CN108287365A - A kind of tri- parameter synchronization inversion methods of VSP and device based on wave equation - Google Patents
A kind of tri- parameter synchronization inversion methods of VSP and device based on wave equation Download PDFInfo
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Abstract
The application provides a kind of tri- parameter synchronization inversion methods of VSP and device based on wave equation.The method includes：The initial estimate of three parameters is obtained using the primary travel time Inversion Calculation in VSP data, three parameters include velocity of longitudinal wave, shear wave velocity, density parameter；The confidence spatial dimension of velocity of longitudinal wave, shear wave velocity and density parameter in refutation process is determined according to the quality of seismic data, as the parameter up-and-down boundary range in wave equation inversion；Establish the object function of the three parameter synchronizations inverting for VSP data；The wave equation inversion of three parameters is carried out to the object function of foundation using fast simulated annealing algorithm, obtain more accurate three parameter, the problems such as precision, efficiency and the inverting of effectively solution p-and s-wave velocity and density parameter Simultaneous Retrieving are easily trapped into local minimum, to provide more structurally sound data basis using seismic data development reservoir prediction and oil-gas possibility identification.
Description
Technical field
The application category field of petroleum geophysical exploration more particularly to a kind of tri- parameter synchronizations of VSP based on wave equation
Inversion method and device.
Background technology
Vertical wave velocity ﹑ shear wave velocitys and density are the most basic parameters in earthquake Rock physical analysis, to these three parameters
The in-depth analysis of (being properly termed as three parameters) can instruct the fields such as pre-stack seismic inversion, lithology prediction and oil-gas possibility identification
Work.Currently, mainly using the velocity of wave in length and breadth in well-log information or petrophysics experiment test data in Rock physical analysis
Degree and density parameter, but the analysis result under the scale still has a certain distance with seismic prospecting scale, therefore be difficult accurate
Petrophysics property of the comprehensive reflection reservoir under earthquake scale.Therefore, how to be obtained under earthquake scale more structurally sound
P-and s-wave velocity and density parameter are weighed very much for being carried out to have for reservoir prediction and oil-gas possibility identification using seismic data
The realistic meaning wanted.
VSP (Vertical Seismic Profiling) i.e. vertical seismic profiling (VSP) is as seismic prospecting side in a kind of well
Method can accurately obtain the when depth relationship at the position of well point, connection surface-seismic data is played in oilfield prospecting developing
With the function served as bridge of well-log information.Currently, vertical to obtain when usually being travelled in practical applications using the transmitted wave in VSP data
Shear wave velocity information, precision are easy the intensity by travail-time pickup error, actual formation difference of impedance and converted wave energy
Etc. factors influence.Density is also the important component of petrophysical parameter, but can only reflect velocity variations information when travelling
And it is unrelated with the variation of density parameter, therefore can not be finally inversed by rational density parameter using information when travelling.Due to not filling
Point using the shape information in VSP data, method when based on travelling still cannot achieve to p-and s-wave velocity and density parameter
Synchronous exact inversion, to limit the ability that VSP data is applied in reservoir prediction and oil-gas possibility identification.Elastic wave fluctuates
Equation can more accurately travelling in inverting seismic wave when and amplitude information, but directly elastic wave wave equation is utilized to carry out
The direct inversion of p-and s-wave velocity and density parameter suffers from the accuracy of initial model, inversion algorithm is easily trapped into part most
The small influence with computational efficiency the problems such as low not yet makes a breakthrough in practical applications.
Therefore, there is an urgent need for information when a kind of waveform that can be made full use of in VSP data and travelling in the prior art, realize more
Increase effect, accurate Simultaneous Retrieving goes out the method for tri- parameters of VSP, to utilize seismic data to carry out reservoir prediction and oil-containing
Gas identification provides more structurally sound data basis.
Invention content
The application is designed to provide a kind of tri- parameter synchronization inversion methods of VSP and device based on wave equation, can be with
Information when making full use of waveform and the travelling in VSP data more efficiently, accurately can realize that Simultaneous Retrieving goes out earthquake scale
Under p-and s-wave velocity, density parameter.
What a kind of tri- parameter synchronization inversion methods of VSP based on wave equation provided by the present application were realized in：
The initial estimate of three parameters, three ginsengs are obtained using the primary travel time Inversion Calculation in VSP data
Number includes velocity of longitudinal wave, shear wave velocity, density parameter；
The confidence of velocity of longitudinal wave, shear wave velocity and density parameter in refutation process is determined according to the quality of seismic data
Spatial dimension, as the parameter up-and-down boundary range in wave equation inversion；
Establish the object function of three parameter synchronization invertings for VSP observational datas；
The wave equation inversion for being carried out three parameters to the object function of foundation using fast simulated annealing algorithm, is obtained
Obtain three velocity of longitudinal wave, shear wave velocity, density parameters.
In preferred embodiment, the primary travel time Inversion Calculation in the data using VSP obtains the initial of three parameters
Estimated value includes：
The position for picking up vertical shear wave waveform ski-jump in VSP records, obtains stratum of the seismic wave more than receiving point position
In transmitted wave hourage, and according to the depth of hourage and receiving point, calculate separately out p-and s-wave velocity value, and utilize
The relationship of speed and density estimates initial density value.
In preferred embodiment, the average speed of velocity of longitudinal wave, shear wave velocity is calculated using following calculation formula：
Wherein, Va is the average speed of velocity of longitudinal wave or shear wave velocity, x0It is expressed as seismic wave excitation position and well head position
Offset distance between setting, h are expressed as the elevation of seismic receiving position from the ground, and t indicates that seismic wave is traveled to from excitation position
When travelling at receiving point position.
In preferred embodiment, the interval velocity of Different Strata is determined using following calculation formula：
In above formula, V0For interval velocity, when n values 1, V0(1)=Va(1), Va is the average speed of velocity of longitudinal wave or shear wave velocity
Degree, n indicate that n-th of stratum, t are expressed as seismic wave from when position being excited to travel to the travelling from receiving point position.
In preferred embodiment, the up-and-down boundary range of velocity of longitudinal wave parameter value is determined using following manner：
Determine the confidence spatial parameter λ of the velocity of longitudinal wave introducedpValue；
The up-and-down boundary range of velocity of longitudinal wave parameter value in refutation process is calculated using following formula：
Vph=Vp0(1+λp)
Vpl=Vp0(1-λp)
In above formula, Vp0The estimated value of the P-wave interval velocity obtained when for using travelling, VphAnd VplRespectively velocity of longitudinal wave confidence
The maximum and minimum value of spatial dimension.
