Three-parameter AVO inversion with PP and PS data using
offset binning
Faranak Mahmoudian and Gary F. Margrave
ABSTRACT
We have investigated a method of inverting amplitudes of both PP and converted PS
prestack data to three parameters — P- and S-wave impedance, plus density. Results
from 3-parameter joint inversion are compared with those from 2-parameter joint
inversion, which uses only P- and S-wave impedance data. The inversion program
performs an AVO inversion using a singular value decomposition (SVD) method. The
advantage of the SVD method over the more commonly used least-squares method lies in
working with matrices that are either singular or else numerically very close to singular.
To investigate the contribution of incorporating both PP and PS data in joint inversion, 3-
parameter joint-inversion results are compared to those from PP- and PS-only inversions.
To reduce the computation cost of prestack migration (used for improving lateral
resolution and correlating PP and PS data in depth), the input datasets are arranged in
limited-offset stack sections. Using only a small number of limited-offset stack traces as
input to the inversion program produces results as good as using all offset traces.
INTRODUCTION
The main objective in interpreting seismic data is the extraction of information most
related to lithology and/or fluid content of rocks being imaged. The quality most closely
related to seismic trace amplitudes — and that which best characterizes rock properties
— is elastic impedance, which can be extracted from seismic data. Theoretical
knowledge about the variation of reflectivity with offset derived from Zoeppritz
equations can be used to estimate impedances. Since the Zoeppritz equations are highly
nonlinear with respect to velocities and density, many approximations have been made in
order to linearize them. Aki and Richards (1980) assumed small, welded-layer contrasts
and simplified the equations. The Aki and Richards linear approximations for PP and PS
reflection coefficients, PP R and PS R , can be reformulated as function of density and P-
wave and S-wave impedance (Larsen 1999), i.e., )//I /I (I ρρ?+αα?=?αρ= and
)//I /I (J ρρ?+ββ?=?βρ= as:
ρρ?θ+?θ+?θ=θ)(C J J )(B I I )(A )(R PP (1)
ρ
ρ??θ+??θ=?θ),(D J J ),(E ),(R PS (2) where,
212)tan ()A(θ+=θ (3)
θαβ?=θ2224sin )(B (4)
????????θαβ?θ?=θ222222sin tan )(C (5) ??
?????θαβ??+β?α?=?θcos cos sin tan ),(D 22122 (6)
???????θαβ??β?α=
?θcos cos sin tan ),(E 222 (7) where α is P-wave velocity, β is S-wave velocity, and ρ is density. The coefficients A, B,
C, D, and E are functions of the P-wave incident angle, θ, the S-wave reflected angle, φ,
and the S- to P-wave velocity ratio.
Using Gardner’s relation between density and P-wave velocity, the density reflectivity
term (?ρ/ρ) can be rewritten as a function of P-wave impedance, I /I ).(/?=ρρ?20.
This assumption reduces the equations (1) and (2) to linear combinations of 2 parameters
?I/I and ?J/J. In this case, inverting equations (1) and (2) to obtain 2 parameters (?I/I and
?J/J) is called 2-parameter joint inversion of PP and PS reflection seismic data.
Introduced by Stewart (1990) following of the weighted stack scheme of Smith and
Gidlow (1987), 2-parameter joint inversion is based on least-squares inversion. Early
applications of 2-parameter joint inversion on real data were by Larsen and Margrave
(1999), and Zhang and Margrave (2003). The 2-parameter joint-inversion method by
least-squares method is fully discussed in Mahmoudian and Margrave (2003).
Here we present an inversion method to invert equations (1) and (2) using a singular
value decomposition (SVD) method to obtain 3 parameters — ?I/I, ?J/J, and ?ρ/ρ. This
method is called 3-parameter joint inversion. Additionally, we have done 2-parameter
joint inversion, 3-parameter PP inversion (for only PP data), and 2-parameter PS
inversion (for only PS data) with the SVD method.
THEORY
Assuming that the PP and PS reflection data provide estimates of PP R and PS R over a
range of source-receiver offsets, the Aki and Richards approximations for different
offsets at a certain depth can be used to express a linear system of 2m linear equations (m
being number of offsets) with 3 unknowns:
133211*********×××????????????????????????????????????=????????????????????ρρ???J J I I D E D E C B A C B A R R R R m m m m m m m PSm PS PPm PP , (8)
or equivalently as the matrix equation:
Ax y =, (9) where T PSm PS PPm PP )R R R R (y ……11= is the reflection data vector. Matrix A is
a 32×m matrix of known coefficients computed by ray-tracing a smoothed background
velocity. T ) /J /J I /I (x ρρ???= is the vector of unknown parameters. The AVO
inversion problem has now been reduced to solving the matrix equation (8) to obtain the
parameters vector x. Problem (9) may be approached by operating on both sides with an
)m (23×’inverse ’ matrix H and the ‘solution ‘, or model, would be,
Hy x
=?. (10) The operator H will be a good inverse if the response of x ?
A fits the refection data and the uncertainties in x ? are not too large, i.e. )x ?
var( is small (Jackson, 1971). To find the inverse of the non-square matrix A , the powerful SVD method is used. The same
procedure has been taken in PP and PS inversion only.
SVD ANALYSIS
For 32×m matrix A (or, in general, for any m n × matrix) with the rank r , there is
always a matrix decomposition called a singular value decomposition (SVD) of matrix A .
