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Improved amplitude preservation for prestack depth migration by inverse scattering theory

Improved amplitude preservation for prestack depth migration by inverse scattering theory
Improved amplitude preservation for prestack depth migration by inverse scattering theory

Geophysical Prospecting,2001,49,592±606

Improved amplitude preservation for prestack depth migration by inverse scattering theory

Changsoo Shin,1*Seonghyung Jang2and Dong-Joo Min3

1School of Civil,Urban and Geosystem Engineering,Seoul National University,San56-1,Sinlim-Dong,Kwanak-ku,Seoul151-742,2Petroleum and Marine Division,KIGAM,Yusung PO Box111,Kajung-dong30,Yusung-Ku,Taejon305-350,and3Marine Environment and Climate Change Laboratory,KORDI,Ansan PO Box29,Kyungki425-600,Korea

Received February1998,revision accepted March2001

A B S T R A C T

A prestack reverse time-migration image is not properly scaled with increasing

depth.The main reason for the image being unscaled is the geometric spreading

of the wavefield arising during the back-propagation of the measured data and

the generation of the forward-modelled wavefields.This unscaled image can be

enhanced by multiplying the inverse of the approximate Hessian appearing in the

Gauss±Newton optimization technique.However,since the approximate Hessian is

usually too expensive to compute for the general geological model,it can be used

only for the simple background velocity model.

We show that the pseudo-Hessian matrix can be used as a substitute for the

approximate Hessian to enhance the faint images appearing at a later time in the2D

prestack reverse time-migration sections.We can construct the pseudo-Hessian

matrix using the forward-modelled wavefields(which are used as virtual sources in

the reverse time migration),by exploiting the uncorrelated structure of the forward-

modelled wavefields and the impulse response function for the estimated diagonal of

the approximate Hessian.Although it is also impossible to calculate directly the

inverse of the pseudo-Hessian,when using the reciprocal of the pseudo-Hessian we

can easily obtain the inverse of the pseudo-Hessian.As examples supporting our

assertion,we present the results obtained by applying our method to2D synthetic

and real data collected on the Korean continental shelf.

I N T R O D U C T I O N

The purpose of seismic migration is to move reflection events to their correct position in depth.Hemon(1978)appeared to be the first person to implement reverse time migration.This post-stack time-reversed back-propagation approach was further developed by Baysal(1982),Loewenthal and Mufti (1983)and McMechan(1983).Prestack reverse time migra-tion was perhaps first initiated by Whitmore(1983)for common-shot gathers.Tarantola(1984),Kolb,Collino and Lailly(1986),Mora(1987),Chavent and Jacewitz(1995)and Pratt,Shin and Hicks(1998)used prestack reverse time migration as a means of implementing seismic waveform inversion to estimate a migration image.

Waveform inversion and reverse time migration share the same algorithmic structure.Both of them exploit the adjoint state of the wave equation,which avoids the direct computation of the partial-derivative wavefields giving rise to a huge Jacobian matrix.In prestack reverse time migration,we back-propagate the measured data,while,in the waveform inversion, we back-propagate the residual between the measured data and the initial model response.If we take our initial model as a smooth background velocity model,the residual in the wave-form inversion becomes the measured https://www.doczj.com/doc/9d15475553.html,illy(1983) q2001European Association of Geoscientists&Engineers

592

*E-mail:css@model.snu.ac.kr

showed that prestack reverse time migration,in that case, becomes the first iteration of the waveform inversion.

In both techniques,we estimate the migration image by calculating the zero-lag convolution between the back-propagated wavefields and the forward-modelled wavefields. There are currently two popular implementations of prestack reverse time migration.One implementation generates the forward-modelled wavefields using the expensive finite-difference method(Whitmore and Lines1986).These forward-modelled wavefields act as virtual sources which can be used to compute the partial-derivative wavefields. The other implementation generates the forward-modelled

wavefields by creating traveltime tables using a ray-tracing method(Chang and McMechan1986;Zhu and Lines 1997),thus saving both computation time and computer memory.

Shin(1988)developed a frequency-domain finite-element waveform inversion algorithm which requires direct compu-tation of the partial-derivative wavefields.Pratt et al.(1998), for the first time,compared waveform inversion using the gradient approach with those using the Gauss±Newton and full Newton methods.Pratt et al.(1998)also showed that the Gauss±Newton method using the inverse Hessian matrix considerably sharpens blurred images obtained by the less expensive gradient method for a fixed number of iterations.

Unfortunately,the Gauss±Newton method requires the approximate Hessian matrix whose size can be extremely large,thereby being too expensive to compute(Pratt et al. 1998).We present a more economical approximation to the Hessian in2D,which is called the pseudo-Hessian matrix. The pseudo-Hessian matrix is computed by the forward-modelled wavefields(used as virtual sources in reverse time migration)and is used to enhance the migration images.We begin by defining a virtual-source function and by reviewing the process of computing a partial-derivative seismogram with numerical implementation of the wave equation,since we define reverse time migration as the zero-lag cross-correlation between the partial-derivative wavefields and the measured seismogram.Next,we discuss how to construct the pseudo-Hessian by using the forward-modelled wavefields. By taking the zero-lag value of convolution between the back-propagated wavefields and the forward-modelled wavefields at each gridpoint in the subsurface,we generate estimated migration images for each common-shot gather.We show how we can improve the faint migration image resulting from geometrical spreading and transmission loss by using the pseudo-Hessian matrix.PA RT I A L-D E R I VAT I V E S E I S M O G R A M A N D V I RT U A L S O U R C E S

Pratt et al.(1998)showed how to calculate the partial-derivative seismogram in the frequency-domain implementation of the scalar and elastic wave equations.Here,we modify the approach for the time-domain implementation.The scalar wave equation is given in a2D medium by

2

2x

1

r

2D

2x

1

2

2z

1

r

2D

2z

2

1

k

22D

2t2

f x Y z Y t Y 1 where x is the horizontal distance(positive to the right),z is the vertical distance(positive downwards),t is the time,D(x, z,t)are the seismic data,r(x,z)is the density,k(x,z)is the bulk modulus and f(x,z,t)is the source function.The discretized equation obtained for the scalar wave equation usin

g a finite-difference or finite-element approach(Marfurt 1984)can be written as

M D1KD f t Y 2

12346789

5

Figure1Finite-difference grid model used to discretize the wave

equation.

Figure22D velocity model used to compute the partial-derivative wavefield with respect to the density of point i.

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where M is the mass matrix,K is the stiffness matrix,f (t )is the source column vector and D is the discretized seismic data arranged as a column vector (Marfurt 1984).Figure 1shows the finite-difference grid set.At any node i ,we identify a bulk modulus k i and a density r i so that we can define our model parameter vector p to be simply p r 1Y k 1Y r 2Y k 2Y ?Y r n Y k n T X

Taking the partial derivatives of (2)with respect to the density or the bulk modulus and rearranging the order of differentiation to preserve the original discretized wave equation gives M

2 D 2p 1K 2D 2p

F *Y 3

where (2D /2p )is the partial-derivative seismogram and F *is the virtual-source matrix (whose each column vector corresponds to a perturbed model parameter r i or k i )defined as F * 2

2M 2p D 22K

2p

D X 4

To synthesize partial-derivative seismograms recorded at

the surface,we begin by exciting a source at the top of the grid set shown in Fig.1.Then,we calculate the forward wavefields D at each gridpoint by using (2).Next,we use the forward wavefields D and (4)to calculate the virtual source F *,necessary to synthesize the partial-derivative wavefields (2D /2p )using (3).We do not solve (3)for the whole virtual-source matrix F *but for each column vector of F *.We combine the solution vectors computed for each column vector of F *only to obtain a huge Jacobian matrix J ( 2D /2p ).Thus we have an extremely large Jacobian matrix (whose size is N r ?N t Y N ),where N r is the number of receivers,N t is the number of time samples and N is the number of parameters such as density or compressibility)for each true source f (t ).