In preferred embodiment, the up-and-down boundary range of velocity of longitudinal wave parameter value is determined using following manner：
Determine the confidence spatial parameter λ of the shear wave velocity introducedsValue；
The up-and-down boundary range of shear wave velocity parameter value in refutation process is calculated using following formula：
Vsh=Vs0(1+λs)
Vsl=Vs0(1-λs)
Wherein, Vs0The estimated value of the shear wave velocity obtained when for using travelling, VshAnd VslRespectively shear wave velocity confidence space
The maximum and minimum value of range.
In preferred embodiment, the confidence spatial parameter λ of the determining shear wave velocity introducedsValue include：
The half of the maximum value of the velocity of longitudinal wave obtained when using travelling and the difference of minimum value is floating as shear wave velocity value
The reference value of range is moved, and utilizes the reference value and ratio the setting as shear wave velocity for utilizing the shear wave velocity obtained when travelling
Believe spatial parameter λsValue.
It is described to determine that velocity of longitudinal wave, shear wave velocity and density are joined according to the quality of seismic data in preferred embodiment
Confidence spatial dimension of the number in refutation process include：
Density values are handled using the statistical formula of velocity of longitudinal wave and density parameter, which is：
Wherein, the initial estimate of density parameter is ρ0A, b are according to the velocity of longitudinal wave and density ginseng in real logging data
Number system,
Meter gained, Vp0The estimated value of the P-wave interval velocity obtained when for using travelling, a and b are velocity of longitudinal wave and density-velocity
Between non-linear relation fitting coefficient, b be Vp0 exponential term；
The confidence spatial dimension of density parameter is：
ρh=ρ0h(1+λρ)
ρl=ρ0l(1-λρ)
Wherein, ρ0hFor ρ0Maximum value, ρ0lFor ρ0Minimum value, ρhAnd ρlRespectively density parameter confidence spatial dimension
Maximum and minimum value, λρFor density confidence spatial parameter, value and λpAnd λsMaximum value it is equal.
In preferred embodiment, the object function for establishing the three parameter synchronizations inverting for VSP observational datas
Including：
Establish the object function of three parameter synchronization invertings of p-and s-wave velocity and density：
Establish the object function of three parameter synchronization invertings of p-and s-wave velocity and density：
Wherein, d is the seismic data of observation；F is elastic wave Wave equation forward modeling as a result, α is constant, the constant
Depending on the quality of inverting data, F is object function, and S.T. indicates to mean that items listed behind are linear programming
The requirement condition of related constraint and satisfaction.
It is described that three parameters are carried out to the object function of foundation using fast simulated annealing algorithm in preferred embodiment
Wave equation inversion include：
The annealing way used in simulated annealing is based on the realization of following formula：
T (K)=T0exp(-CK1/N)
Wherein, K is iterations, and C is constant, and N is the number for waiting for inverted parameters, T0For initial temperature；It is corresponding to wait for instead
The iteration for the model parameter drilled more new formula is：
In above formula, miFor model variable before modification；mjFor model variable after modification；U is random number, and the random number is in [0,1]
It is uniformly distributed in range；[Ai,Bi] be model variable search space.
This specification also provides a kind of tri- parameter synchronization inversion procedure devices of VSP based on wave equation, including processor
And the memory of storage computer executable instructions, the processor are realized any one in this specification when executing described instruction
The execution step of item embodiment of the method.
The application provides a kind of tri- parameter synchronization inversion methods of VSP and device based on wave equation, VSP can be utilized to provide
Travel Time Inversion in material goes out initial p-and s-wave velocity parameter, and the confidence for then establishing p-and s-wave velocity and density parameter inverting is empty
Between range as prior information, it is effective to constrain taking for p-and s-wave velocity and density parameter during elastic wave wave equation inversion
It is worth range, reduces the influencing each other between p-and s-wave velocity and density in inverting, to which Simultaneous Retrieving goes out more accurate knot
Fruit.When the embodiment of the present invention makes full use of travelling abundant in VSP data and shape information, by Travel Time Inversion and elastic wave wave
Dynamic equation inverting organically combines.The prior-constrained of p-and s-wave velocity and density parameter is established on the basis of Travel Time Inversion result
Information defines the confidence spatial dimension of p-and s-wave velocity and density parameter during elastic wave wave equation inversion, establishes a set of
Three parameter synchronization inversion method of p-and s-wave velocity and density for VSP data effectively solves p-and s-wave velocity and density parameter
The problems such as precision, efficiency and the inverting of Simultaneous Retrieving are easily trapped into local minimum.The each embodiment provided using this specification,
More accurately and reliably velocity of longitudinal wave, shear wave velocity and density parameter can be obtained under earthquake scale, provided for well shake calibration
Depth relationship when more structurally sound, the petrophysics property analysis to carry out under earthquake scale provide accurate p-and s-wave velocity and close
Parameter is spent, to provide more structurally sound data basis to be identified using seismic data development reservoir prediction and oil-gas possibility.
Description of the drawings
In order to illustrate the technical solutions in the embodiments of the present application or in the prior art more clearly, to embodiment or will show below
There is attached drawing needed in technology description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments described in application, for those of ordinary skill in the art, in the premise of not making the creative labor property
Under, other drawings may also be obtained based on these drawings.
Fig. 1 is a kind of tri- a kind of embodiments of parameter synchronization inversion method of VSP based on wave equation provided by the present application
Method flow diagram；
Fig. 2 is zero bias VSP data earthquake record vertical components and primary travel time pickup in a kind of embodiment of the application
Result schematic diagram carries out longitudinal wave pickup using the wavelength-division of vertical component uplink and downlink from down going wave later；
Fig. 3 a are the result schematic diagrams that zero bias VSP earthquake record horizontal component zero bias are picked up in a kind of embodiment of the application,
Using the wavelength-division of horizontal component uplink and downlink Extraction of Shear Wave is carried out from down going wave later；
Fig. 3 b are zero bias VSP earthquake records horizontal component (removing through longitudinal wave) and converted wave in a kind of embodiment of the application
Pickup as a result, using the wavelength-division of horizontal component uplink and downlink from later down going wave carry out Extraction of Shear Wave；
Fig. 4 is the restriction range schematic diagram of the velocity of longitudinal wave in the application one embodiment, and L3, L4 dotted line are bound
Limit, the result that L5 solid lines obtain when being using travelling；
Fig. 5 is the schematic diagram of the restriction range of velocity of longitudinal wave in a kind of embodiment of the application, and dotted line is upper and lower boundary, solid line
The result obtained when for using travelling
Fig. 6 is the schematic diagram of the restriction range of density in a kind of embodiment of the application, and dotted line is upper and lower boundary, and solid line is profit
The result obtained with statistical relationship；
Fig. 7 is a schematic diagram using the practical process flow for carrying out three parameter calculating of the embodiment of the present invention；
Fig. 8 is the Comparative result schematic diagram of the tri- parameter synchronization invertings of VSP based on wave equation in the application；
Fig. 9 is a kind of hardware of tri- parameter synchronization inversion procedure devices of VSP based on wave equation of the embodiment of the present invention
Structure diagram.