Singular value decomposition allows the coefficient matrix A to be expressed as the
product of three matrices (Lay, 1996),
T UDV A = (11) The columns of matrix U are the eigenvectors of the matrix T AA , related to the r nonzero
eigenvalues. The columns of matrix V are the eigenvectors of the matrix A A T , related to
the r nonzero eigenvalues. The singular values of the matrix A are the positive square
roots of the eigenvalues of the matrix A A T . D is a diagonal matrix with the non-zero
singular values of the matrix A in the diagonal elements in the form of:
.D r r r r 000211>σ≥≥σ≥σ?????????
?σσ=× (12)
The SVD of the 32×m matrix A , always exists due to exist of matrixes U, V and D . For
any arbitrary matrix A , the matrixes A A T and T AA are symmetric, which based on linear
algebra have real eigenvalues and orthogonal eigenvectors. In this regard by definition
the matrices U, V and D always exist (Lay, 1996).
Since the diagonal entries in matrix D are nonzero, the pseudo-inverse (also the
Lanczos inverse) of matrix A is defined as (Lay, 1996):
T U VD H 1?= (13) T j U diag V H ???
?????????????σ=1 (14) Defining the matrix H , some rules from linear algebra is used including the relations
m T T I U U UU 2== and r T T I V V VV == for orthogonal matrixes U and V . With the
definition of pseudo- inverse matrix in equation (13) the following equations hold:
H HAH = (15) A AHA = (16) Now we return to our inversion problem, equation (9). Using the pseudo-inverse of
matrix A , the parameter vector x ?
can be obtained as:
HAHy Hy x ?HA or y Ax === (17)
Hy x ?=; (18) equivalently,
y U VD x ? T 1?= (19) Knowing the matrices U, V and D from SVD factorization of matrix A , the pseudo-
inverse matrix H can be constructed. Then the parameter vector x ?
can be achieved from equation (19). Any possible instability in the numerical calculation of x ? is identified in
matrix D , because the only thing that can go wrong with using SVD is when inverting a
matrix that has some zero or very small singular value like j σ. As in equation (14), the
value of )/(j σ1 is dominated by a round-off error and therefore unknowable. In such
cases, we can simply replace )/(j σ1 by zero (Press et al., 1992, and Wiggins, 1971). It
may seem paradoxical that this can be so, since zeroing a singular value corresponds to
throwing away one linear combination of the set of equations that we are trying to solve.
Answering this, Press et al., (1992) state that “the resolution of the paradox is that we are
throwing away precisely a combination of equations that is so corrupted by round-off errors as to be at best useless .”
Therefore if the singular values of matrix A are extremely small, round-off errors are almost inevitable, but an error analysis is aided by knowing the entries in D and V. Calculating the x ?error, the )x ?var( is calculated as:
)y var(H )x ?var(i m i ki k ∑==21
2 (20)
For statistically independent data with unit variance, using the definition for inverse matrix H (equation (14)), the x ?error is (Jackson, 1972), ∑=???
?????σ=r j j kj k V )x ?var(12 (21) This allows us to examine each model parameter k x ?
individually. As we mentioned, a sensitive way to control the variance is to construct the inverse H out of only those eigenvectors corresponding to large enough eigenvalues. In our model examples, to set a threshold for deciding which eigenvalue is dominating the round-off error, we looked at the condition number of matrix A . The ratio n /σσ1 of the largest and smallest singular values gives the condition number of matrix A .
IMPLEMENTATION
The joint inversion program is designed to have PP and PS common image gathers, as well as a velocity-depth model as input. The PP and PS gathers were synthetics created in SYNTH (CREWES MATLAB library). Both gathers were created initially as broadband responses and then convolved with the appropriate wavelet. From our experience, PS data recorded on land has about half the bandwidth of the corresponding PP data. Therefore, the PS synthetics were generated with a different initial wavelet than the PP synthetics. The combination of PP and PS data in an inversion requires that the two data types be correlated in time or depth. We followed a procedure to correlate the PP and PS synthetic sections in depth. At each depth sample, the coefficient matrix (matrix A in equation (9)), is calculated. Using the SVD factorization of matrix A , the pseudo-inverse matrix H in equation (13) is constructed using the routine RINV (CREWES MATLAB library). As a last step, the parameters vector x ? is calculated from equation (17). The three components
of parameters vector x ?
are the estimated ?I/I , ?J/J , and ?ρ/ρ. For each depth sample, the estimated reflectivity results, (?I/I , ?J/J , and ?ρ/ρ), were integrated to I , J and ρ using the band-limited impedance routine (BLIMP) from the CREWES MATLAB library. The BLIMP routine is a simple algorithm for band-limited impedance inversion (Ferguson and Margrave, 1996). To approximate the subsurface impedance using seismic data, it is necessary to account for the band-limited nature of seismic data, especially for low-frequencies (Ferguson and Margrave, 1996). The BLIMP routine uses impedance estimated from logs (or a density model) to provide the missing low-frequency components of the input seismic data. In summary, we inverted PP and PS
amplitudes to I, J and ρ including the low-frequency component, which significantly improves the inversion results (Mahmoudian and Margrave, 2003).
2- and 3-parameter joint inversion
The parameter vector x ?
calculated by 2-parameter joint inversion is consisted of ?I/I and ?J/J . The parameter ?ρ/ρ is calculated using Gardener’s rule from ?I/I term as )I /I )(?.(/?20=ρρ. Extending 2-parameter joint inversion to 3-parameter joint
inversion for modelling the same data, helps the response of x ?
A fit the data better by avoiding another approximation for ?ρ/ρ term. Such extension theoretically will result in more accurate estimation for all 3 parameters.