Note that the partial derivatives of the mass matrix with respect to the perturbations of the bulk modulus at the i th nodal point 2M a 2p i have zero values at all other nodal points except the i th nodal point;the partial derivatives of the

stiffness matrix with respect to the perturbation of the density

2K a 2p i have non-zero values at the i th nodal point and its four neighbouring nodal points (see Appendix A).We calculated the virtual sources for the model shown in Fig.2.Figure 3shows the virtual sources computed at the i th node for perturbation of the bulk modulus at the i th node and the true source at the j th node,as shown in Fig.2.Figure 4shows a column of the Jacobian matrix J corresponding to the change in bulk modulus at the i th node for the j th source gather.T H E P S E U D O -H E S S I A N M AT R I X

The zero-lag cross-correlation between the measured seismo-gram and the partial-derivative seismogram is an indication

-1-0.500.511.520

0.1

0.2

0.3

0.4

0.5

Time

(s)

Figure 3A virtual-source trace required to compute the partial-derivative wavefield with respect to the density of point i in Fig.

2.

Figure 4The partial-derivative seismogram generated by the virtual source shown in Fig.3.

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of the sensitivity of the measured seismogram to density or compressibility at the i th depth point.Displaying the zero-lag cross-correlation at each depth point enables us to image the subsurface (Shin and Chung 1999).Hagedoorn (1954)discussed this zero-lag cross-correlation approach,although he did not explicitly define the partial-derivative seismogram in his discussion of maximum convexity surfaces.The zero-lag cross-correlation approach is equivalent to summing seismic signals along the hyperbola used in prestack Kirchh-off depth migration (Shin and Chung 1999).Therefore,we cross-correlate the measured data D with our Jacobian J to obtain the unscaled migration image r :that is,r J T D Y

5

where J is obtained via (3)even though it can be calculated by using the more efficient asymptotic ray theory as in Kirchhoff migration.The unscaled migration image can be more efficiently computed by using the adjoint state technique without explicitly calculating the partial-derivative seismo-gram (Tarantola 1984).Pratt et al.(1998)and Pratt (1999)developed an indirect method of calculating the unscaled migration image using their frequency-domain modelling technique.The method suggested by Tarantola (1984),Pratt et al.(1998)and Pratt (1999)first back-propagates the measured seismogram D to every nodal point of a given model in a time-reversed order and then takes the zero-lag convolution between the back-propagated wavefields and the virtual sources.

The normal equation obtained by applying the Gauss±Newton method to the seismic inverse problem is given by Pratt et al.(1998)as J T J p r Y

6

where r was defined in (5)and we can call J T J the n ?n approximate Hessian matrix (Dennis 1997).In (6),the main diagonal of the approximate Hessian matrix is a zero-lag autocorrelation of the partial-derivative wavefields,which is always positive.For the high-frequency limit and the smooth

1000

2000300040000100200

300400500600700

V e l o c i t y (m /s )

Distance

(m)

Figure 51D velocity model used to compute the partial-derivative wavefield with respect to the densities of entire grids.The model is discretized into 700grids.

200

400

600

200

400

600

0200

400

600

200

400

600

(a)

(b)

Figure 6(a)The approximate Hessian matrix for the 1D velocity model shown in Fig.5.Note that the amplitudes of the diagonal elements decrease in descending order.Side lobes indicate that the partial-derivative wavefields are correlated with each other to some extent.(b)The pseudo-Hessian matrix for the 1D velocity model shown in Fig.5.The pattern of the diagonal elements is similar to that of the approximate Hessian matrix shown in (a).

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velocity model,the partial-derivative seismograms are almost completely uncorrelated to each other.However,for band-limited seismograms,the partial-derivative seismograms at neighbouring points around the perturbed point can only be correlated to each other (Pratt et al.1998).For rough models with strong reflectors,we observe a correlation between a primary event caused by perturbation in deeper parameters and multiple events caused by perturbation in shallow parameters.Although the more complex the velocity model

is,the more the partial-derivative seismograms are correlated to each other,their numerical correlations are too small when compared with the main diagonal.For this reason,if we neglect the off-diagonal terms in (6),we can express the normalized migration image for a common-shot gather as p < diag J T J 21r diag J T J 21J T D X

7

Since it is difficult to compute the huge Jacobian matrix

-0.4

-0.200.20.40.60.810

100

200

300400500

600

700

N o r m a l i z e d R e f l e c t i v i t y

Depth

(m)

(a)

(b)

-1-0.8-0.6-0.4-0.200.20.40.60.80100200

300400500600700

N o r m a l i z e d R e f l e c t i v i t y

Depth

(m)

Figure 7(a)A depth image multiplied by the inverse of the approximate Hessian for the 1D model shown in Fig.5.(b)A depth image without normalization for the 1D model shown in Fig.5.

-0.8

-0.6-0.4-0.200.20.40.60.810100200

300400500600700

N o r m a l i z e d R e f l e c t i v i t y

Depth

(m)

-1

-0.8-0.6-0.4-0.200.20.40.60.810100200

300400500600700

N o r m a l i z e d R e f l e c t i v i t y

Depth

(m)

(a)

(b)

Figure 8(a)A depth image divided by diagonal elements of the approximate Hessian for the 1D model shown in Fig.5.(b)A depth image divided by diagonal elements of the pseudo-Hessian for the 1D model shown in Fig.5.

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explicitly,we cannot use (7)to normalize the zero-lag cross-correlation.

As an alternative normalizing method,we suggest using the virtual-source matrix,obtained using (4).Based on the fact that we are able to generate the partial-derivative seismo-grams by using the virtual-source matrix,we propose replacing the partial-derivative wavefield by the virtual source at each parameter,thereby roughly expressing (7)as diag F *T F * p

8

where we refer to F *T F *as the pseudo-Hessian matrix H *.The main diagonal of the pseudo-Hessian matrix is the zero-lag autocorrelation of the virtual sources at each gridpoint of the model.The off-diagonal elements are the zero-lag cross-correlations of the virtual sources with each other.Owing to the different first-arrival time of the virtual source at each gridpoint,the virtual sources will in general be uncorrelated with each other in the high-frequency limit.Because of these characteristics of the virtual sources,the pseudo-Hessian matrix in (8)exhibits qualitatively a similar pattern to the approximate Hessian in (6).The theoretical basis for replacing the approximate Hessian by our pseudo-Hessian is discussed in Appendix B.

For multiple-shot records,we sum all the migrated images and all the pseudo-Hessian matrices,respectively,to obtain the total normalized migration images and the total pseudo-Hessian matrices.The summation image of multiple common-shot gathers can be expressed as

diag

j

F *T F *

4523

p < j

r 45Y

9

where j denotes the j th common-shot gather.We can employ (9)to image the subsurfaces for 2D examples.

N O R M A L I Z AT I O N O F T H E M I G R AT E D I M A G E

In order to examine the similarity between the pseudo-Hessian and the approximate Hessian we use the simple 1D example shown in Fig.5.First,for a total of 700gridpoints,we compute the virtual source F *and the partial-derivative wavefield J with respect to the bulk modulus parameter at each node.Next,we calculate the approximate Hessian matrix and the pseudo-Hessian matrix by applying H J T J and H * F *T F *Y respectively.Figure 6(a,b)show the approximate Hessian matrix and the pseudo-Hessian matrix computed for the model shown in Fig.5.In Fig.6(a,b),it can be seen that the main diagonals of both matrices are qualitatively similar.

Next,we examine the amount that normalization (i.e.multiplying by the inverse of the approximate Hessian)can enhance the migration image.The inverse of the

approximate

Figure 9A 2D depth model used to test normalization with the pseudo-Hessian matrix.

0100200300400500600

700

100

200

300

400

500

600

700

Figure 10A pseudo-Hessian matrix obtained for the model shown in

Fig.9.

