CN106569262A - Background speed model reconstructing method in absence of low frequency earthquake data - Google Patents

Abstract

The invention relates to a background speed model reconstructing method in absence of low frequency earthquake data. The method comprises the following steps: in step 1), a phase position fitting cross correlation object general function is built for windowing normalization non-zero delay according to an observed earthquake data envelope and a simulative earthquake data envelope based on an initial speed model; in step 2), a corresponding inverse time propagation accompanying seismic center is built based on the cross correlation object general function; in step 3), back propagation of the accompanying seismic center is used for solving an accompanying wave field, envelope inversion is conducted, the initial speed model is reconstructed, and the speed model which is reconstructed in absence of the low frequency data can be obtained; in step 4), precision of the envelope inversion is verified, and the reconstructed speed model is used as the initial speed model and traditional wave equation chromatography operation is performed when the precision meets requirements.

Description

Background velocity model reconstruction method under low frequency seismic data disappearance

Technical field

The present invention relates to oil seismic exploration field, more particularly, to the back of the body under low frequency seismic data disappearance Scape rate pattern reconstructing method.

Background technology

Traditional Full wave shape chromatographic technique based on wave equation due to its utilize earthquake data before superposition kinesiology and Dynamic information, matches waveform, amplitude and the phase information of seismic wave in refutation process, thus has Higher resolution, it is considered to be velocity modeling precision highest method.Due to matching all of letter of seismic wave Breath, when the geological data recorded using complex model carries out inverting, the technology is the nonlinear problem of a height, Cost functional often has substantial amounts of local minimum, and the precision of its inverting depends critically upon initial model Precision (Bunk etc. 1995).In order to weaken (1995) such as the non-linear property of inverting, Bunks, Sigure and Angles of the Pratt (2004) respectively from time and space domain and frequency space domain gives many chis from low to high Degree refutation strategy.Baeten etc. (2013) points out the data pair of 1.5Hz to the 2.0Hz in actual seismic data Vital effect is played in underground medium macroscopic model is recovered.But actual seismic data often lacks The low-frequency information of weary below 5Hz, or low-frequency range unreliable information, thus the geological data lacked using low frequency Carrying out multiple dimensioned Full wave shape chromatographic technique cannot also make inversion result converge to global minimum.

Wu and Luo (2013) goes often to solve using the envelope inverting of data residual error form in field of seismic exploration The inversion result instability problem that rule time domain wave equation chromatography is caused due to geological data low frequency disappearance. In seismic data acquisition process, due to by source level, focus response, top layer attenuation by absorption, various noises The impact such as interference, mechanism of transmission, geologic(al) factor and geophone coupling effect, land seismic data focus and inspection Wave point energy unbalanced phenomena is extremely serious, even if adopting earth surface consistency vibration amplitude compensation, the energy of different focus Amount is also up to an order of magnitude.Envelope inverting can be made using the envelope residual error inverting of various amplitude amount of energy level Solution it is unstable, and when envelope time delay more than envelope signal half period when, envelope inverting is also same Sample is faced with the risk for being absorbed in local extremum.

The content of the invention

For this purpose, the present invention provides a kind of envelope inverting based on normalization nonzero-lag phase-fitting, to reconstruct Initial macroscopic rate pattern, weakens the defect that traditional wave equation chromatography is highly relied on to low frequency, and And make the technology be more applicable for the inverting of land seismic data, improve its robustness.

On the one hand a kind of background velocity model reconstruction method under low frequency seismic data disappearance, the method are proposed Comprise the following steps：1) the simulation earthquake number according to the envelope of observation geological data and based on initial velocity model According to envelope, build adding window normalization nonzero-lag phase-fitting mutually related objects functional；2) based on described Mutually related objects functional builds corresponding inverse time propagation with focus；3) using described with focus back propagation Solve with wave field, and carry out envelope inverting, so as to be reconstructed to the initial velocity model, obtain low Frequency is according to the rate pattern after reconstructing under deletion condition；4) precision of envelope inverting is verified, meeting in precision will In the case of asking, traditional wave equation chromatography is carried out using the rate pattern after reconstruct as initial velocity model.

