t) is the wave impedance curve in the well, model (t) is the low frequency model,
the absolute impedance curve is shown.
Preferably, the absolute impedance curve is calculated by equation (4):
preferably, the absolute wave impedance is calculated by equation (5):
IMPabsolute(t)＝Model(t)*(1+λ*NORM(t)) (5)
wherein, IMPabsolute(t) absolute wave impedance, model (t) low frequency model, lambda is low frequency fusion coefficient, and NORM (t) normalized medium-high frequency component.
Preferably, the method further comprises the following steps: the relative wave impedance is calculated from the reflection coefficient.
Preferably, the relative wave impedance is calculated by equation (6):
wherein, IMPrelative(t) is the relative wave impedance, r (i) is the reflection coefficient, i is 0,1,2, …, t-1, and IMP (0) is the initial wave impedance value.
According to another aspect of the present invention, a time domain linear low frequency fusion system is provided, which is characterized in that the system comprises: a memory storing computer-executable instructions; a processor executing computer executable instructions in the memory to perform the steps of: obtaining relative wave impedance, removing low frequency of the relative wave impedance, and obtaining medium-high frequency components of the relative wave impedance; normalizing the medium-high frequency components of the relative wave impedance to obtain normalized medium-high frequency components; calculating a low-frequency fusion coefficient according to the normalized medium-high frequency components, the normalized wave impedance curve in the well and the normalized low-frequency model; and calculating absolute wave impedance according to the normalized medium-high frequency component, the normalized low-frequency model and the normalized low-frequency fusion coefficient.
Preferably, the medium-high frequency component of the relative wave impedance is obtained by equation (1):
IMPmh(t)＝IMPrelative(t)-Trend(t) (1)
wherein, IMPrelative(t) is the relative wave impedance, and Trend (t) is the low frequency trend of the relative wave impedance.
Preferably, the normalizing the medium-high frequency component of the relative wave impedance to obtain the normalized medium-high frequency component includes: calculating the average value of the medium-high frequency components of the relative wave impedance; subtracting the average value from each value of the medium-high frequency components of the relative wave impedance to obtain an impedance difference value corresponding to the medium-high frequency components of the relative wave impedance; and searching the absolute maximum value of the impedance difference value, and calculating the normalized medium-high frequency component according to the absolute maximum value and the impedance difference value.
Preferably, the normalized medium-high frequency component is calculated by formula (2):
NORM(t)＝TMPmh(t)/TMPmax (2)
wherein NORM (t) is normalized medium-high frequency component TMPmh(t) is the difference in impedance, TMPmaxIs the absolute maximum.
Preferably, the calculation parameter sigma of formula (3) is used as the low-frequency fusion coefficient:
wherein J represents an objectFunction, IMPwell(t) is the wave impedance curve in the well, model (t) is the low frequency model,
the absolute impedance curve is shown.
Preferably, the absolute impedance curve is calculated by equation (4):
preferably, the absolute wave impedance is calculated by equation (5):
IMPabsolute(t)＝Model(t)*(1+λ*NORM(t)) (5)
wherein, IMPabsolute(t) absolute wave impedance, model (t) low frequency model, lambda is low frequency fusion coefficient, and NORM (t) normalized medium-high frequency component.
Preferably, the method further comprises the following steps: the relative wave impedance is calculated from the reflection coefficient.
Preferably, the relative wave impedance is calculated by equation (6):
wherein, IMPrelative(t) is the relative wave impedance, r (i) is the reflection coefficient, i is 0,1,2, …, t-1, and IMP (0) is the initial wave impedance value.
The beneficial effects are that: the method is realized in a time domain, the influence of an initial value on an inversion result can be eliminated, the error accumulation effect generated by recursion operation can be eliminated, the relation between the absolute wave impedance of inversion and the impedance in a well can be better controlled, and better energy consistency is kept; meanwhile, the time domain low-frequency fusion is higher in calculation efficiency than the frequency domain low-frequency fusion.
The method and apparatus of the present invention have other features and advantages which will be apparent from or are set forth in detail in the accompanying drawings and the following detailed description, which are incorporated herein, and which together serve to explain certain principles of the invention.
Drawings
The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts.