FIG.1. A simple velocity model in depth.
To compare the 3-parameter joint inversion with 2-parameter joint inversion, the inversion results for the sample velocity model of Figure 1 is shown in Figure 2. Note that in 2-parameter joint inversion, the estimated ρ comes from the estimated I by using Gardener’s rule. In Figure 2, red plots are the inversion results from the 3-parameter joint inversion and green plots are inversion results from the 2-parameter joint inversion, and the blue plots are true value directly calculated from the logs. Note this example obeys Gardener’s rule, and it is expected that 2-parameter has also good estimation for ?ρ/ρ. Vp
Vs ρ
FIG. 2. Comparing the estimated I,J and ρ from 2-parameter and 3-parameter joint inversions for the sample velocity model in Figure 1. The red line plots the results from 3-parameter joint inversion; the green line plots the results from the 2-parameter joint inversion method, and the blue line plots the true value.
To demonstrate the advantages of 3-parameter joint inversion over 2-parameter joint inversion, the inversion results for the sample velocity model of Figure 3 is shown in Figure 4. Note that, for the velocity model of Figure 3, the density doesn’t obey Gardener’s rule. Figure 4 clearly shows that 3-parameter joint inversion can estimate density even when density is uncorrelated with P-wave velocity. A careful look at Figure 4 reveals that 2-parameter joint inversion can estimate I and J almost as good as 3-
parameter joint inversion.
FIG. 3. A simple velocity model in depth.
FIG. 4. Comparison of the estimated I, J and ρ from 2- and 3-parameter joint inversions for the sample velocity model in Figure 3. The red plots display results from 3-parameter joint inversion; the green plots display the inversion results from the 2-parameter joint inversion method, and the blue plots are true values.
Comparing 3-parameter joint inversion with PP- and PS-only inversions In this paper, we term the separate inversions of either PP or PS reflection data with the SVD method, PP-only and PS-only inversions, respectively. PP inversion only gives estimations for I, J and ρ and PS inversion only gives estimations for J and ρ. The estimation of I in PS-only inversion is calculated from the ρ estimation by Gardener’s rule.
The joint inversion, by co-operating more equations due to the addition of PS data (rather than PP inversion only) or PP data (rather than PS inversion only), theoretically results in a more accurate solution. For the sample velocity model in Figure 3, the advantage of joint inversion over PP- or PS-only inversions are shown in Figures 5–10. In Figures 5–10, the red plots display the results from joint inversion; the black plots display the results from PP- or PS-only inversions; the blue plots are true values. For the velocity model example in Figure 3, the input PP and PS synthetics gather to inversion program, is generated with the initial zero-phase wavelets 5-10-80-100 and 3-7-57-70, respectively. With these initial wavelets for the velocity model in Figure 3, the generated PP and PS gather has an identical wave-number bandwidth. In Figures 5 and 6, the estimated results from above three inversions are compared using synthetic noise-free data. Figures 5 and 6 show that joint inversion can estimate I, J, and ρ better than PP- or
PS-only inversions.
for the sample velocity model in Figure 3.
FIG. 6. Comparing the estimated I, J and ρ from PS-only and joint inversions from noise-free data for the sample velocity model in Figure 3.
Since the joint-inversion method has twice the input data compared to PP or PS inversion only, it is reasonable to assume a corresponding improvement in signal-to-noise is possible (Larsen, 1999). To examine the effect of noise upon inversion accuracy, random noise was added to the synthetics data. Figures 7 and 9 show the inversion results
from noisy data with signal-to-noise ratio of 2. This amount of noise is larger than is
typically encountered in real surface seismic data. The inversion results after adding more noise to the data, to reach a signal-to-noise ratio of 1, are shown in Figures 8 and 10. Figures 7–10 show very clearly that the joint inversion method obtains very good results even from very noisy data. Furthermore, Figures 7 and 8 show that the estimations of J and ρ from PP-only inversion are highly sensitive to the presence of noise, while the same inversion resulted in a good estimation for I. Similarly, Figures 9 and 10 show that the estimation of I from PS-only inversion is highly sensitive to the presence of noise, while providing good estimations for J and ρ.
FIG. 7. Comparing the estimated I, J and ρ from PP-only and joint inversions of noisy data with a signal-to-noise ratio of 2, for the sample velocity model in Figure 3.
FIG. 8. Comparison of the estimated I, J and ρ from PP-only and joint inversions of noisy data with a signal-to-noise ratio of 1, for the sample velocity model in Figure 3.
with signal-to-noise ratio of 2, for the sample velocity model in Figure 3.
FIG. 10. Comparison of the estimated I, J and ρ from PS-only and joint inversions of noisy data with a signal-to-noise ratio of 1, for the sample velocity model in Figure 3.
Inversion of a real log example
In this section, the inversion results for the real velocity model in Figure 11 are examined. The velocity model comes from the Blackfoot Field in southeastern Alberta,
Canada, owned and operated by EnCana. The PP and PS synthetics were generated with
different input wavelets. A zero-phase (Butterworth) wavelet 5-10-80-100 was used for PP synthetics, and another zero-phase wavelet, 3-7-57-70, was used for PS synthetics. Both PP and PS synthetics have the same offset range of 0 to 2000 m.