The invention belongs to the sane macroscopic under low frequency seismic data deletion condition in oil seismic exploration field Velocity modeling method.Chromatograph for Conventional temporal domain wave equation and model in actual land data high precision velocity During heavy dependence geological data low-frequency information, and as earth's surface is inconsistent, focus and cymoscope energy not Inverting instability problem caused by balanced, the present invention are given based on adding window normalization nonzero-lag phase-fitting Envelope data inversion method, weakens the defect that traditional wave equation chromatography is highly relied on to low frequency, and makes this Technology is more applicable for the inverting of land seismic data, improves its robustness.

Description of the drawings

Disclosure illustrative embodiments are described in more detail by combining accompanying drawing, the disclosure it is above-mentioned And other purposes, feature and advantage will be apparent from, wherein, in disclosure illustrative embodiments In, identical reference number typically represents same parts.

Fig. 1 shows the background velocity model under a kind of low frequency seismic data disappearance according to embodiments of the present invention The flow chart of reconstructing method；

Fig. 2 shows the schematic diagram of low frequency disappearance Ricker wavelet and its envelope；

Fig. 3 shows that low frequency disappearance wavelet is just drilling big gun collection；

Fig. 4 shows big gun collection envelope natural logrithm；

Fig. 5 shows true Marmousi models；

Fig. 6 shows normal gradient initial model；

Fig. 7 shows traditional L2 norms wave equation tomographic inversion result；

Fig. 8 shows adding window nonzero-lag normalization phase-fitting envelope inversion result；

Fig. 9 shows envelope inverting+tradition L2 norm wave equation tomographic inversion result；

Figure 10 shows the normalized autocorrelation of observation geological data envelope and observation geological data envelope；

Figure 11 shows the normalized crosscorrelation of observation geological data envelope and initial model analog data envelope；

Figure 12 shows that the normalization for observing geological data envelope and envelope inverse model analog data envelope is mutual Close.

Specific embodiment

The preferred implementation of the disclosure is more fully described below with reference to accompanying drawings.Although showing in accompanying drawing The preferred implementation of the disclosure, however, it is to be appreciated that may be realized in various forms the disclosure and should not be by Embodiments set forth herein is limited.Conversely, thesing embodiments are provided so that the disclosure is more saturating It is thorough and complete, and the scope of the present disclosure intactly can be conveyed to those skilled in the art.

Fig. 1 shows the background velocity model under a kind of low frequency seismic data disappearance according to embodiments of the present invention The flow chart of reconstructing method, the method are comprised the following steps.

Step 101, the envelope according to observation geological data and the simulation geological data based on initial velocity model Envelope, builds the phase-fitting mutually related objects functional of adding window normalization nonzero-lag:

In formula, χ_XcorNenlogFor the normalized crosscorrelation cost functional of earthquake envelope natural logrithm, which can be to add The phase-fitting mutually related objects functional of window normalization nonzero-lag, (τ is h) observation geological data to XcorNen1og The Normalized Cross Correlation Function of envelope natural logrithm and simulation geological data envelope natural logrithm.P (τ) is weighting Time histories sample, τ are time shift amount, and to observe geological data, y (t, h) is simulation geological data, u to u (t, h)_H(t,h) To observe the Hilbert transform of geological data, y_H(t, h) is the Hilbert transform for simulating geological data, e_obs(t, h) be observe geological data envelope, e_syn(t, h) be simulate geological data envelope, c be in order to avoid Natural logrithm antilog is a constant of zero introducing, and h represents the sequence number of cymoscope.Can be permitted using the cost functional Perhaps the envelope delay time for observing data and analog data is more than half envelope cycle, so that inverting is more steady It is strong, it is to avoid the requirement based on envelope residual error to Phase delay in half period.

Step 102, builds corresponding inverse time propagation with shake according to the mutually related objects functional that step 101 is provided Source.

According to the research of Tromp etc. (2005) et al., for different Data Matching, no matter being to solve for two The similarity degree of the residual error of individual signal or two signals, the solution expression formula of gradient is identical, is all adopted Tried to achieve with the adjoint wave field cross-correlation superposition that forward-propagating wave field and inverse time propagate.Unlike unique, for Different Signal Matching modes, the adjoint focus item of adjoint equation right-hand member are differed.The present embodiment can be based on each Realize to the ACOUSTIC WAVE EQUATION in same sex medium, the sound wave for adopting with regard to rate pattern pressure gradient expression formula for：

Wherein Ns represents the number of focus, v_pFor rate pattern, ρ is underground medium model,For positive biography The Particle Vibration Velocity wavefield component broadcast, the adjoint pressure wavefield component that Q was propagated for the inverse time, is represent focus Index, x_iX is represented, y, z direction coordinate, T represent the maximum moment of propagation.