Fig. 1 shows a flow chart of the steps of a time domain linear low frequency fusion method according to the present invention.
Fig. 2 shows a schematic diagram of a reflection coefficient curve according to an embodiment of the invention.
FIG. 3 shows a schematic diagram of a relative wave impedance curve according to one embodiment of the invention.
FIG. 4 shows a schematic of the low frequency fused absolute wave impedance, borehole impedance and low frequency model according to the prior art.
Fig. 5 shows a schematic diagram of the relative wave impedance curve according to fig. 3 with the low frequencies removed.
FIG. 6 shows a schematic of the absolute wave impedance, the impedance in the well, and the low frequency model, according to one embodiment of the invention.
Detailed Description
The invention will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present invention are shown in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
Fig. 1 shows a flow chart of the steps of a time domain linear low frequency fusion method according to the present invention.
In this embodiment, the time domain linear low frequency fusion method according to the present invention may include: step 101, obtaining relative wave impedance, removing low frequency of the relative wave impedance, and obtaining medium-high frequency components of the relative wave impedance; step 102, carrying out normalization processing on medium-high frequency components of relative wave impedance to obtain normalized medium-high frequency components; 103, calculating a low-frequency fusion coefficient according to the normalized medium-high frequency components, the normalized wave impedance curve in the well and the normalized low-frequency model; and step 104, calculating absolute wave impedance according to the normalized medium-high frequency components, the normalized low-frequency model and the normalized low-frequency fusion coefficient.
In one example, the medium-high frequency component of the relative wave impedance is obtained by equation (1):
IMPmh(t)＝IMPrelative(t)-Trend(t) (1)
wherein, IMPrelative(t) is the relative wave impedance, and Trend (t) is the low frequency trend of the relative wave impedance.
In one example, the normalizing process is performed on the medium-high frequency component of the relative wave impedance, and obtaining the normalized medium-high frequency component includes: calculating the average value of medium-high frequency components of the relative wave impedance; subtracting the average value from each value of the medium-high frequency components of the relative wave impedance to obtain an impedance difference value corresponding to the medium-high frequency components of each relative wave impedance; and searching the absolute maximum value of the impedance difference value, and calculating the normalized medium-high frequency component according to the absolute maximum value and the impedance difference value.
In one example, the normalized medium-high frequency content is calculated by equation (2):
NORM(t)＝TMPmh(t)/TMPmax (2)
wherein NORM (t) is normalized medium-high frequency component TMPmh(t) is the difference in impedance, TMPmaxIs the absolute maximum.
In one example, the low-frequency fusion coefficient is given by the calculation parameter sigma of formula (3):
wherein J represents an objective function, IMPwell(t) is the wave impedance curve in the well, model (t) is the low frequency model,
the absolute impedance curve is shown.
In one example, the absolute impedance curve is calculated by equation (4):
in one example, the absolute wave impedance is calculated by equation (5):
IMPabsolute(t)＝Model(t)*(1+λ*NORM(t)) (5)
wherein, IMPabsolute(t) absolute wave impedance, model (t) low frequency model, lambda is low frequency fusion coefficient, and NORM (t) normalized medium-high frequency component.
In one example, further comprising: the relative wave impedance is calculated from the reflection coefficient.
In one example, the relative wave impedance is calculated by equation (6):
wherein, IMPrelative(t) is the relative wave impedance, r (i) is the reflection coefficient, i is 0,1,2, …, t-1, and IMP (0) is the initial wave impedance value.
Specifically, the time domain linear low frequency fusion method according to the present invention may include:
if the input is a reflection coefficient curve, the reflection coefficient curve is converted into a relative wave impedance curve through a formula (6), if the input is the relative wave impedance curve, the low frequency of the relative wave impedance is directly removed, and the medium-high frequency component of the relative wave impedance is obtained through a formula (1), wherein the low frequency of the relative wave impedance can be obtained by adopting a time domain filtering method, including a time domain one-dimensional filtering method such as mean value filtering or median filtering.
Calculating the average value of medium-high frequency components of the relative wave impedance; subtracting the average value from each value of the medium-high frequency components of the relative wave impedance to obtain an impedance difference value corresponding to the medium-high frequency components of each relative wave impedance; and searching the absolute maximum value of the impedance difference value, and calculating the normalized medium-high frequency component through a formula (2) according to the absolute maximum value and the impedance difference value.