In this example, the singular values of a matrix of coefficients A were examined at each sample depth using joint inversion. At 1500 metres, the singular values of coefficient matrix A are 3.22, 1.29, and 0.25. The condition number of matrix A at this depth is approximately 0.07, which is not a very small number and there is no need to eliminate any small singular values. The coefficient matrix A has similar singular values at other depths. At 1500 metres, the errors of I , J , and ρ are 0.2, 1.29, and 14.4, respectively. The errors at other depths are similar. These errors show that joint inversion can estimate I more accurately than J and ρ. Furthermore, they show that joint inversion can estimate J more accurately than density. The estimations for I , J , and ρ obtained by joint inversion for the velocity model in Figure 11 are shown in Figure 12. Figure 12 shows a good estimation for the three parameters I , J , and ρ from 3-parameter joint inversion.
FIG. 11. Real velocity logs from the Blackfoot Field.
The PP-only inversion was done for velocity using SVD method. At 1500 metres, the singular values of coefficient matrix A are 3.1, 0.5, and 0.08. At this depth, the condition number of matrix A equals 0.026, which is a large-enough ratio, and means that there is no need to eliminate any small singular values. The coefficient matrix A has similar singular values for other depths. Therefore, for all sample depths, no singular values were removed. At 1500 metres, the errors of I , J , and ρ are 0.67, 9.21, and 145 respectively. The estimated results from PP-only inversion and joint inversion are compared in Figure
13. Figure 13 shows that 3-parameter joint inversion can better estimate J and ρ than 3-parameter PP-only inversion, although PP-only inversion has very good estimation for I .
---- P-wave velocity
---- S-wave velocity
----Density
Vp Vs ρ
Figure 11. The red lines plot the joint-inversion results, and the blue lines plot true values.
FIG. 13. Comparison of the estimations for I,J, and ρ from 3-parameter PP-only and joint inversions for the real velocity model in Figure 11. The red lines plot the joint-inversion results; the green lines plot PP-only inversion results; and the blue lines plot true values.
In a similar manner, the PS-only inversion was done for the model in Figure 11. At 1500 metres, the singular values of the coefficient matrix A, are 1.26, 0.24. Note that the PS-only inversion estimates J and ρ, and the estimation of I is calculated by Gardener’s
relation. The condition number of matrix A at this depth is approximately 0.19, which is s
large-enough ratio, and means that there is no need to eliminate any small singular values. The coefficient matrix A has similar singular values for other depths. Therefore, in PS-only inversion, no singular values were removed for all sample depths. At 1500 metres, the errors of J and ρ are 1.51 and 16.76, respectively. The estimated results from PS-only and joint inversions are compared in Figure 14. Figure 14 shows that joint inversion can better estimate I, J, and ρ than PS-only inversion, although PS-only inversion has very good estimation for J and ρ.
FIG. 14. Comparing the estimated I,J, and ρ from PS-only and joint inversions for the real velocity model in Figure 11. The red lines plot joint inversion results; the black lines plot PS-only inversion results, and the blue lines plot true values.
To examine the reliability of 3-parameter joint inversion for the velocity model in Figure 11, the input PP and PS synthetics were generated with a broadband initial wavelet. The estimated I, J, and ρ from joint inversion with non-smoothed input velocity is shown in Figure 15. In Figure 15, the black curve is estimated from joint inversion and the blue curve is the true value from the logs. The difference between estimated I, J, and ρ, and true values is mainly due to two reasons — using the linear Aki and Richards approximations instead of exact Zoeppritz equations, and using the smoothed velocity model. To examine the impact of smoothing the velocity, the program is run with highly smoothed velocity as input. The estimated I, J, and ρ from joint inversion with this highly smoothed input velocity is shown in Figure 16. In Figure 16, the red curve is estimated with highly smoothed velocity, the black curve is estimated with non-smoothed velocity, and the blue curve is the true value from the logs. Comparing the black curve and red curve in Figure 16 shows that the joint inversion performs very well with even highly smoothed input velocity for I and J estimations, and provides a decent density estimation. Therefore, there is no need to use exact velocity information in applying the joint inversion.
inversion for the real velocity model in Figure 11.
FIG. 16. The estimated I, J, and ρ from joint inversion for the real velocity model in Figure 11. The red lines plot inversion results with highly smoothed velocity; the black plots display the inversion results with non-smoothed velocity; and the blue plots are true value.
SVD: the best least-squares solution
The SVD solution of the equations (9), parameters vector x?(the estimated ?I/I, ?J/J and ?ρ/ρ), is also a least-squares solution (Jackson, 1972, and Lay, 1996). In general, SVD finds the least-squares best compromise solution (Press et al., 1992). The advantage of using SVD over the normal least-squares method is in dealing with matrices that are
either singular or else numerically very close to singular. A matrix is called singular
when it has some singular value equal to zero. SVD will diagnose precisely when a matrix is singular and give a useful numerical answer.
To demonstrate this, the 3-parameter joint inversion is applied to a velocity model (Figure 1) using two methods — SVD and least-squares. In this example, the input PP and PS synthetic gathers are generated with an initial zero-phase wavelet 5-10-80-100, and a zero-phase wavelet 5-10-30-40, respectively. At each sample depth, the singular values of the matrix of coefficients A were examined. At 1500 metres, the singular values of coefficient matrix A are 3.48, 1.42 and 0.8. At this depth, the condition number of matrix A is 0.23. The coefficient matrix A is also similar for other depths. Theoretically, the SVD method is expected to have identical results for inverting a matrix to those from the least-squares method, which are neither singular nor near singular
Figure 17 shows the estimated I, J, and ρ from the 3-parameter joint inversion program. In this figure, the red lines plot the inversion results using the SVD method, and the green lines plot the results using the least-squares method. As we expected in theory (Figure 2), the identical red and green plots show that the SVD solution is also a least-squares solution.