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Hessian is computed after adding0.01%of the maximum value of the approximate Hessian matrix to its main diagonal. Figure7(a,b)show the migration images obtained with and without normalization,respectively.In Fig.7(a,b),it can be seen that multiplication by the inverse of the approximate Hessian enhances the reflector image at a depth of500m. For the inverse of the approximate Hessian,we have also used two approximate methods:one is to use the reciprocal of the main diagonal of the approximate Hessian and the other is to use the reciprocal of the main diagonal of the pseudo-Hessian.Figure8(a,b)show the normalized images obtained by the two different methods.The two methods give similarly enhanced images for the events appearing at a later https://www.doczj.com/doc/9d15475553.html,pared with the non-normalized image of Fig.7(b), the images of the second reflector appearing at a depth of 500m in Fig.8(a,b)are significantly enhanced. Currently,it is computationally intractable to normalize the images by using the inverse of the approximate Hessian, H21.Although it is also not possible to calculate exactly the approximate Hessian matrix H for the2D model shown in Fig.9,we can compute the pseudo-Hessian matrix H*.Figure 10shows the2D pseudo-Hessian matrix for the model shown in Fig.9.Since it is not possible to show the721801by 721801matrix,we selected every1000th element from the pseudo-Hessian matrix and have displayed721by721 elements.Like the approximate Hessian matrix,the structure of the pseudo-Hessian matrix depends on the way in which the nodal points are ordered(Pratt et al.1998).

It can be seen that the amplitudes of the main diagonal decrease in descending order and the pseudo-Hessian matrix is not diagonally dominant in Fig.10.The off-diagonal components result only from the band-limited content of the seismogram and the geometrical spreading of wave propaga-tion.Although,in the high-frequency limit,the virtual sources would be almost completely uncorrelated with each other,similar to the behaviour of the partial-derivative seismogram,the frequency content is,in fact,band-limited. Thus the virtual sources from adjacent nodes are correlated with each other to some extent.Furthermore,because of geometrical spreading,the virtual sources nearer to a real source will have greater amplitudes,resulting in the high values of zero-lag auto-and cross-correlations of virtual sources at the grids around the source.

The main diagonal elements of the summed pseudo-Hessian matrix and their reciprocals are shown in Fig.11. From Fig.11,it is clear that reciprocals of the diagonal elements of the summed pseudo-Hessian matrix will compensate for geometrical spreading.

(a)

(b)Figure11(a)Diagonal elements of the summed pseudo-Hessian matrix.After sum-ming the pseudo-Hessian matrices generated by multiple shots and collecting diagonal elements below the surface in the vertical grid direction,their values are shown in the same way as the usual seismic trace.(b)Recipro-cals of diagonal elements of the summed pseudo-Hessian matrix.After summing the pseudo-Hessian matrices generated by multi-ple shots and taking reciprocals of diagonal elements below the surface in the vertical grid direction,their values are shown in the same way as the usual seismic trace.

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In order to test the normalization using the pseudo-Hessian,we obtained the migration images before and after normalization for the model shown in Fig.9.Figure 12(a,b)show the migration image before and after normalization,respectively.The normalization was carried out using (9).To simplify comparison,the central trace of each image is plotted on the right of Fig.12(a,b).Note that the amplitudes of the images appearing below 3km in Fig.12(b)are greater than those of Fig.12(a).This is a good example showing the effect of the normalization using (9)in the migration.All the examples including the real seismogram were made using (9).Following the successful experiment on synthetic data,we then migrated a real data set.These data,obtained over the continental shelf of Korea,consist of 270shot records containing 240receivers.The shot interval was 30m,the receiver interval was 15m and the time sample interval was 2ms.Figure 13shows a representative field seismogram used for the migration.Each trace in a common-shot gather was back-propagated as a single source function.Owing to the limitations of CPU time and computer memory,we low-pass filtered the data to 30Hz,which enabled us to increase the finite-difference grid interval to 2m,within the range preventing grid dispersion.

Since the grid interval necessary for accurate finite-difference modelling is significantly finer than that required by the Nyquist sampling theory,we computed the virtual-source functions and back-propagated wavefields at every fourth gridpoint (8m)and every 10ms time interval.Because of this,we muted out the seismogram after 2s and took the 11-layer model with maximum depth 2.1km (shown in Fig.14)as an initial model.We used only 230shot records.

Figure 15(a)shows the image section without normaliz-ation;Fig.15(b)shows the image section with

normalization

Figure 12(a)2D depth image without normalization for the model shown in Fig.9.The centre trace of the depth image is shown on the right.(b)2D depth image normalized using the pseudo-Hessian matrix for the model shown in Fig.9.The centre trace of the depth image is shown on the right.

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Figure13An initial velocity model used for

migration of the2D field

data.

Figure14A shot-gather field seismogram

obtained over the Korean continental shelf

for prestack reverse time migration.

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obtained by summing 230shot images.In Fig.15(a),the non-normalized image below 1.0km shows indistinct impedance changes;the normalized section of Fig.15(b)shows a more distinct reflector image.

C O N C L U S I O N S

By exploiting the uncorrelated nature of the virtual sources,the partial-derivative wavefields and the impulse response functions,we have developed a relatively efficient means of estimating the main diagonal of the approximate Hessian without direct computation of the Jacobian matrix.Our indirect estimation of the diagonal element of the approx-imate Hessian using virtual sources enables us to enhance the unscaled reverse time-migration image without applying

AGC.Although the waveform computation of the virtual source costs more than ray tracing,we can use the virtual source to estimate the pseudo-Hessian matrix using little computation time.Since our approach is limited to the case of computing the forward-modelled wavefields using the finite-difference or the finite-element method,we have to pay for the extra computation time necessary to compute the main diagonal of the pseudo-Hessian matrix.However,we believe that the extension of the true inverse of the Hessian to the field seismogram will be a significant advantage in the future of seismic inversion and migration.

A C K N O W L E D G E M E N T

This work was supported financially by the

National

Figure 15(a)The final image of the 2D field data obtained without normalization.(b)The final image of the 2D field data obtained with the normalization proposed in this paper.

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Laboratory Project of the Ministry of Science and Technol-ogy,the Brain Korea 21project of the Ministry of Education,and grant no.PN0041300from the Basic Research Program of the Korea Science &Engineering Foundation.R E F E R E N C E S

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Chavent G.and Jacewitz C.A.1995.Determination of background velocities by multiple migration fitting.Geophysics 60,476±490.Dennis J.1977.Nonlinear least squares and equations.In:The State of the Art of Numerical Analysis (ed.D.Jacobs).Academic Press,Inc.

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A P P E N D I X A

We explain the derivatives with respect to the perturbations of the bulk modulus and the density at the i th nodal point 2M j a 2p i and 2K j a 2p i in detail.In order to obtain the derivatives with respect to the perturbations of the bulk modulus or the density at any nodal point,we first discretize (1)using either the finite-difference or the finite-element method.In this section,we only use the discretized forms obtained using the finite-difference method.We can write five difference equations (including the discretized bulk modulus k m ,n and the discretized density r m ,n )for the five gridpoints shown in Fig.16as follows:

1k m 21Y n u l 11m 21Y n 22u l m 21Y n 1u l 21m 21Y n

D t

22

3

1D x 2

r m Y n 1r m 21Y n u l m Y n 2u l m 21Y n D x

2

2

2

r m 21Y n 1r m 22Y n u l m 21Y n 2u l m 22Y n D x 3

1

1D z 2

r m 21Y n 111r m 21Y n

u l m 21Y n 112u l m 21Y n D z 2

2

2

r m 21Y n 1r m 21Y n 21u l m 21Y n 2u l m 21Y n 21D z

3

A1

Figure 16Diagram showing the five gridpoints referred to in Appendix A.