And searching a time domain linear low-frequency fusion coefficient according to the normalized medium-high frequency component, the normalized wave impedance curve and the normalized low-frequency model, obtaining different absolute impedances by taking different sigma values according to the formula (3), calculating the maximum deviation of the absolute impedance curve and the low-frequency model, and obtaining the corresponding sigma which is the low-frequency fusion coefficient when the deviation is minimum.
And (4) calculating absolute wave impedance according to the normalized medium-high frequency component, the normalized low-frequency model and the normalized low-frequency fusion coefficient by using a formula (4).
According to the method, the influence of the initial value and recursion of the wave impedance on the relative wave impedance is eliminated through low frequency removal, normalization and linear embedded low frequency fusion, and the obtained absolute wave impedance can keep better energy consistency with the impedance in the well.
Application example
To facilitate understanding of the solution of the embodiments of the present invention and the effects thereof, a specific application example is given below. It will be understood by those skilled in the art that this example is merely for the purpose of facilitating an understanding of the present invention and that any specific details thereof are not intended to limit the invention in any way.
The time domain linear low-frequency fusion method comprises the following steps:
fig. 2 shows a schematic diagram of a reflection coefficient curve according to an embodiment of the invention.
FIG. 3 shows a schematic diagram of a relative wave impedance curve according to one embodiment of the invention.
FIG. 4 shows a schematic of the low frequency fused absolute wave impedance, borehole impedance and low frequency model according to the prior art.
Fig. 5 shows a schematic diagram of the relative wave impedance curve according to fig. 3 with the low frequencies removed.
From the reflection coefficient curve as shown in fig. 2, the reflection coefficient curve is converted into a relative wave impedance curve by the equation (6), as shown in fig. 3, and it can be seen from the graph that the curve has a certain low frequency tendency and the relative wave impedance is obtained recursively. According to a recursion formula, accumulated errors can be continuously amplified along with time from shallow to deep, and fig. 4 is a schematic diagram of absolute wave impedance, well impedance and a low-frequency model of low-frequency fusion according to the prior art, wherein a solid line is a well impedance curve, a plus sign curve is the low-frequency model, and a dot-dash line is a traditional absolute wave impedance curve after low-frequency fusion. It can be seen from the figure that the absolute wave impedance after low-frequency fusion is relatively smaller in impedance error with the well in the shallow layer (i.e. when the time is smaller (left end)), and with the increase of the depth, the absolute wave impedance not only deviates from the low-frequency model, but also has larger deviation with the impedance curve in the well, and the trend matching effect is not good. Therefore, the low frequency of the relative wave impedance is removed, and the medium-high frequency component of the relative wave impedance is obtained through the formula (1), as shown in fig. 5, wherein, as can be seen from the figure, the medium-high frequency information of the impedance can be well preserved after the low frequency of the relative wave impedance is removed. Wherein, the low frequency of the relative wave impedance can be obtained by adopting three-point mean value filtering.
Calculating the average value of medium-high frequency components of the relative wave impedance; subtracting the average value from each value of the medium-high frequency components of the relative wave impedance to obtain an impedance difference value corresponding to the medium-high frequency components of each relative wave impedance; and searching the absolute maximum value of the impedance difference value, and calculating the normalized medium-high frequency component through a formula (2) according to the absolute maximum value and the impedance difference value.
And searching a time domain linear low-frequency fusion coefficient according to the normalized medium-high frequency component, the normalized wave impedance curve and the normalized low-frequency model, obtaining different absolute impedances by taking different sigma values according to the formula (3), calculating the maximum deviation of the absolute impedance curve and the low-frequency model, and obtaining the corresponding sigma which is the low-frequency fusion coefficient when the deviation is minimum.
FIG. 6 shows a schematic of the absolute wave impedance, the impedance in the well, and the low frequency model, according to one embodiment of the invention.