In order to accurately solve ladder of the normalization nonzero-lag envelope mutually related objects functional with regard to rate pattern Degree, needs accurately to solve with wave field.And solved by adjoint equation with wave field, itself and forward direction are passed The ACOUSTIC WAVE EQUATION broadcast is consistent, the focus item of unique except for the difference that right-hand member.Therefore accurately derive corresponding adjoint Focus is very necessary.Can be solved with regard to the gradient for simulating wave field by cost functional with focus：

Can obtain through a series of mathematical derivations：

WhereinTo observe the envelope of geological data With the cross-correlation of the envelope of simulation geological data.Hilbert represents the Hilbert transform of signal.

It is corresponding with focus to be：

Step 103, is solved with wave field using the adjoint focus back propagation for building, and carries out envelope inverting, So as to be reconstructed to initial velocity model, the rate pattern after reconstruct under low-frequency data deletion condition is obtained；

When solving with wave field using the Acoustic Wave-equation in isotropic medium, wherein u (x, t) is represented With wave field：

In formula：

Inverses of the wherein b for density, κ is bulk moduluses, u (x, t)=[v_x(x,t),v_y(x,t),v_z(x,t),p(x,t)]^T, S (x, t)=[0,0,0, Adjsource]^T.▽ represents the derivative to space,It is the derivative to x directions,It is Derivative to y directions,Represent the derivative to z directions.v_x(x,t),v_y(x,t),v_z(x, t), is x respectively, y, z direction Particle vibration velocity with wave field, p (x, t) is with stress wave field.It is the time with wave field Derivative (abbreviated form).

The inverting flow process that envelope inverting of the present invention is adopted is consistent with traditional wave equation waveform tomography flow process, envelope Inverting can adopt fore condition LBFGS optimized algorithms, may also be employed intend newton fore condition PLBFGS algorithms with The rate of convergence of inverting is improved, is to weaken spherical diffusion effect, balance model deep layer and shallow-layer speed renewal amount, The precondition operator that the present embodiment is adopted can be for：

In formula, z represents depth.

Step 104, verifies the precision of envelope inverting, in the case where precision meets requirement, the speed after reconstruct Degree model carries out traditional wave equation chromatography as initial velocity model.

In one example, mould can be obtained to the rate pattern forward simulation after reconstruct on the basis of step 103 Intend geological data, and solve its envelope, with the envelope of the envelope and the simulation geological data of observation geological data Carry out adding window normalization zero-lag cross-correlation, and with the adding window normalization zero-lag of observation geological data envelope from Correlation is contrasted, and verifies the precision of envelope inverting, with the model matter that the inverting of quality monitoring Jing envelopes is reconstructed The quality of amount.Result of the comparison is closer to the precision for representing envelope inverting is higher.

In another example, can be with the rate pattern after reconstruct is as initial velocity model and carries out conventional ripple After dynamic equation chromatography, if tomographic results do not have noise, then it represents that the precision of envelope inverting meets requirement, if going out Existing noise is then unsatisfactory for requiring.Those skilled in the art can carry out the judgement of noise using any means known.

In one example, when the precision of envelope inverting is unsatisfactory for requiring, modification initial velocity model is again Execution step 101, or modification inverted parameters, re-execute step 103；Want when the precision of envelope inverting meets When asking, traditional wave equation chromatography is carried out using envelope inversion result as initial velocity model, complete final Velocity modeling.Fore condition PLBFGS optimized algorithms can be equally adopted when traditional wave equation is chromatographed.

Due to the restriction of acquisition technique, seismic prospecting is difficult the low-frequency information component that recorded below 5Hz, profit When the geological data lacked with low frequency carries out traditional time domain wave equation waveform tomography, inversion result can fall into Enter local extremum, it is impossible to obtain accurate inversion speed model.Other actual seismic data shot point geophone station energy Amount is unbalanced serious, and earthquake envelope time delay is when being more than envelope half period, using the bag of envelope residual error It is unstable that network inverting can also become, it is impossible to adapts to the macro-scale velocity modeling of land seismic data.For this Invention provides a kind of envelope inversion method based on normalization nonzero-lag phase-fitting, and the method is used for earthquake Macromodel when data low frequency is lacked builds, and weakens traditional wave equation chromatography and low frequency height dependence is lacked Fall into, and the introducing of normalization nonzero-lag phase-fitting makes the technology time delay of envelope be allowed more than bag The half period of network signal, which is more sane effective to make the present invention.The present invention can be traditional land data ripple Dynamic equation chromatographic technique provides an accurately initial velocity model comprising lower wave number information, and then makes tradition Wave equation chromatography converges to global minimum solution.