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for the m21Y n)th nodal point,

1 k m Y n21

u l11m Y n2122u l m Y n211u l21m Y n21

D t2

23

1

D x

2

r m11Y n211r m Y n21

u l m11Y n212u l m Y n21

D x

2

2

2

r m Y n211r m21Y n21

u l m Y n212u l m21Y n21

D x

3

1

1

D z

2

r m Y n1r m Y n21

u l m Y n2u l m Y n21

D z

2

2

2

r m Y n211r m Y n22

u l m Y n212u l m Y n22

D z

3

A2

for the(m,n21 th nodal point,

1 k m Y n

u l11m Y n22u l m Y n1u l21m Y n

D t2

23

1

D x

2

r m11Y n1r m Y n

u l m11Y n2u l m Y n

D x

2

2

2

r m Y n r m21Y n

u l m Y n2u l m21Y n

3

1

1

D z

2

r m Y n111r m Y n

u l m Y n112u l m Y n

D z

2

2

2

r m Y n1r m Y n21

u l m Y n2u l m Y n21

D z

3

A3

for the(m,n)th nodal point,

1 k m11Y n

u l11m11Y n22u l m11Y n1u l21m11Y n

D t2

23

1

D x

2

r m12Y n1r m11Y n

u l m12Y n2u l m11Y n

D x

2

2

2

r m11Y n1r m Y n

u l m11Y n2u l m Y n

D x

3

1

1

D z

2

r m11Y n111r m11Y n

u l m11Y n112u l m11Y n

D z

2

2

2

r m11Y n1r m11Y n21

u l m11Y n2u l m11Y n21

D z

3

A4

for the m11Y n)th nodal point,and

1

k m Y n11

u l11m Y n1122u l m Y n111u l21m Y n11

D t2

23

1

D x

2

r m11Y n111r m Y n11

u l m11Y n112u l m Y n11

D x

2

2

2

r m Y n111r m21Y n11

u l m Y n112u l m21Y n11

D x

3

1

1

D z

2

r m Y n121r m Y n11

u l m Y n122u l m Y n11

D z

2

2

2

r m Y n111r m Y n

u l m Y n112u l m Y n

D z

3

A5

for the(m,n11 th nodal point,where t l D t Y x m D x and

z n D z X

If we differentiate(A1)to(A5)with respect to the bulk

modulus k m,n,we obtain only the non-zero values for M m,n

as

2M m Y n

2k m Y n 2

1

k2m Y n

u l11m Y n22u l m Y n1u l21m Y n

D t2

23

Y A6

where M m,n indicates the mass term on the left-hand side

of the difference equation for the(m,n)th nodal point.

Differentiating(A1)to(A5)with respect to the density r m,n

gives

2K m21Y n

2r m Y n

2

1

D x

2

r m Y n1r m21Y n

232

u l m Y n2u l m21Y n

D x

A7

for the m21Y n)th nodal point,

2K m Y n21

2r m Y n

2

1

D z

2

r m Y n1r m Y n21

232

u l m Y n2u l m Y n21

D z

A8

for the(m,n21 th nodal point,

2K m Y n

2r m Y n

2

1

D x

2

r m11Y n1r m Y n

232

u l m11Y n2u l m Y n

D x

1

1

D x

2

r m Y n1r m21Y n

232

u l m Y n2u l m21Y n

D x

2

1

D z

2

r m Y n111r m Y n

232

u l m Y n112u l m Y n

D z

1

1

D z

2

r m Y n1r m Y n21

232

u l m Y n2u l m Y n21

D z

A9

Amplitude preservation by inverse scattering theory603

q2001European Association of Geoscientists&Engineers,Geophysical Prospecting,49,592±606

for the(m,n)th nodal point,

2K m11Y n 2r m Y n

1

D x

2

r m11Y n1r m Y n

232

u l m11Y n2u l m Y n

D x

A10

for the m11Y n)th nodal point,and

2K m Y n11 2r m Y n 1

D z

2

r m Y n111r m Y n

232

u l m Y n112u l m Y n

D z

A11

for the(m,n11 th nodal point,where K m,n indicates the right-hand side of the difference equation for the(m,n)th nodal point.

From(A6)and(A11),we know that the derivatives of the mass matrix with respect to the bulk modulus at a given node have non-zero values only at the node(indicated by the clear circle in Fig.16),and in the case of perturbation of the density,the derivatives of the stiffness matrix have non-zero values only at the perturbed nodal point and its four neighbouring nodal points(indicated by solid circles in Fig.16).

A P P E N D I X B

We now show qualitatively how(6)can be expressed in discrete matrix notation.For example,the time-domain, finite-element or finite-difference formulation for scalar and elastic wave equations can be given by(Marfurt1984)

M p 22D p Y t

22

1K p D p Y t f t Y B1

where M(p)is the n?n global mass matrix,K(p)is the n?n global stiffness matrix,f(t)is the n?1force vector,D(p,t)is the n?1wavefield vector,and p is the parameter vector, which includes parameters such as the velocity,the density and the digitized coordinates.In visualizing the virtual-source matrix and the partial-derivative wavefield,we used the time-domain numerical implementation scheme.Since the deriva-tion of(6)in the time domain is cumbersome,we proceed to derive(6)in the frequency domain.Taking the temporal Fourier transform of(B1)gives

K p d p Y v 2v2M p d p Y v F v Y B2 where v is the angular frequency.For simplicity,(B2)is often expressed as

S p Y v d p Y v F v Y B3 where the complex impedance matrix S is given by

S p Y v K p 2v2M p X

In the actual calculation of the synthetic seismogram in the frequency domain,we do not directly invert the square complex impedance matrix.The computation of the inverse complex impedance matrix S p Y v 21is intractable for a large-scale exploration geological model;in this case, S p Y v 21is equivalent to Green's function obtained by the numerical modelling technique.The usual method of generating the synthetic seismogram in the frequency domain is first to decompose the complex impedance matrix into the product of two matrices L and U,where L is a lower triangle matrix and U is an upper triangle matrix with1's on its diagonal,and then to calculate the wavefield by forward and backward substitution.In this way,we can obtain the one row or several rows(when computing the synthetic seismo-gram for multiple shots)of the inverse of the complex impedance matrix.A more sophisticated LU decomposition such as the nested dissection method(Marfurt and Shin1989) can be employed for large-scale seismic modelling. Taking the partial derivative of(B3)with respect to the parameter p i yields

S p Y v

2d p Y v

2p i1

2S p Y v

2p i d p Y

v 0X B4 After rearranging(B4),we obtain

S p Y v

2d p Y v

2p i f

*

i

Y B5 where f*i is given by

f*i 2

2S p Y v

2p i

d p Y v

and denotes the n?1virtual-source matrix for the perturba-tion of the i th parameters p i.

The partial-derivative wavefield can be simply given as

2d p Y v

2p i

S p Y v 21f*i Y B6

where S p Y v 21is the inverse of the complex impedance matrix.Once we factorize the complex impedance matrix,

604 C.Shin,S.Jang and D.-J.Min

q2001European Association of Geoscientists&Engineers,Geophysical Prospecting,49,592±606

the calculation of the partial-derivative wavefield adds only additional sparse right-hand side vectors in (B6).The use of this efficient method for the seismic inverse problem can be found in Shin (1988).However,this approach tends to be expensive and will be a formidable task as the number of unknown parameters increases unless the source and receiver reciprocity is exploited for the computation of the partial-derivative wavefield (Shin and Chung 1999).The discrete matrix notation of (B6)can be given as 2d 1 p Y v 2p 1...2d n p Y v 2p 1

H f f f f f f

d I

g

g g g g g e S p Y v 21f *11 p Y v ...f *n

1 p Y v

H f f f d I

g g g e Y B7

where f *is the virtual source required to generate the partial-derivative seismogram and can be expressed as f *11 p Y v

..

.f *n 1 p Y v

H f

f f d I

g g g e 22S p Y v 2p 1d 1 p Y v

...d n p Y v

H

f f f d

I g

g g e

X B8

Taking the transpose of (B7)gives 2d 1 p Y v 2p 1?2d n p Y v 2p 1

f *11 p Y v ?f *n 1 p Y v ? S p Y v 21 T X

B9

After generalizing the virtual-source matrix for the parameter

j 2Y ?Y m Y we have 2d 1 p Y v 2p 2?2d n p Y v

2p 2

f *12 p Y v ?f *n 2 p Y v S p Y v 21 T Y

..

...

.

.....