And (4) calculating absolute wave impedance according to the normalized medium-high frequency component, the normalized low-frequency model and the normalized low-frequency fusion coefficient by using a formula (4). Fig. 6 is a schematic diagram of the absolute wave impedance, the well impedance and the low frequency model obtained by the present invention, wherein a straight line is a well impedance curve, a plus sign curve is a low frequency model, and a dash-dot line is a low frequency fused absolute wave impedance curve obtained by the present invention. It can be seen from the figure that the trend of the absolute wave impedance curve can be well consistent with the trend of the low-frequency model, and the jitter amplitude of the waveform can be equivalent to the well impedance curve. For this example, the rms amplitude of the well impedance curve was 6731.20117, the rms amplitude of the absolute wave impedance curve was 6802.18994, and the difference between the two was 1.05%, which gave better energy matching.
Compared with the traditional frequency domain low-frequency fusion technology, the method is realized in a time domain, the influence of an initial value on an inversion result can be eliminated, the error accumulation effect generated by recursion operation can be eliminated, the relation between the inverted absolute wave impedance and the well wave impedance can be better controlled, better energy consistency is kept, and the root mean square amplitude deviation can be controlled within 5%; meanwhile, the time domain low-frequency fusion is higher in calculation efficiency than the frequency domain low-frequency fusion.
In conclusion, the method eliminates the influence of the initial value and recursion of the wave impedance on the relative wave impedance through low frequency removal, normalization and linear embedded low frequency fusion, and the obtained absolute wave impedance can keep better energy consistency with the impedance in the well.
It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.
According to an embodiment of the present invention, there is provided a time domain linear low frequency fusion system, which includes: a memory storing computer-executable instructions; a processor executing computer executable instructions in the memory to perform the steps of: obtaining relative wave impedance, removing low frequency of the relative wave impedance, and obtaining medium-high frequency components of the relative wave impedance; normalizing the medium-high frequency components of the relative wave impedance to obtain normalized medium-high frequency components; calculating a low-frequency fusion coefficient according to the normalized medium-high frequency components, the normalized wave impedance curve in the well and the normalized low-frequency model; and calculating absolute wave impedance according to the normalized medium-high frequency components, the normalized low-frequency model and the normalized low-frequency fusion coefficient.
In one example, the medium-high frequency component of the relative wave impedance is obtained by equation (1):
IMPmh(t)＝IMPrelative(t)-Trend(t) (1)
wherein, IMPrelative(t) is the relative wave impedance, and Trend (t) is the low frequency trend of the relative wave impedance.
In one example, the normalizing process is performed on the medium-high frequency component of the relative wave impedance, and obtaining the normalized medium-high frequency component includes: calculating the average value of medium-high frequency components of the relative wave impedance; subtracting the average value from each value of the medium-high frequency components of the relative wave impedance to obtain an impedance difference value corresponding to the medium-high frequency components of each relative wave impedance; and searching the absolute maximum value of the impedance difference value, and calculating the normalized medium-high frequency component according to the absolute maximum value and the impedance difference value.
In one example, the normalized medium-high frequency content is calculated by equation (2):
NORM(t)＝TMPmh(t)/TMPmax (2)
wherein NORM (t) is normalized medium-high frequency component TMPmh(t) is the difference in impedance, TMPmaxIs the absolute maximum.
In one example, the low-frequency fusion coefficient is given by the calculation parameter sigma of formula (3):
wherein J represents an objective function, IMPwell(t) is the wave impedance curve in the well, model (t) is the low frequency model,
the absolute impedance curve is shown.
In one example, the absolute impedance curve is calculated by equation (4):
in one example, the absolute wave impedance is calculated by equation (5):
IMPabsolute(t)＝Model(t)*(1+λ*NORM(t)) (5)
wherein, IMPabsolute(t) absolute wave impedance, model (t) low frequency model, lambda is low frequency fusion coefficient, and NORM (t) normalized medium-high frequency component.
In one example, further comprising: the relative wave impedance is calculated from the reflection coefficient.
In one example, the relative wave impedance is calculated by equation (6):
wherein, IMPrelative(t) is the relative wave impedance, r (i) is the reflection coefficient, i is 0,1,2, …, t-1, and IMP (0) is the initial wave impedance value.