FIG. 17. Comparing the estimated I and J and ρ from 3-parameter joint inversion by SVD and least-squares methods, for the sample velocity model in Figure 1. The red lines plot inversion results using the SVD method, and the green lines plot the inversion results using the least-squares method.
To demonstrate the advantage of using SVD over the common least-squares method, the real velocity model in Figure 11 is used for PP-only inversion. The input PP gather was generated with an initial zero-phase wavelet, 5-10-80-100. At 8400 ft, the singular
10?. At this depth, the condition values of coefficient matrix A are 1.6633, 0.0078, and6
number of matrix A is approximately 7
10?. The coefficient matrix A has similar singular
values for other depths. To stabilize the inversion, we zeroed the smallest singular value at all depths. The PP-only inversion results with the least-squares and SVD methods are shown in Figures 18 and 19. In Figure 18, the incorrect estimation for J and very poor estimation for ρ is clear. Compare this to Figure 19, where the inversion results using the SVD method show very accurate estimations for I , J , and ρ. Comparing I , J , and ρ in Figures 18 and 19 is a very good example showing the advantage of using the powerful SVD method over the more common least-squares method.
FIG. 18. A real velocity model, with measurements in feet. For greater clarity, the density log was
shifted to the right by a constant. The log comes from UNOCAL.
FIG. 19. The estimated I, J , and ρ from PP-only inversion for the real velocity model in Figure 18. The black lines plot display inversion results using the least-squares method, and the blue lines plot the true values. Vp
Vs ρ
FIG. 20. The estimated I,J, and ρ from PP-only inversion for the real velocity model in Figure 18. The red lines plot the SVD method inversion results, and the blue lines plot true values.
Binning size effect on inversion results
Conventional seismic inversion uses a single seismic trace, assumed to be at vertical incidence, for impedance inversion. The joint-inversion algorithm uses several seismic traces which share a common subsurface reflection or conversion point, but which have different angles of incidence (Henley et al., 2002). We first converted the CDP (PP case) and CCP (PS case) gathers to depth, and used these gathers as input to the inversion program. In the case of real datasets, converting to depth requires prestack migration. Prestack migration takes considerable computation time, due to the large number of traces in each gather. Computation cost can be significantly reduced using a more favourable arrangement of raw CDP and CCP gathers. Henley et al. (2002) describes using the limited-offset stack traces from either CDP or CCP gathers as input for the joint-inversion module in ProMAX. Each limited-offset stack trace is the result of stacking NMO-corrected PP or PS traces from a limited range of offsets, and represents the mean offset for traces which were stacked.
For the real log model in Figure 11, a PP and PS gather was created with 21 traces within the offset range of 0–2000 metres with a signal-to-noise ratio of 2, as shown in the topmost plots in Figure 21. The limited-offset stack sections, with 5 non-overlapping
bins, are shown in the lower plots in Figure 21 for this PP and PS gather.
FIG. 21. Top: The PP and PS gather for the real log model in Figure 11. Bottom: The PP limited-stack section with five limited-offset stack traces (5 bins with no overlap) on the left and the PS limited-stack section with five limited-offset stack traces (5 bins with 50% overlap) on the right. After the limited-offset stack sections were entered into the inversion program, a poststack migration was performed as opposed to a full prestack migration. This method reduces the expense of inversion at the risk of decreasing the accuracy of the result. The number of input limited-offset stack traces is called the binning size. For the real log example in Figure 11, we calculated the RMS error for the I , J and ρ estimations, to see the impact of binning size on inversion results. These estimations for different bin sizes are compared to the actual values. The RMS error of estimated I , J and ρ in the zone of interest, between 1400–1500 metres, is shown in Figure (21).
The P- and S-wave impedance, and density estimations from the 3-parameter joint inversion of 3 bins, 5 bins with no overlaps, full-offset traces with no binning, and the actual value are shown in Figure 22. The red lines are inversion results using 3-bin input; green lines, results using 5 bins; black lines show results using full-offset traces; and blue lines are true values. The RMS error plots show a general progression of increasing accuracy as the number of bins increases. However, it is not a simple linear trend, as certain bin sizes appear much more effective than others: five bins seem to work better than three, although three bins still perform very well.
PP limited-offset stack section
5 bins without overlap PP gather
PS gather
PS limited-offset stack section 5 bins with 50% overlap
FIG. 22. The RMS-error plots of inversion results using different binning sizes. The input log is shown in Figure 11.
At present, we do not know whether these results are particular to the geometry and lithology of our example or are more general. We suspect that the effectiveness of a particular binning scheme will depend upon the behaviour with offset of PP R and PS R . If these functions vary linearly across the bin, then the average reflection coefficient over the bin is well approximated by the value of the coefficient at the bin centre. In this case, the binning scheme should succeed. It does seem safe to conclude that there is little need to maintain all offset traces without binning and a small number of bins will give excellent results. Since offset binning leads to very efficient prestack migration schemes, there is a strong economic incentive for binning.