Specific implementation mode
In order to make those skilled in the art better understand the technical solutions in the application, below in conjunction with the application reality
The attached drawing in example is applied, technical solutions in the embodiments of the present application is clearly and completely described, it is clear that described implementation
Example is merely a part but not all of the embodiments of the present application.Based on the embodiment in the application, this field is common
The every other embodiment that technical staff is obtained without creative efforts should all belong to the application protection
Range.
VSP (Vertical Seismic Profiling) i.e. vertical seismic profiling (VSP)s, are a kind of seismological observation methods.It with
The seismic profile of usual ground observation is corresponding.Vertical seismic profiling (VSP) method is to excite earthquake on some points of adjacent ground surface
Wave is observed on some the multistage multicomponent geophone stations arranged along wellhole different depth.In vertical seismic profiling (VSP), because
It is placed in inside stratum by well for wave detector, so the uplink longitudinal wave propagated from bottom to top and uplink conversion can not only be received
Wave can also receive the downlink longitudinal wave propagated from top to bottom and down conversion wave, or even can receive shear wave.
Information when how to make full use of waveform and the travelling in VSP data, Simultaneous Retrieving go out accurate vertical under earthquake scale
Shear wave velocity and density parameter, depth relationship when can not only obtain more accurate, additionally it is possible to realize the storage under earthquake scale
Layer petrophysics property analysis, to more structurally sound to be provided based on seismic data development reservoir prediction and oil-gas possibility identification
Foundation.
When the present invention makes full use of travelling abundant in VSP data and shape information, by Travel Time Inversion and elastic wave wave
Dynamic equation inverting organically combines, and the prior-constrained of p-and s-wave velocity and density parameter is established on the basis of Travel Time Inversion result
Information defines the confidence spatial dimension of p-and s-wave velocity and density parameter during elastic wave wave equation inversion, establishes a set of
Three parameter of p-and s-wave velocity and density (or being three parameters) Simultaneous Retrieving method for VSP data, effectively solves in length and breadth
The problems such as wave velocity and precision of density parameter Simultaneous Retrieving, efficiency and inverting are easily trapped into local minimum.To in earthquake ruler
Degree is lower to obtain more accurately and reliably velocity of longitudinal wave, shear wave velocity and density parameter (i.e. three parameters), shakes to demarcate for well and provides
Depth relationship when more structurally sound, the petrophysics property analysis to carry out under earthquake scale provide accurate p-and s-wave velocity and close
Parameter is spent, to provide more structurally sound data basis to be identified using seismic data development reservoir prediction and oil-gas possibility.
In one embodiment of the method provided by the present application, implementation process may include：Based on zero bias VSP numbers
Information when vertical component and horizontal component in are travelled, calculates separately to obtain p-and s-wave velocity；Speed is recycled to join with density
Empirical relation between number obtains the initial estimate of density parameter, and according to the quality of seismic data come determine velocity of longitudinal wave,
The confidence spatial dimension of shear wave velocity and density parameter in refutation process, above and below the parameter in wave equation inversion
Bounds；The p-and s-wave velocity and density parameter Simultaneous Retrieving object function for VSP observational datas are established on this basis,
Three parameter fluctuation equation inverting of elastic wave is carried out using fast simulated annealing algorithm, obtains more accurate p-and s-wave velocity and close
Spend parameter.
It may be used in one embodiment provided by the present application and realize the more accurate longitudinal and shear wave of acquisition including such as under type
Speed and density parameter.It should be noted that according to the description of following modes, the application can also include based on following
The deformation, transformation of technical characteristic, equivalent or extension other embodiment in embodiment.
This specification embodiment is illustrated by taking a specific application scenarios as an example below.Specifically, Fig. 1 is this
A kind of flow diagram of the tri- parameter synchronization inversion methods of VSP based on wave equation that specification provides.Although this theory
Bright book is provided such as following embodiments or method operating procedure shown in the drawings, but based on conventional or be not necessarily to performing creative labour
Less operating procedure after may include more in the method or part merging.There is no necessary causes and effects in logicality
In the step of relationship or structure, the execution sequence of these steps is not limited to this specification embodiment or execution shown in the drawings is suitable
Sequence.Device, server or the end product of the method in practice are in application, can be according to shown in embodiment or attached drawing
Either parallel execute of method carry out sequence execution (such as the environment of parallel processor or multiple threads, even include point
Cloth processing, server cluster implementation environment).
A kind of specific tri- parameter synchronization inversion method one embodiment of VSP based on wave equation provided by the present application
In, may include：
S0：The initial estimate of three parameters, three ginseng are obtained using the primary travel time Inversion Calculation in VSP data
Number includes velocity of longitudinal wave, shear wave velocity, density parameter；
S2：Determine velocity of longitudinal wave, shear wave velocity and density parameter in refutation process according to the quality of seismic data
Confidence spatial dimension, as the parameter up-and-down boundary range in wave equation inversion；
S6：Establish the object function of three parameter synchronization invertings for VSP data；
S8：The wave equation for carrying out three parameters to the object function of foundation using fast simulated annealing algorithm is anti-
It drills, obtains three velocity of longitudinal wave, shear wave velocity, density parameters.
Described quality typically refers to the data quality degree being an actually-received in this specification embodiment.Art technology
If personnel are it is understood that its meaning is good including the data quality received, the confidence spatial dimension of inverted parameters can
To be very easy to determine, and in inverting, reliability may will reduce if data quality is bad, this when usually requires
Stringent constraint is carried out, the undesirable of inversion result otherwise may be caused.Attribute related with seismic data quality includes
Imitate signal energy, frequency, noise energy, frequency, data signal-to-noise ratio etc., the measurement earthquake that can implement in the present invention accordingly
There are many quality methods of data, such as spectrum sigtral response method, relative resolution method of estimation, signal-noise ratio estimation method,
It can obtain the data information of quantitative measurement seismic data quality.