.2d 1 p Y v 2p j ?2d n p Y v 2p j

f *1j p Y v ?f *n j p Y v S p Y v 21 T Y

..

...

.

.....

.2d 1 p Y v 2p m ?2d n p Y v

2p m

f *1m p Y v ?f *n m p Y v S p Y v 21 T

X

B10

The transpose matrix of the global virtual-source matrix

can be written as

F T

f *11 v Y p

f *21 v Y p ?f *n

1 v Y p

f *1

2 v Y p f *22 v Y p

?f *n 2 v Y p ......]...f *1m v Y p f *2m v Y p

?f *n

m v Y p

H f f f f f f d

I

g g g

g g g e

X B11

The size of the virtual-source matrix depends on the number

of parameters to be included in imaging the subsurface.It is the n ?n matrix when all parameter gridpoints of the geological model are included.Owing to the local numerical supports defined by finite-element or finite-difference algorithms,the non-diagonal elements of the virtual-source matrix will be almost zero.In other words,when perturbing the bulk modulus in the finite-difference grid,the virtual source is zero except at the perturbed gridpoint.

The transpose of the Jacobian matrix in the frequency domain can be expressed as J T 2d 1

p Y v

2p 12d 2 p Y v 2p 1?2d n p Y v 2p 12d 1 p Y v 2p 2

2d 2 p Y v 2p 2?2d n p Y v 2p 2......]...2d 1 p Y v

2m

2d 2 p Y v 2m

?

2d n p Y v 2m

H f f f

f f f

f f

f f f

d I g g

g

g

g g g g g g g e X

B12

Using (B7),(B9),(B10)and (B12),we can express the

approximate Hessian in (6),in the frequency domain,as J T

J <

v max 2v min

J T v ~J v d v

2v min

F T S p Y v

21 T

~S p Y v 21~F d v

Y

B13

where ?denotes the complex conjugate.We limit the matrix

multiplication to the inverse of the complex impedance matrix by noting again that the virtual-source matrix is almost zero except along the main diagonal.Since each column of the inverse of the complex impedance matrix corresponds to Green's function (the impulse response function),each impulse response function will be perfectly correlated to itself and uncorrelated to other impulse functions.The impulse response function has the same characteristics as the virtual source and the partial-derivative wavefield.Therefore,matrix multiplication of the inverse of the complex impedance matrix by the inverse of the complex

matrix, S p Y v 21 T ~S

p Y v 21Y results in a diagonally Amplitude preservation by inverse scattering theory 605

q 2001European Association of Geoscientists &Engineers,Geophysical Prospecting ,49,592±606

dominant matrix.The value of the main diagonal maintains a similar pattern to the diagonal elements of the pseudo-Hessian.Therefore,we may use the pseudo-Hessian matrix as an approximation of the approximate Hessian.Since geophy-sicists measure aperture-limited seismograms(on the surface or in the borehole),we also use aperture-limited partial-derivative seismograms for the computation of the approximate Hessian, although we can compute the partial-derivative seismograms in the entire subsurface.However,unlike the approximate Hessian,our pseudo-Hessian corresponds to the approximate Hessian computed using partial-derivative seismograms in the whole subsurface.

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to与for的用法和区别

to与for的用法和区别 一般情况下, to后面常接对象; for后面表示原因与目的为多。 Thank you for helping me. Thanks to all of you. to sb.表示对某人有直接影响比如,食物对某人好或者不好就用to; for表示从意义、价值等间接角度来说,例如对某人而言是重要的,就用for. for和to这两个介词,意义丰富,用法复杂。这里仅就它们主要用法进行比较。 1. 表示各种“目的” 1. What do you study English for? 你为什么要学英语? 2. She went to france for holiday. 她到法国度假去了。 3. These books are written for pupils. 这些书是为学生些的。 4. hope for the best, prepare for the worst. 作最好的打算,作最坏的准备。 2.对于 1.She has a liking for painting. 她爱好绘画。 2.She had a natural gift for teaching. 她对教学有天赋/ 3.表示赞成同情,用for不用to. 1. Are you for the idea or against it? 你是支持还是反对这个想法? 2. He expresses sympathy for the common people.. 他表现了对普通老百姓的同情。 3. I felt deeply sorry for my friend who was very ill. 4 for表示因为,由于(常有较活译法) 1 Thank you for coming. 谢谢你来。 2. France is famous for its wines. 法国因酒而出名。 5.当事人对某事的主观看法,对于(某人),对…来说(多和形容词连用)用介词to,不用for.. He said that money was not important to him. 他说钱对他并不重要。 To her it was rather unusual. 对她来说这是相当不寻常的。 They are cruel to animals. 他们对动物很残忍。 6.for和fit, good, bad, useful, suitable 等形容词连用,表示适宜,适合。 Some training will make them fit for the job. 经过一段训练,他们会胜任这项工作的。 Exercises are good for health. 锻炼有益于健康。 Smoking and drinking are bad for health. 抽烟喝酒对健康有害。 You are not suited for the kind of work you are doing. 7. for表示不定式逻辑上的主语,可以用在主语、表语、状语、定语中。 1.It would be best for you to write to him. 2.The simple thing is for him to resign at once. 3.There was nowhere else for me to go. 4.He opened a door and stood aside for her to pass.

of与for的用法以及区别

of与for的用法以及区别 for 表原因、目的 of 表从属关系 介词of的用法 (1)所有关系 this is a picture of a classroom (2)部分关系 a piece of paper a cup of tea a glass of water a bottle of milk what kind of football,American of soccer? (3)描写关系 a man of thirty 三十岁的人 a man of shanghai 上海人 (4)承受动作 the exploitation of man by man.人对人的剥削。 (5)同位关系 It was a cold spring morning in the city of London in England. (6)关于,对于 What do you think of Chinese food? 你觉得中国食品怎么样? 介词 for 的用法小结 1. 表示“当作、作为”。如: I like some bread and milk for breakfast. 我喜欢把面包和牛奶作为早餐。What will we have for supper? 我们晚餐吃什么?

2. 表示理由或原因,意为“因为、由于”。如: Thank you for helping me with my English. 谢谢你帮我学习英语。 Thank you for your last letter. 谢谢你上次的来信。 Thank you for teaching us so well. 感谢你如此尽心地教我们。 3. 表示动作的对象或接受者,意为“给……”、“对…… (而言)”。如: Let me pick it up for you. 让我为你捡起来。 Watching TV too much is bad for your health. 看电视太多有害于你的健康。 4. 表示时间、距离,意为“计、达”。如: I usually do the running for an hour in the morning. 我早晨通常跑步一小时。We will stay there for two days. 我们将在那里逗留两天。 5. 表示去向、目的,意为“向、往、取、买”等。如: let’s go for a walk. 我们出去散步吧。 I came here for my schoolbag.我来这儿取书包。 I paid twenty yuan for the dictionary. 我花了20元买这本词典。 6. 表示所属关系或用途,意为“为、适于……的”。如: It’s time for school. 到上学的时间了。 Here is a letter for you. 这儿有你的一封信。 7. 表示“支持、赞成”。如: Are you for this plan or against it? 你是支持还是反对这个计划? 8. 用于一些固定搭配中。如: Who are you waiting for? 你在等谁? For example, Mr Green is a kind teacher. 比如,格林先生是一位心地善良的老师。

延时子程序计算方法

学习MCS-51单片机,如果用软件延时实现时钟,会接触到如下形式的延时子程序:delay:mov R5,#data1 d1:mov R6,#data2 d2:mov R7,#data3 d3:djnz R7,d3 djnz R6,d2 djnz R5,d1 Ret 其精确延时时间公式:t=(2*R5*R6*R7+3*R5*R6+3*R5+3)*T (“*”表示乘法,T表示一个机器周期的时间)近似延时时间公式:t=2*R5*R6*R7 *T 假如data1,data2,data3分别为50,40,248,并假定单片机晶振为12M,一个机器周期为10-6S,则10分钟后,时钟超前量超过1.11秒,24小时后时钟超前159.876秒(约2分40秒)。这都是data1,data2,data3三个数字造成的,精度比较差,建议C描述。