Compared with existing disclosed technology, the invention has the beneficial effects as follows：Employ adding window normalization non-zero to prolong Slow phase-fitting mutually related objects functional, can process simulation earthquake envelope big with the time delay of observation data envelopment In half envelope cycle this situation, the robustness of envelope inverting, and the introducing of normalized crosscorrelation are improve Real data focus and the unbalanced inverting noise for causing of cymoscope envelope energy can be effectively suppressed, by this Bright can be that traditional wave equation tomographic inversion is built comprising accurate lower wave number under real data low frequency deletion condition The initial background rate pattern of information, is that the high precision velocity modeling of real data lays the foundation.

Using example

For ease of understanding the scheme and its effect of the embodiment of the present invention, one is provided specifically below in conjunction with Fig. 2-12 Using example.It will be understood by those skilled in the art that the example is of the invention only for the purposes of understanding, its any tool Body details is not intended to limit the present invention by any way.

This using example by low frequency disappearance Ricker wavelet as a example by, Fig. 2 show low frequency disappearance Ricker wavelet and its The schematic diagram of envelope；Fig. 3 shows that low frequency disappearance wavelet is just drilling big gun collection；Fig. 4 shows big gun collection envelope nature Logarithm；Fig. 5 shows true Marmousi models；Fig. 6 shows normal gradient initial model；Fig. 7 is illustrated Traditional L2 norms wave equation tomographic inversion result；Fig. 8 shows that adding window nonzero-lag normalization phase place is intended Close envelope inversion result；Fig. 9 shows envelope inverting+tradition L2 norm wave equation tomographic inversion result； Figure 10 shows the normalized autocorrelation of observation geological data envelope and observation geological data envelope；Figure 11 shows The normalized crosscorrelation of observation geological data envelope and initial model analog data envelope is gone out；Figure 12 shows The normalized crosscorrelation of observation geological data envelope and envelope inverse model analog data envelope.

Specifically, Fig. 7 is that the routine fluctuations equation carried out using the normal gradient initial model of Fig. 6 is chromatographed instead Result is drilled, it can be seen from figure 7 that when low-frequency data is lacked, occurring noise in inversion result, is affected The precision of inverting.And this application example, carry out adding window non-zero and prolong initially with the normal gradient initial model of Fig. 6 The phase-fitting envelope inverting of normalization late, obtains underground medium macromodel (Fig. 8), afterwards with shown in Fig. 8 Model as initial model and then traditional wave equation tomographic inversion is carried out, obtain Fig. 9, from Fig. 9 and Tu 7 Comparative results can be seen that the noise of Fig. 9 substantially without and matching more with Fig. 5 (true model) It is good.

The disclosure can be system, method and/or computer program.Computer program can include Computer-readable recording medium, containing the computer for being used to make processor realize various aspects of the disclosure Readable program instructions.

Computer-readable recording medium can be to keep and store the instruction used by instruction execution equipment Tangible device.Computer-readable recording medium can for example be-- but be not limited to-- storage device electric, Magnetic storage apparatus, light storage device, electromagnetism storage device, semiconductor memory apparatus or above-mentioned any conjunction Suitable combination.The more specifically example (non exhaustive list) of computer-readable recording medium includes：It is portable Formula computer disks, hard disk, random access memory (RAM), read only memory (ROM), erasable type can Program read-only memory (EPROM or flash memory), static RAM (SRAM), portable pressure Contracting disk read only memory (CD-ROM), digital versatile disc (DVD), memory stick, floppy disk, machinery are compiled Decoding apparatus, the punch card for being for example stored thereon with instruction or groove internal projection structure and above-mentioned any conjunction Suitable combination.Computer-readable recording medium used herein above is not construed as instantaneous signal itself, such as The electromagnetic wave of radio wave or other Free propagations, the electromagnetic wave propagated by waveguide or other transmission mediums (for example, by the light pulse of fiber optic cables) or the signal of telecommunication by wire transfer.