The embodiment of the present invention proposes a kind of reliable three parametric inversion side to the elastic wave wave equation based on VSP data
Method.The initial estimate of p-and s-wave velocity and density parameter is obtained when specifically can be first with travelling, according to data quality
The space fiducial range of three parameters is determined, and as the parameter value range in elastic wave wave equation inversion, according to elasticity
Wave wave equation carries out multi-parameter Simultaneous Retrieving using fast simulated annealing algorithm to zero bias VSP data, while obtaining more may be used
The p-and s-wave velocity and density parameter leaned on.Compared with conventional method, when this method takes full advantage of the travelling in VSP data and wave
Shape information effectively controls the search range of inverted parameters by the setting of inverted parameters confidence spatial dimension, is three parameters
Simultaneous Retrieving provides more reliable and effective constraint information, so as to pass through Seismic reflection character abundant in VSP data
More accurate p-and s-wave velocity and density parameter are obtained, is that the well under earthquake scale shakes Fine calibration and petrophysics property point
Analysis provides more structurally sound data basis, has weight for being based on seismic data and carrying out reservoir prediction and oil-gas possibility identification
The practical significance wanted
In some embodiments of the method provided by the invention, the realization step being referred in following application scenarios is real
Now obtain more accurate p-and s-wave velocity and density parameter：
1) estimation of longitudinal and shear wave primary travel time pickup and average speed.
In general, longitudinal wave energy in the vertical component of earthquake record is strong, and energy of the shear wave in horizontal component is strong.Cause
This, can utilize the vertical component of VSP data and horizontal component to pick up longitudinal wave and shear wave respectively in one embodiment of the application
Primary travel time, and longitudinal wave and shear wave can be calculated according to when travelling accordingly at the depth of receiving point and the depth location
Average speed.The embodiment is mainly to pick up the position of vertical shear wave waveform ski-jump in VSP data, obtains seismic wave and is receiving
The transmitted wave hourage in stratum more than point position, and according to the transmitted wave hourage and corresponding receiving point position
The depth at place calculates separately out the initial estimate of velocity of longitudinal wave, the initial estimate of shear wave velocity；Then utilize speed with it is close
The empirical relation spent between parameter obtains the initial estimate of density parameter.It should be noted that institute in this specification embodiment
State transmitted wave travelling when be exactly primary travel time, i.e., seismic wave from ground through earth-layer propagation to receiving point time, in VSP
Two concepts are the same in data, that is to say, that seismic wave is (first through the initial time for reaching receiving point behind stratum from ground
To when travelling), but there was only the concept of primary travel time in surface seismic exploration, only it is different earthquake data processing rank herein
The term of section is different.The empirical relation can be determined according to after existing well-log information statistical analysis.A specific embodiment party
In formula, following calculation formula may be used and estimate to obtain the average speed V of longitudinal wavea：
Wherein, x0The offset distance being expressed as between seismic wave excitation position and pithead position, h are expressed as seismic receiving position
Elevation from the ground is set, t is expressed as seismic wave from when position being excited to travel to the travelling from receiving point position.
It should be noted that can also be to utilize above-mentioned (1) this formula meter when seeking shear wave initial average speed
It obtains.
For the VSP datas offset distance used in the present embodiment implement scene for 50m, focus is hypocenter of the explosion.It can be first
First the VSP of vertical component is recorded and carries out uplink and downlink wavelength-division from recycling down going wave carries out first break pickup VSP data earthquake records
Vertical component and first arrival (in Fig. 2 shown in L1 lines) carry out longitudinal wave from down going wave later using the wavelength-division of vertical component uplink and downlink and pick up
It takes, the average speed of longitudinal wave is then calculated using above formula.Downlink of the horizontal component uplink and downlink wavelength-division of earthquake record from after
Wave such as Fig. 3.The speed of shear wave can be picked up in the embodiment of the present invention using the stronger converted shear wave of energy in horizontal component
Degree.From Fig. 3 (a), the stronger down going wave A and B of two energy is chosen, as can be seen that wherein A waves are apparent from Fig. 3 (a)
Through longitudinal wave, and then need to analyze the hourage that this two waves travel to same depth when judging converted wave, and utilize public affairs
Formula (1) estimates longitudinal wave average speed, is then determined as converted shear wave according to by the B waves near 0.6 times of A wave velocities.VSP is provided
After the direct wave of horizontal component is cut away in material, by uplink and downlink wavelength-division from the down going wave that can obtain horizontal classification as a result, such as Fig. 3
(b), when L2 lines are the converted shear wave travelling of pickup, so as to corresponding cross is calculated when being travelled based on the converted shear wave
Wave average speed., can be according to the statistical relationship between the p-and s-wave velocity being finally inversed by one embodiment of the application, and adopt
The shear wave velocity of shallow-layer is fitted with the statistical relationship.It can solve in this way in some complex environments because shallow-layer converted shear wave is unknown
Aobvious the problem of leading to not directly converted wave be utilized to seek shear wave velocity, and then improve the applicability and practicability of the application method.
It should be noted that：Formula (1) calculates the formula of average speed, is not only suitable for longitudinal wave and is also applied for shear wave.Exist in Fig. 3 (a)
Shear wave and longitudinal wave, to pick up the speed of converted shear wave using the figure, it is necessary first to distinguish longitudinal and shear wave.The present invention one
The stronger wave A and B of two energy can be chosen in embodiment, calculate separately out two average speeds using formula (1), A waves are bright
Aobvious is direct wave, and the speed of B waves is 0.6 times of A waves, judges that B waves are exactly converted shear wave in combination with vibration polarization direction, this
Sample can be obtained by the speed of converted shear wave by B waves.Numerical statistic relationship refers to the linear of velocity of longitudinal wave and shear wave velocity
Or nonlinear fitting relationship, it is intended to which the place for data missing obtains a basic numerical value by the fit correlation.0.6 times
Be a practical application uses in the present embodiment case data obtain as a result, common, as long as meeting the model of practical Poisson's ratio
It encloses, just the ratio of available velocity distinguishes longitudinal and shear wave.Therefore its range is mentioned above generally between 0.5-0.7, pass through
This range can more accurately go to determine whether shear wave.
2) velocity of longitudinal wave upper and lower limits are determined.