上表中e=-1的行(共11行)满足(2*R5*R6*R7+3*R5*R6+3*R5+3)=999,999 e=1的行(共2行)满足(2*R5*R6*R7+3*R5*R6+3*R5+3)=1,000,001 假如单片机晶振为12M,一个机器周期为10-6S,若要得到精确的延时一秒的子程序,则可以在之程序的Ret返回指令之前加一个机器周期为1的指令(比如nop指令), data1,data2,data3选择e=-1的行。比如选择第一个e=-1行,则精确的延时一秒的子程序可以写成: delay:mov R5,#167 d1:mov R6,#171 d2:mov R7,#16 d3:djnz R7,d3 djnz R6,d2

djnz R5,d1 nop ;注意不要遗漏这一句 Ret 附: #include"iostReam.h" #include"math.h" int x=1,y=1,z=1,a,b,c,d,e(999989),f(0),g(0),i,j,k; void main() { foR(i=1;i<255;i++) { foR(j=1;j<255;j++) { foR(k=1;k<255;k++) { d=x*y*z*2+3*x*y+3*x+3-1000000; if(d==-1) { e=d;a=x;b=y;c=z; f++; cout<<"e="<

常用介词用法(for to with of)

For的用法 1. 表示“当作、作为”。如: I like some bread and milk for breakfast. 我喜欢把面包和牛奶作为早餐。 What will we have for supper? 我们晚餐吃什么? 2. 表示理由或原因,意为“因为、由于”。如: Thank you for helping me with my English. 谢谢你帮我学习英语。 3. 表示动作的对象或接受者,意为“给……”、“对…… (而言)”。如: Let me pick it up for you. 让我为你捡起来。 Watching TV too much is bad for your health. 看电视太多有害于你的健康。 4. 表示时间、距离,意为“计、达”。如: I usually do the running for an hour in the morning. 我早晨通常跑步一小时。 We will stay there for two days. 我们将在那里逗留两天。 5. 表示去向、目的,意为“向、往、取、买”等。如: Let’s go for a walk. 我们出去散步吧。 I came here for my schoolbag.我来这儿取书包。 I paid twenty yuan for the dictionary. 我花了20元买这本词典。 6. 表示所属关系或用途,意为“为、适于……的”。如: It’s time for school. 到上学的时间了。 Here is a letter for you. 这儿有你的一封信。 7. 表示“支持、赞成”。如: Are you for this plan or against it? 你是支持还是反对这个计划? 8. 用于一些固定搭配中。如: Who are you waiting for? 你在等谁? For example, Mr Green is a kind teacher. 比如,格林先生是一位心地善良的老师。 尽管for 的用法较多,但记住常用的几个就可以了。 to的用法: 一:表示相对,针对 be strange (common, new, familiar, peculiar) to This injection will make you immune to infection. 二:表示对比,比较 1:以-ior结尾的形容词,后接介词to表示比较,如:superior ,inferior,prior,senior,junior 2: 一些本身就含有比较或比拟意思的形容词,如equal,similar,equivalent,analogous A is similar to B in many ways.

of和for的用法

of 1....的,属于 One of the legs of the table is broken. 桌子的一条腿坏了。 Mr.Brown is a friend of mine. 布朗先生是我的朋友。 2.用...做成的;由...制成 The house is of stone. 这房子是石建的。 3.含有...的;装有...的 4....之中的;...的成员 Of all the students in this class,Tom is the best. 在这个班级中,汤姆是最优秀的。 5.(表示同位) He came to New York at the age of ten. 他在十岁时来到纽约。 6.(表示宾格关系) He gave a lecture on the use of solar energy. 他就太阳能的利用作了一场讲演。 7.(表示主格关系) We waited for the arrival of the next bus. 我们等待下一班汽车的到来。

I have the complete works of Shakespeare. 我有莎士比亚全集。 8.来自...的;出自 He was a graduate of the University of Hawaii. 他是夏威夷大学的毕业生。 9.因为 Her son died of hepatitis. 她儿子因患肝炎而死。 10.在...方面 My aunt is hard of hearing. 我姑妈耳朵有点聋。 11.【美】(时间)在...之前 12.(表示具有某种性质) It is a matter of importance. 这是一件重要的事。 For 1.为,为了 They fought for national independence. 他们为民族独立而战。 This letter is for you. 这是你的信。

单片机C延时时间怎样计算

C程序中可使用不同类型的变量来进行延时设计。经实验测试,使用unsigned char类型具有比unsigned int更优化的代码,在使用时 应该使用unsigned char作为延时变量。以某晶振为12MHz的单片 机为例,晶振为12M H z即一个机器周期为1u s。一. 500ms延时子程序 程序: void delay500ms(void) { unsigned char i,j,k; for(i=15;i>0;i--) for(j=202;j>0;j--) for(k=81;k>0;k--); } 计算分析: 程序共有三层循环 一层循环n:R5*2 = 81*2 = 162us DJNZ 2us 二层循环m:R6*(n+3) = 202*165 = 33330us DJNZ 2us + R5赋值 1us = 3us 三层循环: R7*(m+3) = 15*33333 = 499995us DJNZ 2us + R6赋值 1us = 3us

循环外: 5us 子程序调用 2us + 子程序返回2us + R7赋值 1us = 5us 延时总时间 = 三层循环 + 循环外 = 499995+5 = 500000us =500ms 计算公式:延时时间=[(2*R5+3)*R6+3]*R7+5 二. 200ms延时子程序 程序: void delay200ms(void) { unsigned char i,j,k; for(i=5;i>0;i--) for(j=132;j>0;j--) for(k=150;k>0;k--); } 三. 10ms延时子程序 程序: void delay10ms(void) { unsigned char i,j,k; for(i=5;i>0;i--) for(j=4;j>0;j--) for(k=248;k>0;k--);

for和to区别

1.表示各种“目的”,用for (1)What do you study English for 你为什么要学英语? (2)went to france for holiday. 她到法国度假去了。 (3)These books are written for pupils. 这些书是为学生些的。 (4)hope for the best, prepare for the worst. 作最好的打算,作最坏的准备。 2.“对于”用for (1)She has a liking for painting. 她爱好绘画。 (2)She had a natural gift for teaching. 她对教学有天赋/ 3.表示“赞成、同情”,用for (1)Are you for the idea or against it 你是支持还是反对这个想法? (2)He expresses sympathy for the common people.. 他表现了对普通老百姓的同情。 (3)I felt deeply sorry for my friend who was very ill. 4. 表示“因为,由于”(常有较活译法),用for (1)Thank you for coming. 谢谢你来。

(2)France is famous for its wines. 法国因酒而出名。 5.当事人对某事的主观看法,“对于(某人),对…来说”,(多和形容词连用),用介词to,不用for. (1)He said that money was not important to him. 他说钱对他并不重要。 (2)To her it was rather unusual. 对她来说这是相当不寻常的。 (3)They are cruel to animals. 他们对动物很残忍。 6.和fit, good, bad, useful, suitable 等形容词连用,表示“适宜,适合”,用for。(1)Some training will make them fit for the job. 经过一段训练,他们会胜任这项工作的。 (2)Exercises are good for health. 锻炼有益于健康。 (3)Smoking and drinking are bad for health. 抽烟喝酒对健康有害。 (4)You are not suited for the kind of work you are doing. 7. 表示不定式逻辑上的主语,可以用在主语、表语、状语、定语中。 (1)It would be best for you to write to him. (2) The simple thing is for him to resign at once.