Computer-readable program instructions as described herein can download to each from computer-readable recording medium Calculating/processing equipment, or downloaded by network, such as the Internet, LAN, wide area network and/or wireless network To outer computer or External memory equipment.Network can include copper transmission cable, fiber-optic transfer, wireless biography Defeated, router, fire wall, switch, gateway computer and/or Edge Server.Each calculates/processes and sets Adapter or network interface in standby receives computer-readable program instructions from network, and forwards the meter Calculation machine readable program instructions, for being stored in the computer-readable recording medium in each calculating/processing equipment.

Computer program instructions for performing disclosure operation can be assembly instruction, instruction set architecture (ISA) instruction, machine instruction, machine-dependent instructions, microcode, firmware instructions, condition setup data, Or the source code write with the combination in any of one or more programming language or object code, the programming language Speech includes OO programming language-Smalltalk, C++ etc., and the process type programming language of routine Speech-such as " C " language or similar programming language.Computer-readable program instructions fully can be counted in user Perform on calculation machine, partly perform on the user computer, performing as an independent software kit, part Part performs or completely on remote computer or server on the remote computer on the user computer Perform.In the situation of remote computer is related to, remote computer can be by the network-bag of any kind LAN (LAN) or wide area network (WAN)-be connected to subscriber computer are included, or, it may be connected to outside meter Calculation machine (such as using ISP come by Internet connection).In certain embodiments, pass through Using the status information of computer-readable program instructions come personalized customization electronic circuit, such as FPGA Circuit, field programmable gate array (FPGA) or programmable logic array (PLA), the electronic circuit can To perform computer-readable program instructions, so as to realize various aspects of the disclosure.

Referring herein to the stream of the method according to the embodiment of the present disclosure, device (system) and computer program Journey figure and/or block diagram describe various aspects of the disclosure.It should be appreciated that each side of flow chart and/or block diagram The combination of each square frame in frame and flow chart and/or block diagram, can be realized by computer-readable program instructions.

These computer-readable program instructions can be supplied to general purpose computer, special-purpose computer or other can compile The processor of journey data processing equipment, so as to produce a kind of machine so that these instructions are by computer Or other programmable data processing units computing device when, generate in flowchart and/or block diagram The device of function/action specified in one or more square frames.Can also be these computer-readable program instructions Storage in a computer-readable storage medium, these instruct cause computer, programmable data processing unit and/ Or other equipment is worked in a specific way, so as to the computer-readable medium of the instruction that is stored with then includes one Manufacture, which includes flowchart and/or function/action specified in one or more square frames in block diagram The instruction of various aspects.

Can also computer-readable program instructions be loaded into computer, other programmable data processing units, Or on miscellaneous equipment so that one is performed on computer, other programmable data processing units or miscellaneous equipment Series of operative steps, to produce computer implemented process, so that in computer, other programmable numbers According to one or more sides in the instruction flowchart and/or block diagram performed in processing meanss or miscellaneous equipment Function/action specified in frame.

Flow chart and block diagram in accompanying drawing shows system, method and the meter of the multiple embodiments according to the disclosure The architectural framework in the cards of calculation machine program product, function and operation.At this point, flow chart or block diagram In each square frame can represent the part of module, program segment or an instruction, the module, program segment Or a part for instruction is used for the executable instruction of the logic function that realization specifies comprising one or more.Having In a little realizations as replacement, the function of being marked in square frame can also be with suitable different from what is marked in accompanying drawing Sequence occurs.For example, two continuous square frames can essentially be performed substantially in parallel, and they sometimes can also Perform in the opposite order, this is depending on involved function.It is also noted that block diagram and/or flow chart In each square frame and block diagram and/or the square frame in flow chart combination, can use perform regulation function Or the special hardware based system of action is realizing, or specialized hardware can be used with computer instruction Combine to realize.

It is described above the presently disclosed embodiments, described above is exemplary, and non-exclusive, And it is also not necessarily limited to disclosed each embodiment.In the scope and spirit without departing from illustrated each embodiment In the case of, many modifications and changes will be apparent from for those skilled in the art. The selection of term used herein, it is intended to best explain the principle of each embodiment, practical application or to market In technology technological improvement, or other those of ordinary skill of the art is understood that Each embodiment.