After having obtained longitudinal wave average speed when using travelling, average speed can be converted to interval velocity.Specifically, can be with
Using the interval velocity of following formula Different Stratas：
In above formula (2), V0For interval velocity, when n values 1, V0(1)=Va(1), Va is the flat of velocity of longitudinal wave or shear wave velocity
Equal speed, n indicate that n-th of stratum, t are expressed as seismic wave from when position being excited to travel to the travelling from receiving point position.
It should be noted that can also be to be calculated using above-mentioned (2) this formula when seeking shear wave initial interval velocity
It obtains.
The present invention determines velocity of longitudinal wave number when carrying out wave equation inversion using the P-wave interval velocity determined when travelling
Distribution value range.Determine what bound distribution can be realized by (3) formula, the Vp0 in formula and Vs0, the value of n can be with
It is the number of plies on the stratum from ground to seismic receiving point, is determined according to actual conditions, minimum 1, maximum is
The total number of plies in stratum.In specific implementation process, present invention introduces confidence spatial parameter λ, and inverting is waited in refutation process for characterizing
The maximum perturbation degree of parameter, the size of confidence spatial parameter are related with the quality of seismic data.When seismic data quality is higher,
Confidence spatial parameter can suitably become smaller, that is, when utilizing the travelling of the higher data of quality, the estimated value precision of obtained parameter compared with
Height, therefore when carrying out three parametric inversion of wave equation, effective search range of the parameter can be suitably reduced, so that the parameter is begun
Value is carried out in range estimation narrower range eventually, so as to effectively improve the stability of refutation process and the receipts of inverting
Hold back speed；Conversely, then needing to become larger in confidence space, to ensure true parameter value within the search range of inverting.This hair
The value of the confidence spatial parameter of the velocity of longitudinal wave used in bright one embodiment can be for：λp=5%, it may thereby determine that anti-
The up-and-down boundary range (dotted line in such as Fig. 4) of velocity of longitudinal wave parameter value during drilling：
Vph=Vp0(1+λp)
Vpl=Vp0(1-λp) (3)
Wherein, Vp0The estimated value of the P-wave interval velocity obtained when for using travelling, VphAnd VplRespectively velocity of longitudinal wave confidence is empty
Between range maximum and minimum value.
3) shear wave velocity upper and lower limits are determined.
Can be interval velocity by the rate conversion, then again into one on the basis of step 1) obtains shear wave average speed
Step determines the range of shear wave velocity.The precision of the shear wave velocity picked up when usually using travelling is high without velocity of longitudinal wave, because
The confidence spatial parameter λ of shear wave velocity in this one embodiment of the present of inventionsConfidence space compared to velocity of longitudinal wave can be set
Parameter becomes larger.The present embodiment can be according to the initial velocity value of Travel Time Inversion to shear wave velocity confidence spatial parameter λsIt is fitted
When estimation, you can the difference of velocity of longitudinal wave maximum value and minimum value obtained when using using travelling is as shear wave velocity confidence sky
Between the maximum value of range and the difference of minimum value, the value be 363.5m/s.It should be noted that an implementation provided by the present application
In example, when asking shear wave velocity confidence space, velocity of longitudinal wave is utilized as reference, it is assumed that the half for the difference that velocity of longitudinal wave is most worth
The difference being most worth for shear wave velocity, that is, being most worth between the maximum value of shear wave velocity and minimum value according to velocity of longitudinal wave
Difference, an only parameter, for determining the width of shear wave velocity range of disturbance, this belongs in specific implementation process
One embodiment way.The application is not excluded in other embodiments it is also assumed that specifying a range.One of the present invention
The half of the maximum value of the velocity of longitudinal wave obtained when can be using travelling in embodiment and the difference of minimum value takes as shear wave velocity
It is worth the reference value of domain of walker, and using the reference value and using the ratio of the shear wave velocity obtained when travelling as shear wave velocity
Confidence spatial parameter λsValue.Therefore one embodiment of the present of invention can be by λsIt is chosen for 15%.It is hereby achieved that horizontal
The confidence spatial dimension (dotted line in such as Fig. 5) of wave velocity parameter.Here 15% is obtained according to the data of actual treatment
Actual value.Here's a hypothesis is：The interval velocity of the shear wave obtained above is one smooth as a result, the result is downward upwards
The half of disturbance maximum value and minimum difference is exactly entire disturbance space.The difference of shear wave velocity being most worth is 363.5m/s,
The result that the half of the value divided by the interval velocity of shear wave obtain is about 15%, this certain numerical value can also change, in this example
It is determined according to real data situation, contributes to preferably to handle practical problem in this way.Specifically, provided by the present application one
In a embodiment, the up-and-down boundary range that following manner determines shear wave velocity parameter value may be used：
Determine the confidence spatial parameter λ of the shear wave velocity introducedsValue；
The up-and-down boundary range of shear wave velocity parameter value in refutation process is calculated using following formula：
Vsh=Vs0(1+λs)
Vsl=Vs0(1-λs)
Wherein, Vs0The estimated value of the shear wave velocity obtained when for using travelling, VshAnd VslRespectively shear wave velocity confidence space
The maximum and minimum value of range.
In general, shear wave velocity first arrival estimation is as velocity o P wave mode or substantially identical, region is two
The mode picked up when travelling is different.
4) density parameter upper and lower limits are determined.
Due to can not individually directly obtain the estimated value and its range of density parameter, the present invention one according to information when travelling
The statistical formula of velocity of longitudinal wave and density parameter may be used in the existing well-log information of the survey region to density number in a embodiment
Value unit is handled, which can be：
Wherein, a, b are according to velocity of longitudinal wave and density parameter statistics gained in real logging data, value.Vp0 is to utilize
The estimated value of the P-wave interval velocity obtained when travelling, a and b are the fitting systems of non-linear relation between velocity of longitudinal wave and density-velocity
Number, b are the exponential term of Vp0.One example value can be：
A=1.6289, b=0.2254,
The size of the two coefficients needs individually to count when handling data with different.According to formula (4) and utilize
The longitudinal wave initial velocity that Travel Time Inversion obtains can obtain the initial estimate ρ of density parameter0.Due to ρ0It is rule of thumb
Relationship obtains, in order to ensure that the confidence spatial dimension of density parameter can include actual value, density confidence space to greatest extent
λρIt cannot be too small.It therefore can be by λ in one embodiment of the present of inventionpAnd λsMaximum value as density confidence space be λρ,
That is λρ=15%, so as to obtain the confidence spatial dimension of density parameter.