The system eliminates the influence of the initial value and recursion of the wave impedance on the relative wave impedance through low frequency removal, normalization and linear embedded low frequency fusion, and the obtained absolute wave impedance can keep better energy consistency with the impedance in the well.
It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.
Claims (9)
1. A time domain linear low frequency fusion method is characterized by comprising the following steps:
obtaining relative wave impedance, removing low frequency of the relative wave impedance, and obtaining medium-high frequency components of the relative wave impedance;
normalizing the medium-high frequency components of the relative wave impedance to obtain normalized medium-high frequency components;
calculating a low-frequency fusion coefficient according to the normalized medium-high frequency components, the normalized wave impedance curve in the well and the normalized low-frequency model;
calculating absolute wave impedance according to the normalized medium-high frequency component, the normalized low-frequency model and the normalized low-frequency fusion coefficient;
wherein, the calculation parameter sigma of the formula (3) is used as a low-frequency fusion coefficient of an absolute impedance curve:
wherein J represents an objective function, IMPwell(t) is the wave impedance curve in the well, model (t) is the low frequency model,
the absolute impedance curve is shown.
2. A time-domain linear low-frequency fusion method according to claim 1, wherein the medium-high frequency component of the relative wave impedance is obtained by equation (1):
IMPmh(t)＝IMPrelative(t)-Trend(t) (1)
wherein, IMPrelative(t) is the relative wave impedance, and Trend (t) is the low frequency trend of the relative wave impedance.
3. The time domain linear low-frequency fusion method according to claim 1, wherein the normalizing process is performed on the medium-high frequency component of the relative wave impedance, and obtaining the normalized medium-high frequency component comprises:
calculating the average value of the medium-high frequency components of the relative wave impedance;
subtracting the average value from each value of the medium-high frequency components of the relative wave impedance to obtain an impedance difference value corresponding to the medium-high frequency components of the relative wave impedance;
and searching the absolute maximum value of the impedance difference value, and calculating the normalized medium-high frequency component according to the absolute maximum value and the impedance difference value.
4. A time-domain linear low frequency fusion method according to claim 3 wherein the normalized mid-to-high frequency content is calculated by equation (2):
NORM(t)＝TMPmh(t)/TMPmax (2)
wherein NORM (t) is normalized medium-high frequency component TMPmh(t) is the difference in impedance, TMPmaxIs the absolute maximum.
5. The time-domain linear low frequency fusion method of claim 1, wherein the absolute impedance curve is calculated by equation (4):
wherein NORM (t) is normalized medium-high frequency component.
6. The time-domain linear low frequency fusion method of claim 1, wherein the absolute wave impedance is calculated by equation (5):
IMPabsolute(t)＝Model(t)*(1+λ*NORM(t)) (5)
wherein, IMPabsolute(t) absolute wave impedance, model (t) low frequency model, lambda is low frequency fusion coefficient, and NORM (t) normalized medium-high frequency component.
7. The time domain linear low frequency fusion method of claim 1, further comprising:
the relative wave impedance is calculated from the reflection coefficient.
8. The time-domain linear low frequency fusion method of claim 7 wherein the relative wave impedance is calculated by equation (6):
wherein, IMPrelative(t) is the relative wave impedance, r (i) is the reflection coefficient, i is 0,1,2, …, t-1, and IMP (0) is the initial wave impedance value.
9. A time domain linear low frequency fusion system, comprising:
a memory storing computer-executable instructions;
a processor executing computer executable instructions in the memory to perform the steps of:
obtaining relative wave impedance, removing low frequency of the relative wave impedance, and obtaining medium-high frequency components of the relative wave impedance;
normalizing the medium-high frequency components of the relative wave impedance to obtain normalized medium-high frequency components;
calculating a low-frequency fusion coefficient according to the normalized medium-high frequency components, the normalized wave impedance curve in the well and the normalized low-frequency model;
calculating absolute wave impedance according to the normalized medium-high frequency component, the normalized low-frequency model and the normalized low-frequency fusion coefficient;
wherein, the calculation parameter sigma of the formula (3) is used as a low-frequency fusion coefficient of an absolute impedance curve:
wherein J represents an objective function, IMPwell(t) is the wave resistance in the wellThe impedance curve, model (t), is a low frequency model,
the absolute impedance curve is shown.
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