Claims (10)

1. a kind of background velocity model reconstruction method under low frequency seismic data is lacked, the method include following step Suddenly：

1) envelope of envelope according to observation geological data and the simulation geological data based on initial velocity model, Build the phase-fitting mutually related objects functional of adding window normalization nonzero-lag；

2) corresponding inverse time propagation is built with focus based on the mutually related objects functional；

3) solved with wave field with focus back propagation using described, and carry out envelope inverting, so as to institute State initial velocity model to be reconstructed, obtain the rate pattern after reconstruct under low-frequency data deletion condition；

4) precision of envelope inverting is verified, in the case where precision meets requirement, the rate pattern after reconstruct Traditional wave equation chromatography is carried out as initial velocity model.

2. the background velocity model reconstruction method under low frequency seismic data according to claim 1 is lacked, Wherein, phase-fitting mutually related objects functional χ of adding window normalization nonzero-lag_XcorNenlogIt is expressed as：

${\mathrm{\χ}}_{XcorNen\log }=-\frac{1}{2}\underset{h}{\Σ}\underset{\mathrm{\τ}}{\Σ}{\left(P\right(\mathrm{\τ}\left)XcorNen\log \right(\mathrm{\τ},h\left)\right)}^2$

$XcorNenlog(\mathrm{\τ},h)=\frac{\underset{t}{\Σ}\left(ln\right(e_{syn}\left(t,h\right)+c\left)\right)\left(ln\right(e_{obs}\left(t+\mathrm{\τ},h\right)+c\left)\right)}{\left|\right|\left(ln\right(e_{syn}\left(h\right)+c\left)\right)\left|\right|\left|\right|\left(ln\right(e_{obs}\left(h\right)+c\left)\right)\left|\right|}$

$e_{obs}(t,h)=\sqrt{u^2(t,h)+u_H^2(t,h)}$

$e_{syn}(t,h)=\sqrt{y^2(t,h)+y_H^2(t,h)}$

Wherein, (τ is h) observation geological data envelope natural logrithm and simulation geological data envelope to XcorNen1og The Normalized Cross Correlation Function of natural logrithm, to weight time histories sample, τ is time shift amount to P (τ), and u (t, h) is to see Earthquake prediction data, y (t, h) are simulation geological data, u_H(t, h) is the Hilbert transform for observing geological data, y_H(t, h) be simulate geological data Hilbert transform, e_obs(t, h) is the envelope for observing geological data, e_syn(t, h) is the envelope for simulating geological data, c be in order to avoid natural logrithm antilog is zero introducing one often Number, h represent the sequence number of cymoscope.

3. the background velocity model reconstruction method under low frequency seismic data according to claim 2 is lacked, Wherein, it is expressed as with focus Adjsource：

$\begin{array}{c}Adjsource=-\left(P^2\left(\mathrm{\τ}\right)XcorNen\log \left(\mathrm{\τ},h\right)\right)*\\ \left[\begin{array}{c}\frac{\frac{\ln \left(e_{obs}\left(t+\mathrm{\τ},h\right)+c\right)y\left(t,h\right)}{e_{syn}\left(t,h\right)\left(e_{syn}\left(t,h\right)+c\right)}}{\left|\right|\ln \left(e_{syn}\left(h\right)+c\right)\left|\right|\left|\right|\ln \left(e_{obs}\left(h\right)+c\right)\left|\right|}-\\ \frac{Hilbert\left(\frac{\ln \left(e_{obs}\left(t+\mathrm{\τ},h\right)+c\right)y_H\left(t,h\right)}{e_{syn}\left(t,h\right)\left(e_{syn}\left(t,h\right)+c\right)}\right)}{\left|\right|\ln \left(e_{syn}\left(h\right)+c\right)\left|\right|\left|\right|\ln \left(e_{obs}\left(h\right)+c\right)\left|\right|}-\\ \frac{Xcoren\log \left(\mathrm{\τ},h\right)\frac{y\left(t,h\right)\left(\ln \left(e_{syn}\left(t,h\right)+c\right)\right)}{\left(e_{syn}\left(t,h\right)+c\right)e_{syn}\left(t,h\right)}}{\left|\right|\ln \left(e_{syn}\left(h\right)+c\right)\left|{|}^3\right|\left|\ln \left(e_{obs}\left(h\right)+c\right)\right||}+\\ \frac{Xcoren\log \left(\mathrm{\τ},h\right)Hilbert\left(\frac{\left(\ln \left(e_{syn}\left(t,h\right)+c\right)\right)y_H\left(t,h\right)}{\left(e_{syn}\left(t,h\right)+c\right)e_{syn}\left(t,h\right)}\right)}{\left|\right|\ln \left(e_{syn}\left(h\right)+c\right)\left|{|}^3\right|\left|\ln \left(e_{obs}\left(h\right)+c\right)\right||}+\end{array}\right]\end{array}$