ρh=ρ0h(1+λρ)
ρl=ρ0l(1-λρ) (6)
Wherein, ρ0hFor ρ0Maximum value, ρ0lFor ρ0Minimum value, ρhAnd ρlRespectively density parameter confidence spatial dimension
Maximum and minimum value (dotted line in such as Fig. 6), λρFor density confidence spatial parameter, value and λpAnd λsMaximum value it is equal.
5) p-and s-wave velocity and density parameter Simultaneous Retrieving object function are established.
The present invention using the wave character of VSP data come inverting p-and s-wave velocity and density when, it may be determined that three parameters
The object function of Simultaneous Retrieving, for weighing the matching degree between actual observation data and Wave equation forward modeling data.
Different object functions will produce different inversion results, in one embodiment provided by the invention, can consider L-2 models simultaneously
Number computational efficiency height and L-1 norms have the advantages that very strong noise resisting ability, and velocity of wave in length and breadth is established in conjunction with the characteristics of two norms
The object function of degree and three parameter synchronization invertings of density：
Wherein, d is the seismic data of observation；F is the result of elastic wave Wave equation forward modeling；α is constant, the constant
Depending on the quality of inverting data, when data quality is higher, can suitably take it is small, and when waiting for that inverted parameters spatial variations compare
It then needs to obtain bigger, in one embodiment, α=0.5 when acutely；F is object function, wherein velocity of longitudinal wave, shear wave velocity
With the inverting confidence spatial dimension of density parameter can according at least to step 2), 3), 4) in a determination.I.e. the present embodiment carries
The inversion objective function of confession can be the progress iterative numerical optimizing in effective confidence spatial dimension of three parameters, it is ensured that target
Function F reaches error minimum.S.T. indicate to mean that items listed behind are the related constraint and satisfaction of linear programming
Requirement condition, be the abbreviation of English word suject to, belong to the basic mathematical term in linear programming problem, herein
The meaning is exactly while meeting first formula again to minimize, and three parameters meet three formulas of ST listed thereafters respectively, from
And improve specific aim when object function solves.
6) the three parameter iteration invertings based on Fast simulating method.
In one embodiment of the present of invention, is establishing inversion objective function and p-and s-wave velocity and density parameter is determined
After confidence spatial dimension, fast simulated annealing algorithm may be used according to the object function determined in step 5) to zero bias VSP
Data carries out three parameter synchronization invertings.The p-and s-wave velocity and density (V that the initial model of inverting obtains when being using travellingp0,
Vs0,ρ0).In one embodiment, the annealing way used in simulated annealing can be for based on the realization of following formula：
T (K)=T0exp(-CK1/N)(8)
Wherein, K is iterations, and C is constant, and N is the number for waiting for inverted parameters, T0For initial temperature.The present invention is above-mentioned
In one embodiment of formula (8), C=1 may be used；N=3；T0=200；K=947.The corresponding model parameter for waiting for inverting
Iteration more new formula can be：
In above formula, miFor model variable before modification；mjFor model variable after modification；U is random number, and the random number is in [0,1]
It is uniformly distributed in range；[Ai,Bi] be model variable search space.Fig. 7 is to utilize three parameters of practical progress of the embodiment of the present invention
One schematic diagram of the process flow of calculating.In one example, inverting obtains that the results are shown in Figure 8, and solid line is using this hair
The obtained Zong ﹑ shear wave velocitys of bright method Simultaneous Retrieving and density parameter, wherein dotted line is only with the knot obtained when travelling
Fruit.There is Fig. 8, it is apparent that compared with when merely with travelling, longitudinal wave in the VSP data that the embodiment of the present invention obtains speed
Du ﹑ shear wave velocitys and density parameter change more reasonable, information when can more accurately reflect the travelling in VSP seismic datas
With seismic reflection feature.
The embodiment of the present invention proposes a kind of reliable three parametric inversion side to the elastic wave wave equation based on VSP data
Method.It can utilize when travelling and obtain the initial estimate of p-and s-wave velocity and density parameter, three ginsengs are determined according to data quality
Several space fiducial ranges, and as the parameter value range in elastic wave wave equation inversion.According to elastic wave wave equation
Multi-parameter Simultaneous Retrieving is carried out to zero bias VSP data using fast simulated annealing algorithm, while obtaining more structurally sound longitudinal and shear wave
Speed and density parameter.Compared with conventional method, when this method takes full advantage of the travelling in VSP data and shape information, lead to
The setting for crossing inverted parameters confidence spatial dimension effectively controls the search range of inverted parameters, is carried for the Simultaneous Retrieving of three parameters
More reliable and effective constraint information has been supplied, it is more smart so as to be obtained by Seismic reflection character abundant in VSP data
True p-and s-wave velocity and density parameter.Utilize embodiment three obtained parameter (velocity of longitudinal wave, shear wave provided by the invention
Speed and density parameter), under earthquake scale well shake Fine calibration and petrophysics property analysis provide it is more structurally sound
Data basis has important practical significance to carrying out based on seismic data for reservoir prediction and oil-gas possibility identification.
Based on same inventive concept, the device in a kind of embodiment provided by the present application is as described in the following examples.Institute
The device stated may include that the system (including distributed system) of this specification embodiment the method, software has been used (to answer
With), module, component, server, client etc. and combine the necessary apparatus for implementing hardware.Since device solves the problems, such as
Implementation it is similar to method, therefore the implementation of the specific device of the application may refer to the implementation of preceding method, repetition
Place repeats no more.Although preferably being realized with software with device described in following embodiment, hardware or software and
The combination of hardware being realized and may and being contemplated specific.The processing method that this specification embodiment provides can counted
Corresponding program instruction is executed to realize, such as using windows, the application programming of (SuSE) Linux OS by processor in calculation machine
Language is realized at the ends PC or the necessary hardware of the corresponding application design language set of other such as android, iOS system is real
It is existing, or realization of the processing logic based on quantum computer etc..Specifically, the application provides a kind of VSP based on wave equation
Three parameter synchronization inversion procedure devices, including processor and the memory for storing computer executable instructions, the processor
It is realized when executing described instruction：
The initial estimate of three parameters, the three parameters packet are obtained using the primary travel time Inversion Calculation in VSP data
Include velocity of longitudinal wave, shear wave velocity, density parameter；
The confidence of velocity of longitudinal wave, shear wave velocity and density parameter in refutation process is determined according to the quality of seismic data
Spatial dimension, as the parameter up-and-down boundary range in wave equation inversion；
Establish the object function of the three parameter synchronizations inverting for VSP observational datas；
The wave equation inversion of three parameters is carried out to the object function of foundation using fast simulated annealing algorithm, at least
Obtain a parameter after velocity of longitudinal wave, shear wave velocity, density parameter Simultaneous Retrieving.