With的用法全解 with结构是许多英语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。 一、 with结构的构成 它是由介词with或without+复合结构构成，复合结构作介词with或without的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二部分补足语由形容词、副词、介词短语、动词不定式或分词充当，分词可以是现在分词，也可以是过去分词。With结构构成方式如下： 1. with或without-名词/代词+形容词； 2. with或without-名词/代词+副词； 3. with或without-名词/代词+介词短语； 4. with或without-名词/代词 +动词不定式； 5. with或without-名词/代词 +分词。 下面分别举例： 1、 She came into the room，with her nose red because of cold.（with+名词+形容词，作伴随状语）
2、 With the meal over ， we all went home.（with+名词+副词，作时间状语） 3、The master was walking up and down with the ruler under his arm。（with+名词+介词短语，作伴随状语。） The teacher entered the classroom with a book in his hand. 4、He lay in the dark empty house，with not a man ，woman or child to say he was kind to me.（with+名词+不定式，作伴随状语）He could not finish it without me to help him.（without+代词 +不定式，作条件状语） 5、She fell asleep with the light burning.（with+名词+现在分词，作伴随状语） Without anything left in the with结构是许多英 语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。 二、with结构的用法 with是介词，其意义颇多，一时难掌握。为帮助大家理清头绪，以教材中的句子为例，进行分类，并配以简单的解释。在句子中with结构多数充当状语，表示行为方式，伴随情况、时间、原因或条件（详见上述例句）。 1.带着，牵着…… (表动作特征)。如： Run with the kite like this.
1. with+宾语+形容词。比如：. The boy wore a shirt with the neck open, showing his bare chest. 那男孩儿穿着一件衬衫，颈部敞开，露出光光的胸膛。Don’t talk with your mouth full. 嘴里有食物时不要讲话。 2. with+宾语+副词。比如：She followed the guide with her head down. 她低着头，跟在导游之后。 What a lonely world it will be with you away. 你不在，多没劲儿呀！ 3. with+宾语+过去分词。比如：He was listening to the music with his eyes half closed. 他眼睛半闭着听音乐。She sat with her head bent. 她低着头坐着。 4. with+宾语+现在分词。比如：With winter coming, it’s time to buy warm clothes. 冬天到了，该买些保暖的衣服了。 He soon fell asleep with the light still burning. 他很快就睡着了，（可）灯还亮着。 5. with+宾语+介词短语。比如：He was asleep with his head on his arms. 他的头枕在臂膀上睡着了。 The young lady came in, with her two- year-old son in her arms. 那位年轻的女士进来了，怀里抱着两岁的孩子。 6. with+宾语+动词不定式。比如： With nothing to do in the afternoon, I went to see a film. 下午无事可做，我就去看了场电影。Sorry, I can’t go out with all these dishes to wash. 很抱歉，有这么多盘子要洗，我不能出去。 7. with+宾语+名词。比如： He died with his daughter yet a school-girl.他去逝时，女儿还是个小学生。 He lived a luxurious life, with his old father a beggar . 他过着奢侈的生活，而他的老父亲却沿街乞讨。(8)With so much work to do ,I can't go swimming with you. (9)She stood at the door,with her back towards us. (10)He entered the room,with his nose red with cold. with复合结构与分词做状语有啥区别 [ 标签：with, 复合结构, 分词状语] Ciro Ferrara 2009-10-18 16:17 主要是分词形式与主语的关系 满意答案好评率：100%
精神分裂症的病因及发病机理 精神分裂症病因：尚未明，近百年来的研究结果也仅发现一些可能的致病因素。（一）生物学因素1．遗传遗传因素是精神分裂症最可能的一种素质因素。国内家系调查资料表明：精神分裂症患者亲属中的患病率比一般居民高6.2倍，血缘关系愈近，患病率也愈高。双生子研究表明：遗传信息几乎相同的单卵双生子的同病率远较遗传信息不完全相同 的双卵双生子为高，综合近年来11项研究资料：单卵双生子同病率（56.7%），是双卵双生子同病率（12.7%）的4.5倍，是一般人口患难与共病率的35-60倍。说明遗传因素在本病发生中具有重要作用，寄养子研究也证明遗传因素是本症发病的主要因素，而环境因素的重要性较小。以往的研究证明疾病并不按类型进行遗传，目前认为多基因遗传方式的可能性最大，也有人认为是常染色体单基因遗传或多源性遗传。Shields发现病情愈轻，病因愈复杂，愈属多源性遗传。高发家系的前瞻性研究与分子遗传的研究相结合，可能阐明一些问题。国内有报道用人类原癌基因Ha-ras-1为探针，对精神病患者基因组进行限止性片段长度多态性的分析，结果提示11号染色体上可能存在着精神分裂症与双相情感性精神病有关的DNA序列。2．性格特征：约40%患者的病前性格具有孤僻、冷淡、敏感、多疑、富于幻想等特征，即内向
型性格。3．其它：精神分裂症发病与年龄有一定关系，多发生于青壮年，约1/2患者于20～30岁发病。发病年龄与临床类型有关，偏执型发病较晚，有资料提示偏执型平均发病年龄为35岁，其它型为23岁。80年代国内12地区调查资料：女性总患病率（7.07%。）与时点患病率（5.91%。）明显高于男性（4.33%。与3.68%。）。Kretschmer在描述性格与精神分裂症关系时指出：61%患者为瘦长型和运动家型，12.8%为肥胖型，11.3%发育不良型。在躯体疾病或分娩之后发生精神分裂症是很常见的现象，可能是心理性生理性应激的非特异性影响。部分患者在脑外伤后或感染性疾病后发病；有报告在精神分裂症患者的脑脊液中发现病毒性物质；月经期内病情加重等躯体因素都可能是诱发因素，但在精神分裂症发病机理中的价值有待进一步证实。（二）心理社会因素1．环境因素①家庭中父母的性格，言行、举止和教育方式（如放纵、溺爱、过严）等都会影响子女的心身健康或导致个性偏离常态。②家庭成员间的关系及其精神交流的紊乱。③生活不安定、居住拥挤、职业不固定、人际关系不良、噪音干扰、环境污染等均对发病有一定作用。农村精神分裂症发病率明显低于城市。2．心理因素一般认为生活事件可发诱发精神分裂症。诸如失学、失恋、学习紧张、家庭纠纷、夫妻不和、意处事故等均对发病有一定影响，但这些事件的性质均无特殊性。因此，心理因素也仅属诱发因