51单片机延时时间计算和延时程序设计

一、关于单片机周期的几个概念 ●时钟周期 时钟周期也称为振荡周期,定义为时钟脉冲的倒数(可以这样来理解,时钟周期就是单片机外接晶振的倒数,例如12MHz的晶振,它的时间周期就是1/12 us),是计算机中最基本的、最小的时间单位。 在一个时钟周期内,CPU仅完成一个最基本的动作。 ●机器周期 完成一个基本操作所需要的时间称为机器周期。 以51为例,晶振12M,时钟周期(晶振周期)就是(1/12)μs,一个机器周期包 执行一条指令所需要的时间,一般由若干个机器周期组成。指令不同,所需的机器周期也不同。 对于一些简单的的单字节指令,在取指令周期中,指令取出到指令寄存器后,立即译码执行,不再需要其它的机器周期。对于一些比较复杂的指令,例如转移指令、乘法指令,则需要两个或者两个以上的机器周期。 1.指令含义 DJNZ:减1条件转移指令 这是一组把减1与条件转移两种功能结合在一起的指令,共2条。 DJNZ Rn,rel ;Rn←(Rn)-1 ;若(Rn)=0,则PC←(PC)+2 ;顺序执行 ;若(Rn)≠0,则PC←(PC)+2+rel,转移到rel所在位置DJNZ direct,rel ;direct←(direct)-1 ;若(direct)= 0,则PC←(PC)+3;顺序执行 ;若(direct)≠0,则PC←(PC)+3+rel,转移到rel 所在位置 2.DJNZ Rn,rel指令详解 例:

MOV R7,#5 DEL:DJNZ R7,DEL; rel在本例中指标号DEL 1.单层循环 由上例可知,当Rn赋值为几,循环就执行几次,上例执行5次,因此本例执行的机器周期个数=1(MOV R7,#5)+2(DJNZ R7,DEL)×5=11,以12MHz的晶振为例,执行时间(延时时间)=机器周期个数×1μs=11μs,当设定立即数为0时,循环程序最多执行256次,即延时时间最多256μs。 2.双层循环 1)格式: DELL:MOV R7,#bb DELL1:MOV R6,#aa DELL2:DJNZ R6,DELL2; rel在本句中指标号DELL2 DJNZ R7,DELL1; rel在本句中指标号DELL1 注意:循环的格式,写错很容易变成死循环,格式中的Rn和标号可随意指定。 2)执行过程

双宾语 to for的用法

1.两者都可以引出间接宾语,但要根据不同的动词分别选用介词to 或for:(1) 在give, pass, hand, lend, send, tell, bring, show, pay, read, return, write, offer, teach, throw 等之后接介词to。 如: 请把那本字典递给我。 正:Please hand me that dictionary. 正:Please hand that dictionary to me. 她去年教我们的音乐。 正:She taught us music last year. 正:She taught music to us last year. (2) 在buy, make, get, order, cook, sing, fetch, play, find, paint, choose,prepare, spare 等之后用介词for 。如: 他为我们唱了首英语歌。 正:He sang us an English song. 正:He sang an English song for us. 请帮我把钥匙找到。 正:Please find me the keys. 正:Please find the keys for me. 能耽搁你几分钟吗(即你能为我抽出几分钟吗)? 正:Can you spare me a few minutes? 正:Can you spare a few minutes for me? 注:有的动词由于搭配和含义的不同,用介词to 或for 都是可能的。如:do sb a favour=do a favour for sb 帮某人的忙 do sb harm=do harm to sb 对某人有害

双宾语tofor的用法

1. 两者都可以引出间接宾语,但要根据不同的动词分别选用介词to 或for: (1) 在give, pass, hand, lend, send, tell, bring, show, pay, read, return, write, offer, teach, throw 等之后接介词to。 如: 请把那本字典递给我。 正:Please hand me that dictionary. 正:Please hand that dictionary to me. 她去年教我们的音乐。 正:She taught us music last year. 正:She taught music to us last year. (2) 在buy, make, get, order, cook, sing, fetch, play, find, paint, choose,prepare, spare 等之后用介词for 。如: 他为我们唱了首英语歌。 正:He sang us an English song. 正:He sang an English song for us. 请帮我把钥匙找到。 正:Please find me the keys. 正:Please find the keys for me. 能耽搁你几分钟吗(即你能为我抽出几分钟吗)? 正:Can you spare me a few minutes? 正:Can you spare a few minutes for me? 注:有的动词由于搭配和含义的不同,用介词to 或for 都是可能的。如: do sb a favou r do a favour for sb 帮某人的忙 do sb harnn= do harm to sb 对某人有害

for和of的用法

for的用法: 1. 表示“当作、作为”。如: I like some bread and milk for breakfast. 我喜欢把面包和牛奶作为早餐。 What will we have for supper? 我们晚餐吃什么? 2. 表示理由或原因,意为“因为、由于”。如: Thank you for helping me with my English. 谢谢你帮我学习英语。 Thank you for your last letter. 谢谢你上次的来信。 Thank you for teaching us so well. 感谢你如此尽心地教我们。 3. 表示动作的对象或接受者,意为“给……”、“对…… (而言)”。如: Let me pick it up for you. 让我为你捡起来。 Watching TV too much is bad for your health. 看电视太多有害于你的健康。 4. 表示时间、距离,意为“计、达”。如:

I usually do the running for an hour in the morning. 我早晨通常跑步一小时。 We will stay there for two days. 我们将在那里逗留两天。 5. 表示去向、目的,意为“向、往、取、买”等。如: Let’s go for a walk. 我们出去散步吧。 I came here for my schoolbag.我来这儿取书包。 I paid twenty yuan for the dictionary. 我花了20元买这本词典。 6. 表示所属关系或用途,意为“为、适于……的”。如: It’s time for school. 到上学的时间了。 Here is a letter for you. 这儿有你的一封信。 7. 表示“支持、赞成”。如: Are you for this plan or against it? 你是支持还是反对这个计划? 8. 用于一些固定搭配中。如:

英语形容词和of for 的用法

加入收藏夹 主题: 介词试题It’s + 形容词 + of sb. to do sth.和It’s + 形容词 + for sb. to do sth.的用法区别。 内容: It's very nice___pictures for me. A.of you to draw B.for you to draw C.for you drawing C.of you drawing 提交人:杨天若时间:1/23/2008 20:5:54 主题:for 与of 的辨别 内容:It's very nice___pictures for me. A.of you to draw B.for you to draw C.for you drawing C.of you drawing 答:选A 解析:该题考查的句型It’s + 形容词+ of sb. to do sth.和It’s +形容词+ for sb. to do sth.的用法区别。 “It’s + 形容词+ to do sth.”中常用of或for引出不定式的行为者,究竟用of sb.还是用for sb.,取决于前面的形容词。 1) 若形容词是描述不定式行为者的性格、品质的,如kind,good,nice,right,wrong,clever,careless,polite,foolish等,用of sb. 例: It’s very kind of you to help me. 你能帮我,真好。 It’s clever of you to work out the maths problem. 你真聪明,解出了这道数学题。 2) 若形容词仅仅是描述事物,不是对不定式行为者的品格进行评价,用for sb.,这类形容词有difficult,easy,hard,important,dangerous,(im)possible等。例: It’s very dangerous for children to cross the busy street. 对孩子们来说,穿过繁忙的街道很危险。 It’s difficult for u s to finish the work. 对我们来说,完成这项工作很困难。 for 与of 的辨别方法: 用介词后面的代词作主语,用介词前边的形容词作表语,造个句子。如果道理上通顺用of,不通则用for. 如: You are nice.(通顺,所以应用of)。 He is hard.(人是困难的,不通,因此应用for.) 由此可知,该题的正确答案应该为A项。 提交人:f7_liyf 时间:1/24/2008 11:18:42

to和for的用法有什么不同(一)

to和for的用法有什么不同(一) 一、引出间接宾语时的区别 两者都可以引出间接宾语,但要根据不同的动词分别选用介词to 或for,具体应注意以下三种情况: 1. 在give, pass, hand, lend, send, tell, bring, show, pay, read, return, write, offer, teach, throw 等之后接介词to。如: 请把那本字典递给我。 正:Please hand me that dictionary. 正:Please hand that dictionary to me. 她去年教我们的音乐。 正:She taught us music last year. 正:She taught music to us last year. 2. 在buy, make, get, order, cook, sing, fetch, play, find, paint, choose, prepare, spare 等之后用介词for 。如: 他为我们唱了首英语歌。 正:He sang us an English song. 正:He sang an English song for us. 请帮我把钥匙找到。 正:Please find me the keys. 正:Please find the keys for me. 能耽搁你几分钟吗(即你能为我抽出几分钟吗)? 正:Can you spare me a few minutes?