Wherein $Xcoren\log \left(\mathrm{\τ},h\right)=\underset{t}{\Σ}\ln \left(e_{syn}\left(t,h\right)+c\right)\ln \left(e_{obs}\left(t+\mathrm{\τ},h\right)+c\right)$ To observe the envelope of geological data With the cross-correlation of the envelope of simulation geological data, Hilbert represents the Hilbert transform of signal.

4. the background velocity model reconstruction method under low frequency seismic data according to claim 3 is lacked, Wherein, solve it is described with wave field when using the Acoustic Wave-equation in following isotropic medium：

${\∂}_{t}u(x,t)-N\left(m\right(x\left)\right)H(\▿)u(x,t)-N^{\′}\left(m\right(x\left)\right)s(x,t)=0$

In formula：

$N\left(m\right(x\left)\right)=\left(\begin{array}{cccc}b& 0& 0& 0\\ 0& b& 0& 0\\ 0& 0& b& 0\\ 0& 0& 0& \mathrm{\κ}\end{array}\right),H(\▿)=\left(\begin{array}{cccc}0& 0& 0& {\∂}_x\\ 0& 0& 0& {\∂}_y\\ 0& 0& 0& {\∂}_z\\ {\∂}_x& {\∂}_y& {\∂}_z& 0\end{array}\right),N^{\′}\left(m\right(x\left)\right)=\left(\begin{array}{cccc}b& 0& 0& 0\\ 0& b& 0& 0\\ 0& 0& b& 0\\ 0& 0& 0& 1\end{array}\right)$

Inverses of the wherein b for density, κ is bulk moduluses, u (x, t)=[v_x(x,t),v_y(x,t),v_z(x,t),p(x,t)]^T, S (x, t)=[0,0,0, Adjsource]^T, with wave field, ▽ represents the derivative to space for u (x, t) expressions,It is to x The derivative in direction,It is the derivative to y directions,Represent the derivative to z directions, v_x(x,t),v_y(x,t),v_z(x,t), It is x respectively, with wave field, p (x, t) is adjoint stress wave field to the particle vibration velocity in y, z direction, It is the time-derivative with wave field.

5. the background velocity model reconstruction method under low frequency seismic data according to claim 1 is lacked, Wherein, envelope inverting adopts fore condition LBFGS optimized algorithms or intends the fore condition PLBFGS algorithms of newton.

6. the background velocity model reconstruction method under low frequency seismic data according to claim 5 is lacked, Wherein, the precondition operator for adopting for：

In formula, z represents depth.

7. the background velocity model reconstruction method under low frequency seismic data according to claim 1 is lacked, Wherein, verify that the precision of envelope inverting includes：

Forward simulation is carried out to the rate pattern after reconstruct, the simulation ground of the rate pattern after obtaining based on reconstruct Shake data simultaneously solve its envelope, carry out adding with the envelope of the simulation geological data with the envelope of observation geological data Window normalization zero-lag cross-correlation, and enter with the adding window normalization zero-lag auto-correlation of observation geological data envelope Row contrast, verifies the precision of envelope inverting.

8. the background velocity model reconstruction method under low frequency seismic data according to claim 1 is lacked, Wherein, verify that the precision of envelope inverting includes：

With the rate pattern after reconstruct is as initial velocity model and carries out routine fluctuations equation chromatography, if chromatography As a result no noise, then it represents that the precision of envelope inverting meets and requires, is unsatisfactory for requiring if there is noise.

9. the background velocity model reconstruction method under low frequency seismic data according to claim 1 is lacked, Also include：

In the case where the precision of envelope inverting is unsatisfactory for requiring, initial velocity model is changed, step is re-executed It is rapid 1).

10. the background velocity model reconstruction method under low frequency seismic data according to claim 1 is lacked, Also include：In the case where the precision of envelope inverting is unsatisfactory for requiring, inverted parameters are changed, step is re-executed It is rapid 3).