with的用法大全----四级专项训练with结构是许多英语复合结构中最常用的一种。学好它对学好复合宾语结构、不定式复合结构、动名词复合结构和独立主格结构均能起很重要的作用。本文就此的构成、特点及用法等作一较全面阐述，以帮助同学们掌握这一重要的语法知识。 一、 with结构的构成 它是由介词with或without+复合结构构成，复合结构作介词with或without的复合宾语，复合宾语中第一部分宾语由名词或代词充当，第二部分补足语由形容词、副词、介词短语、动词不定式或分词充当，分词可以是现在分词，也可以是过去分词。With结构构成方式如下： 1. with或without-名词/代词+形容词; 2. with或without-名词/代词+副词; 3. with或without-名词/代词+介词短语; 4. with或without-名词/代词+动词不定式; 5. with或without-名词/代词+分词。 下面分别举例：
1、 She came into the room，with her nose red because of cold.(with+名词+形容词，作伴随状语) 2、 With the meal over ， we all went home.(with+名词+副词，作时间状语) 3、The master was walking up and down with the ruler under his arm。(with+名词+介词短语，作伴随状语。) The teacher entered the classroom with a book in his hand. 4、He lay in the dark empty house，with not a man ，woman or child to say he was kind to me.(with+名词+不定式，作伴随状语) He could not finish it without me to help him.(without+代词 +不定式，作条件状语) 5、She fell asleep with the light burning.(with+名词+现在分词，作伴随状语) 6、Without anything left in the cupboard， she went out to get something to eat.(without+代词+过去分词，作为原因状语) 二、with结构的用法 在句子中with结构多数充当状语，表示行为方式，伴随情况、时间、原因或条件(详见上述例句)。
一、选择题 1、With time ____ by , they got to know each other better. A. passes B. passing C. passed D. to be passed 2、 the economic crisis getting more and more serious, the government is searching for ways to improve people’s life. A. As B. With C. When D. If 3John received an invitation to dinner, and with his work ____, he gladly accepted it. A. finished B. finishing C. having finished D. was finished 4、With all flights___, they had to come by bus. A. had canceled B.canceled C.have been canceled D. having canceled 5、With a large number of people _______ camping, it has now become one of the most popular activities in the UK. A. take part in B. took part in C. taking part in D. to be taking part in 6、None of us had expected that the middle﹣aged engineer died with his design _________（） A．.to uncomplete B．.uncompleted C．uncompleting．D．.uncomplete 7、______，we managed to get out of the forest．（） A．The guide led the way B．The guide leading the way C．With the guide to lead the way D．Having led the way 8、Will all his work ,he could have a good rest. A.to do B.doing C.did D.done 9、 ______, her suggestion is of greater value than yours. A. All things considering B. All things considered C. All things were considered D. With all things were considered 10、With the kind boy ________ the way, we found the park soon. A. leads B. to lead C. led D. leading 11、 She stood there, ______ from her cheeks. A. tears' rolling down B. tears rolled down C. with tears rolled down D. tears rolling down 12、 While watching television, __________. A. the doorbell rang B. the doorbell rings C. we heard the doorbell ring D. we heard the doorbell rings 13、The murderer was brought in, with his hands______ behind his back. A. be tied B. having tied C. to be tied D. tied 14、 With a lot of difficult problem _____, the newly-elected president is having a hard time.
英语中的五种基本句型结构 一、句型1：Subject (主语) ＋Verb (谓语) 这种句型中的动词大多是不及物动词，所谓不及物动词，就是这种动词后不可以直接接宾语。常见的动词如：work, sing, swim, fish, jump, arrive, come, die, disappear, cry, happen等。如： 1) Li Ming works very hard.李明学习很努力。 2) The accident happened yesterday afternoon.事故是昨天下午发生的。 3）Spring is coming. 4) We have lived in the city for ten years. 二、句型2：Subject (主语) ＋Link. V(系动词) ＋Predicate(表语) 这种句型主要用来表示主语的特点、身份等。其系动词一般可分为下列两类： (1)表示状态。这样的词有：be, look, seem, smell, taste, sound, keep等。如： 1) This kind of food tastes delicious.这种食物吃起来很可口。 2) He looked worried just now.刚才他看上去有些焦急。 (2)表示变化。这类系动词有：become, turn, get, grow, go等。如： 1) Spring comes. It is getting warmer and warmer.春天到了，天气变得越来越暖和。 2) The tree has grown much taller than before.这棵树比以前长得高多了。 三、句型3：Subject(主语) ＋V erb (谓语) ＋Object (宾语) 这种句型中的动词一般为及物动词, 所谓及物动词，就是这种动词后可以直接接宾语，其宾语通常由名词、代词、动词不定式、动名词或从句等来充当。例： 1) He took his bag and left.（名词）他拿着书包离开了。 