It should be noted that the device described in this specification above-described embodiment, also according to the description of related method embodiment
May include other embodiments.Concrete implementation mode is referred to the description of embodiment of the method, does not go to live in the household of one's in-laws on getting married one by one herein
It states.
The embodiment of the method that the embodiment of the present application is provided can be in mobile terminal, terminal, server or class
As execute in arithmetic unit.For running on the server, Fig. 9 is a kind of based on wave equation of the embodiment of the present invention
The hardware block diagram of tri- parameter synchronization inversion procedure devices of VSP.As shown in figure 9, server 9 may include one or more
(processor 102 can include but is not limited to Micro-processor MCV or programmable logic device to (one is only shown in figure) processor 102
The processing unit of part FPGA etc.), memory 104 for storing data and the transmission module 106 for communication function.This
Field those of ordinary skill is appreciated that structure shown in Fig. 9 is only to illustrate, and is not caused to the structure of above-mentioned electronic device
It limits.For example, server 10 may also include more than shown in Fig. 9 or less component, such as can also include others
Handle hardware, such as GPU (Graphics Processing Unit, image processor), display, or with shown in Fig. 9
Different configurations.
Memory 104 can be used for storing the software program and module of application software, such as the search in the embodiment of the present invention
Corresponding program instruction/the module of method, processor 102 are stored in software program and module in memory 104 by operation,
To perform various functions application and data processing, that is, realize the processing method of above-mentioned navigation interactive interface content displaying.It deposits
Reservoir 104 may include high speed random access memory, may also include nonvolatile memory, as one or more magnetic storage fills
It sets, flash memory or other non-volatile solid state memories.In some instances, memory 104 can further comprise relative to place
The remotely located memory of device 102 is managed, these remote memories can pass through network connection to terminal 10.Above-mentioned network
Example include but not limited to internet, intranet, LAN, mobile radio communication and combinations thereof.
Transmission module 106 is used to receive via a network or transmission data.Above-mentioned network specific example may include
The wireless network that the communication providers of terminal 10 provide.In an example, transmission module 106 includes that a network is suitable
Orchestration (Network Interface Controller, NIC), can be connected with other network equipments by base station so as to
Internet is communicated.In an example, transmission module 106 can be radio frequency (Radio Frequency, RF) module,
For wirelessly being communicated with internet.
Each embodiment in this specification is described in a progressive manner, identical similar portion between each embodiment
Point just to refer each other, and each embodiment focuses on the differences from other embodiments.Especially for hardware+
For program class embodiment, since it is substantially similar to the method embodiment, so description is fairly simple, related place is referring to side
The part of method embodiment illustrates.
It is above-mentioned that this specification specific embodiment is described.Other embodiments are in the scope of the appended claims
It is interior.In some cases, the action recorded in detail in the claims or step can be come according to different from the sequence in embodiment
It executes and desired result still may be implemented.In addition, the process described in the accompanying drawings not necessarily require show it is specific suitable
Sequence or consecutive order could realize desired result.In some embodiments, multitasking and parallel processing be also can
With or it may be advantageous.
Although mentioning the estimation of different p-and s-wave velocities and density, calculating and upper and lower limits in teachings herein to determine
Formula and mode, still, the application are not limited to be situation described in embodiment etc., certain professional standards, usually
Embodiment modified slightly can also be realized on formula or the practice processes described using self-defined mode or embodiment
Above-described embodiment is identical, after equivalent or close or deformation it is anticipated that implementation result.Using these modifications or deformed data
The embodiment of the acquisitions such as acquisition, processing mode still may belong within the scope of the optional embodiment of the application.
The device that above-described embodiment illustrates can specifically be realized by computer chip or entity.Those skilled in the art
Know, it, completely can be by the way that method and step be carried out other than realizing controller in a manner of pure computer readable program code
Programming in logic makes the controller with logic gate, switch, application-specific integrated circuit, programmable logic controller (PLC) and embedded microcontroller
Deng form realize identical function.Therefore this controller is considered a kind of hardware component, and includes to its inside
The device for realizing various functions can also be considered as the structure in hardware component.It or even, can will be for realizing each
The device of kind function is considered as either the software module of implementation method can be the structure in hardware component again.
The application can describe in the general context of computer-executable instructions executed by a computer, such as program
Module.Usually, program module includes routines performing specific tasks or implementing specific abstract data types, program, object, group
Part, data structure, class etc..The application can also be put into practice in a distributed computing environment, in these distributed computing environments,
By executing task by the connected remote processing devices of communication network.In a distributed computing environment, program module can
With in the local and remote computer storage media including storage device.
As seen through the above description of the embodiments, those skilled in the art can be understood that the application can
It is realized by the mode of software plus required general hardware platform.Based on this understanding, the technical solution essence of the application
On in other words the part that contributes to existing technology can be expressed in the form of software products, the computer software product
It can be stored in a storage medium, such as ROM/RAM, magnetic disc, CD, including some instructions are used so that a computer equipment
(can be personal computer, mobile terminal, server either network equipment etc.) executes each embodiment of the application or implementation
Method described in certain parts of example.
Each embodiment in this specification is described by the way of progressive, same or analogous portion between each embodiment
Point just to refer each other, and each embodiment focuses on the differences from other embodiments.The application can be used for crowd
In mostly general or special purpose computing system environments or configuration.Such as：Personal computer, server computer, handheld device or
Portable device, laptop device, multicomputer system, microprocessor-based system, set top box, programmable electronics set
Standby, network PC, minicomputer, mainframe computer include the distributed computing environment etc. of any of the above system or equipment.
Although depicting the application by embodiment, it will be appreciated by the skilled addressee that the application there are many deformation and
Variation is without departing from spirit herein, it is desirable to which the attached claims include these deformations and change without departing from the application's
Spirit.
Claims (11)
1. a kind of tri- parameter synchronization inversion methods of VSP based on wave equation, which is characterized in that the method includes：
The initial estimate of three parameters, three parameter packets are obtained using the primary travel time Inversion Calculation in VSP data
Include velocity of longitudinal wave, shear wave velocity, density parameter；
The confidence space of velocity of longitudinal wave, shear wave velocity and density parameter in refutation process is determined according to the quality of seismic data
Range, as the parameter up-and-down boundary range in wave equation inversion；
Establish the object function of three parameter synchronization invertings for VSP data；
The wave equation inversion for being carried out three parameters to the object function of foundation using fast simulated annealing algorithm, is indulged
Three wave velocity, shear wave velocity, density parameters.