正:Can you spare a few minutes for me? 3. 有的动词由于用法和含义不同,用介词to 或for 都是可能的。如: do sb a favor=do a favor for sb 帮某人的忙 do sb harm=do harm to sb 对某人有害 在有的情况下,可能既不用for 也不用to,而用其他的介词。如: play sb a trick=play a trick on sb 作弄某人 请比较: play sb some folk songs=play some folk songs for sb 给某人演奏民歌 有时同一个动词,由于用法不同,所搭配的介词也可能不同,如leave sbsth 这一结构,若表示一般意义的为某人留下某物,则用介词for 引出间接宾语,即说leave sth for sb;若表示某人死后遗留下某物,则用介词to 引出间接宾语,即说leave sth to sb。如: Would you like to leave him a message? / Would you like to leave a message for him? 你要不要给他留个话? Her father left her a large fortune. / Her father left a large fortune to her. 她父亲死后给她留下了一大笔财产。 二、表示目标或方向的区别 两者均可表示目标、目的地、方向等,此时也要根据不同动词分别对待。如: 1. 在come, go, walk, move, fly, ride, drive, march, return 等动词之后通常用介词to 表示目标或目的地。如: He has gone to Shanghai. 他到上海去了。 They walked to a river. 他们走到一条河边。

延时计算

t=n*(分频/f) t:是你所需的延时时间 f:是你的系统时钟(SYSCLK) n:是你所求,用于设计延时函数的 程序如下: void myDelay30s() reentrant { unsigned inti,k; for(i=0;i<4000;i++) /*系统时钟我用的是24.576MHZ,分频是12分频,达到大约10s延时*/ for(k=0;k<8000;k++); } //n=i*k |评论 2012-2-18 20:03 47okey|十四级 debu(g调试),左侧有运行时间。在你要测试的延时子函数外设一断点,全速运行到此断点。记下时间,再单步运行一步,跳到下一步。再看左侧的运行时间,将这时间减去上一个时间,就是延时子函数的延时时间了。不知能不能上图。 追问 在delayms处设置断点,那么对应的汇编语言LCALL是否被执行呢?还有,问问您,在C8051F020单片机中,MOV指令都是多少指令周期呢?我在KEIL下仿真得出的结果,与我通过相应的汇编语言分析的时间,总是差了很多。 回答 C编译时,编译器都要先变成汇编。只想知道延时时间,汇编的你可以不去理会。只要看运行时间就好了。 at8051单片机12m晶振下,机器周期为1us,而c8051 2m晶振下为1us。keil 调试里频率默认为24m,你要设好晶振频率。

|评论 2012-2-23 11:17 kingranran|一级 参考C8051单片机内部计时器的工作模式,选用合适的计时器进行中断,可获得较高精度的延时 |评论 2012-2-29 20:56 衣鱼ccd1000|一级 要是精确延时的话就要用定时器,但定的时间不能太长,长了就要设一个变量累加来实现了; 要是不要求精确的话就用嵌套for函数延时,比较简单,但是程序复杂了就会增添不稳定因素,所以不推荐。 |评论

202X中考英语:to和for的区别与用法.doc

202X中考英语:to和for的区别与用法中考栏目我为考生们整理了“202X中考英语:to和for的区别与用法”,希望能帮到大家,想了解更多考试资讯,本网站的及时更新哦。 202X中考英语:to和for的区别与用法 to和for的区别与用法是什么 一般情况下, to后面常接对象; for后面表示原因与目的为多。 Thank you for helping me. Thanks to all of you. to sb. 表示对某人有直接影响比如,食物对某人好或者不好就用to; for 表示从意义、价值等间接角度来说,例如对某人而言是重要的,就用for. for和to这两个介词,意义丰富,用法复杂。这里仅就它们主要用法进行比较。 1. 表示各种“目的” 1. What do you study English for? 你为什么要学英语? 2. She went to france for holiday. 她到法国度假去了。 3. These books are written for pupils. 这些书是为学生些的。 4. hope for the best, prepare for the worst. 作最好的打算,作最坏的准备。

2.对于 1.She has a liking for painting. 她爱好绘画。 2.She had a natural gift for teaching. 她对教学有天赋。 3.表示赞成同情,用for不用to. 1. Are you for the idea or against it? 你是支持还是反对这个想法? 2. He expresses sympathy for the common people.. 他表现了对普通老百姓的同情。 3. I felt deeply sorry for my friend who was very ill. 4 for表示因为,由于(常有较活译法) 1.Thank you for coming. 谢谢你来。 2. France is famous for its wines. 法国因酒而出名。 5.当事人对某事的主观看法,对于(某人),对?来说(多和形容词连用)用介词to,不用for.. He said that money was not important to him. 他说钱对他并不重要。 To her it was rather unusual. 对她来说这是相当不寻常的。 They are cruel to animals. 他们对动物很残忍。

keep的用法及of 、for sb.句型区别

keep的用法 1. 用作及物动词 ①意为"保存;保留;保持;保守"。如: Could you keep these letters for me, please? 你能替我保存这些信吗? ②意为"遵守;维护"。如: Everyone must keep the rules. 人人必须遵守规章制度。 The teacher is keeping order in class.老师正在课堂上维持秩序。 ③意为"使……保持某种(状态、位置或动作等)"。这时要在keep的宾语后接补足语,构 成复合宾语。其中宾语补足语通常由形容词、副词、介词短语、现在分词和过去分词等充当。如: 例:We should keep our classroom clean and tidy.(形容词) 我们应保持教室整洁干净。 You'd better keep the child away from the fire.(副词)你最好让孩子离火远一点。 The bad weather keeps us inside the house.(介词短语)坏天气使我们不能出门。 Don't keep me waiting for long.(现在分词)别让我等太久。 The other students in the class keep their eyes closed.(过去分词) 班上其他同学都闭着眼睛。 2. 用作连系动词 构成系表结构:keep+表语,意为"保持,继续(处于某种状态)"。其中表语可用形容词、副词、介词短语等充当。如: 例:You must look after yourself and keep healthy.(形容词) 你必须照顾好自己,保持身体健康。 Keep off the grass.(副词)请勿践踏草地。 Traffic in Britain keeps to the left.(介词短语)英国的交通是靠左边行驶的。 注意:一般情况下,keep后接形容词较为多见。再如: She knew she must keep calm.她知道她必须保持镇静。 Please keep silent in class.课堂上请保持安静。 3. ①keep doing sth. 意为"继续干某事",表示不间断地持续干某事,keep后不 能接不定式或表示静止状态的v-ing形式,而必须接延续性的动词。 例:He kept working all day, because he wanted to finish the work on time. 他整天都在不停地工作,因为他想准时完成工作。 Keep passing the ball to each other, and you'll be OK.坚持互相传球,你们就

to of和for的区别

to , of 和for的区别 1.to有到的意思,常常和go,come,get连用引出地点。Go to school , go to the shop , go to the cinema. 常见的短语:the way to 去---的路 On one’s way to 在某人去---的路上 以上的用法中,当地点是副词home,here,there等是to 要去掉。如:get home,the way here To后跟动词原形,是不定式的标志 It is +形容词+(for/of +人+)to do sth.(括号内部分可以省略) It is easy for me to learn English. It is very kind of you to lend me your money. 当形容词表示人的行为特征时用of表示to do的性质时用for Want, hope ,decide, plan , try , fail等词后跟to do I want to join the swimming club. Would like to do I’d like to play basketball with them. It is time to have a break. Next to , close to , from ---to--- 2.for 为,表示目的。 Thank you for Buy sth for sb =buy sb sth It is time for bed. Here is a letter for you.

I will study for our country. 3.of表示所属关系意思是:---的 a map of the world a friend of mine

for和of引导的不定式结构的区别

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