2. the method as described in claim 1, which is characterized in that the primary travel time Inversion Calculation in the data using VSP
The initial estimate for obtaining three parameters includes：
The position for picking up vertical shear wave waveform ski-jump in VSP data, obtains in stratum of the seismic wave more than receiving point position
Transmitted wave hourage；
According to the depth at the transmitted wave hourage and corresponding receiving point position, the initial of velocity of longitudinal wave is calculated separately out
The initial estimate of estimated value, shear wave velocity；
Using between speed and density parameter empirical relation obtain density parameter initial estimate, the empirical relation according to
It is determined after existing well-log information statistical analysis.
3. method as claimed in claim 2, which is characterized in that velocity of longitudinal wave, shear wave is calculated using following calculation formula
The average speed V of speeda：
Wherein, Va is the average speed of velocity of longitudinal wave or shear wave velocity, x0It is expressed as between seismic wave excitation position and pithead position
Offset distance, h is expressed as the elevation of seismic receiving position from the ground, and t indicates that seismic wave travels to receiving point from excitation position
When travelling at position.
4. method as claimed in claim 3, which is characterized in that determine the interval velocity of Different Strata using following calculation formula：
In above formula, V0For interval velocity, when n values 1, V0(1)=Va(1), Va is the average speed of velocity of longitudinal wave or shear wave velocity, n
Indicate that n-th of stratum, t are expressed as seismic wave from when position being excited to travel to the travelling from receiving point position.
5. method as claimed in claim 4, which is characterized in that determine the upper and lower of velocity of longitudinal wave parameter value using following manner
Bounds：
Determine the confidence spatial parameter λ of the velocity of longitudinal wave introducedpValue；
The up-and-down boundary range of velocity of longitudinal wave parameter value in refutation process is calculated using following formula：
Vph=Vp0(1+λp)
Vpl=Vp0(1-λp)
In above formula, Vp0The estimated value of the P-wave interval velocity obtained when for using travelling, VphAnd VplRespectively velocity of longitudinal wave confidence space
The maximum and minimum value of range.
6. method as claimed in claim 5, which is characterized in that determine the upper and lower of shear wave velocity parameter value using following manner
Bounds：
Determine the confidence spatial parameter λ of the shear wave velocity introducedsValue；
The up-and-down boundary range of shear wave velocity parameter value in refutation process is calculated using following formula：
Vsh=Vs0(1+λs)
Vsl=Vs0(1-λs)
Wherein, Vs0The estimated value of the shear wave velocity obtained when for using travelling, VshAnd VslRespectively shear wave velocity confidence spatial dimension
Maximum and minimum value.
7. method as claimed in claim 6, which is characterized in that the confidence spatial parameter λ of the determining shear wave velocity introduceds
Value include：
The half of the maximum value of the velocity of longitudinal wave obtained when using travelling and the difference of minimum value is as shear wave velocity value floating model
The reference value enclosed, and using the reference value and using the ratio of the shear wave velocity obtained when travelling as the confidence of shear wave velocity sky
Between parameter lambdasValue.
8. method as claimed in claim 6, which is characterized in that it is described according to the quality of seismic data come determine velocity of longitudinal wave,
The confidence spatial dimension of shear wave velocity and density parameter in refutation process includes：
Density values are handled using the statistical formula of velocity of longitudinal wave and density parameter, which is：
Wherein, the initial estimate of density parameter is ρ0, a, b are according to the velocity of longitudinal wave and density parameter system in real logging data
Meter gained, Vp0The estimated value of the P-wave interval velocity obtained when for using travelling, a and b are non-thread between velocity of longitudinal wave and density-velocity
The fitting coefficient of sexual intercourse, b are the exponential term of Vp0；
The confidence spatial dimension of density parameter is：
ρh=ρ0h(1+λρ)
ρl=ρ0l(1-λρ)
Wherein, ρ0hFor ρ0Maximum value, ρ0lFor ρ0Minimum value, ρhAnd ρlThe respectively maximum of density parameter confidence spatial dimension
And minimum value, λρFor density confidence spatial parameter, value and λpAnd λsMaximum value it is equal.
9. method as claimed in claim 8, which is characterized in that the foundation is same for three parameter of VSP observational datas
Step inverting object function include：
Establish the object function of three parameter synchronization invertings of p-and s-wave velocity and density：
Wherein, d is the seismic data of observation；F is elastic wave Wave equation forward modeling as a result, α is constant, which depends on
In the quality of inverting data, F is object function, and S.T. indicates to mean the correlation that items listed behind are linear programming
Constraint and the requirement condition met.
10. method as claimed in claim 9, which is characterized in that it is described using fast simulated annealing algorithm to described in foundation
Object function carry out three parameters wave equation inversion include：
The annealing way used in simulated annealing is based on the realization of following formula：
T (K)=T0exp(-CK1/N)
Wherein, K is iterations, and C is constant, and N is the number for waiting for inverted parameters, T0For initial temperature；The corresponding mould for waiting for inverting
The iteration of shape parameter more new formula is：
In above formula, miFor model variable before modification；mjFor model variable after modification；U is random number, and the random number is in [0,1] range
Inside it is uniformly distributed；[Ai,Bi] be model variable search space.
11. a kind of tri- parameter synchronization inversion procedure devices of VSP based on wave equation, which is characterized in that including processor and
The memory of computer executable instructions is stored, the processor is realized any one in claim 1-10 when executing described instruction
The execution step of item the method.
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| CN110954950A (en) * | 2019-10-31 | 2020-04-03 | 南方科技大学 | Underground transverse wave velocity inversion method, device, computing equipment and storage medium |
| CN111399045A (en) * | 2020-04-13 | 2020-07-10 | 北京中恒利华石油技术研究所 | Post-stack density inversion method based on statistical constraint |
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| CN113640871A (en) * | 2021-08-10 | 2021-11-12 | 成都理工大学 | Seismic wave impedance inversion method based on heavily-weighted L1 norm sparse constraint |
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| CN113640871A (en) * | 2021-08-10 | 2021-11-12 | 成都理工大学 | Seismic wave impedance inversion method based on heavily-weighted L1 norm sparse constraint |
| CN113640871B (en) * | 2021-08-10 | 2023-09-01 | 成都理工大学 | Seismic wave impedance inversion method based on re-weighted L1 norm sparse constraint |
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