2) Li Lei always helps me when I have difficulties. (代词)当我遇到困难时，李雷总能给我帮助。 3) She plans to travel in the coming May Day.（不定式）她打算在即将到来的“五一”外出旅游。 4) I don’t know what I should do next. (从句)我不知道下一步该干什么。 注意：英语中的许多动词既是及物动词，又是不及物动词。 四、句型4：Subject(主语)＋Verb(谓语)＋Indirect object(间接宾语)＋Direct object (直接宾语) 这种句型中，直接宾语为主要宾语，表示动作是对谁做的或为谁做的，在句中不可或缺，常常由表示“物”的名词来充当；间接宾语也被称之为第二宾语，去掉之后，对整个句子的影响不大，多由指“人”的名词或代词承担。引导这类双宾语的常见动词有：buy, pass, lend, give, tell, teach, show, bring, send等。如： 1) Her father bought her a dictionary as a birthday present.她爸爸给她买了一本词典作为生日礼物。 2）The old man always tells the children stories about the heroes in the Long March. 老人经常给孩子们讲述长征途中那些英雄的故事。上述句子还可以表达为： 1）Her father bought a dictionary for her as a birthday present. 2）The old man always tells stories about the heroes to the children in the Long March. 五、句型5：Subject(主语)＋Verb (动词)＋Object (宾语)＋Complement(补语) 这种句型中的“宾语＋补语”统称为“复合宾语”。宾语补足语的主要作用或者是补充、说明宾语的特点、身份等；或者表示让宾语去完成的动作等。担任补语的常常是名词、形容词、副词、介词短语、分词、动词不定式等。如： 1）You should keep the room clean and tidy. 你应该让屋子保持干净整洁。（形容词） 2) We made him our monitor.(名词)我们选他当班长。 3) His father told him not to play in the street.(不定式)他父亲告诉他不要在街上玩。
with用法归纳 （1）“用……”表示使用工具，手段等。例如： ①We can walk with our legs and feet. 我们用腿脚行走。 ②He writes with a pencil. 他用铅笔写。 （2）“和……在一起”，表示伴随。例如： ①Can you go to a movie with me? 你能和我一起去看电影'>电影吗？ ②He often goes to the library with Jenny. 他常和詹妮一起去图书馆。 （3）“与……”。例如： I’d like to have a talk with you. 我很想和你说句话。 （4）“关于，对于”，表示一种关系或适应范围。例如： What’s wrong with your watch? 你的手表怎么了？ （5）“带有，具有”。例如： ①He’s a tall kid with short hair. 他是个长着一头短发的高个子小孩。 ②They have no money with them. 他们没带钱。 （6）“在……方面”。例如： Kate helps me with my English. 凯特帮我学英语。 （7）“随着，与……同时”。例如： With these words, he left the room. 说完这些话，他离开了房间。 [解题过程] with结构也称为with复合结构。是由with+复合宾语组成。常在句中做状语，表示谓语动作发生的伴随情况、时间、原因、方式等。其构成有下列几种情形： 1.with+名词(或代词)+现在分词 此时，现在分词和前面的名词或代词是逻辑上的主谓关系。 例如:1)With prices going up so fast, we can't afford luxuries. 由于物价上涨很快，我们买不起高档商品。（原因状语） 2)With the crowds cheering, they drove to the palace. 在人群的欢呼声中，他们驱车来到皇宫。（伴随情况） 2.with+名词(或代词)+过去分词 此时，过去分词和前面的名词或代词是逻辑上的动宾关系。
with独立主格结构(即with复合结构) with独立主格结构是英语中一种重要的句法现象，在句子结构方面具有相对独立的特点。多年来也一直是命题的热点、重点，因此应该引起我们的高度重视。众所周知，with引导的独立主格结构非常活跃，虽然它在句子中只作状语，但是可以表示伴随、方式、原因、结果等各种复杂的情况。 现将with引导的独立主格结构总结如下。 一、句法结构 【结构一】 with ＋名词（代词）＋介词短语 例１ He sat there thinking, with his chin on his hand． 他手托下巴，坐在那儿沉思。 【结构二】 with ＋名词（代词）＋形容词 例２ He stared at his friend with his mouth wide open． 他张大嘴巴凝视着他的朋友。 【结构三】with ＋名词（代词）＋副词 例３ With production up by 60％, the company has had another excellent year． 产量上升了60％, 公司又是一个好年景。 【结构四】 with ＋名词（代词）＋名词 例４ She used to sit reading in the evening with her pet dog her only companion． 她从前总爱在晚上坐着看书，她的宠物狗便是她唯一的伙伴。 【结构五】with ＋名词（代词）＋现在分词 例５ She stood there chatting with her friend, with her child playing beside her． 她站在那儿跟朋友闲聊，孩子在旁边玩。 【结构六】with ＋名词（代词）＋过去分词
独立主格结构练习题及解析 1. I have a lot of books, half of ___ novels. A. which B. that C. whom D. them 2. __ more and more forests destroyed, many animals are facing thedanger of dying out. A. because B. as C. With D. Since 3. The bus was crowded with passengers going home from market, most of __ carrying heavy bags and baskets full of fruit and vegetables they hadbought there. A. them B. who C. whom D. which 4. The largest collection ever found in England was one of about 200,000 silverpennies, all of ___ over 600 years old. A. which B. that C. them
D. it 5. The cave __ very dark, he lit some candles ___ light. A. was; given B. was; to give C. being; given D. being; to give 6. The soldier rushed into the cave, his right hand __ a gun and his face ____ with sweat.A held; covered B. holding; covering C. holding; covered D. held; covering 7. The girl in the snapshot was smiling sweetly, her long hair ___ . A. flowed in the breeze B. was flowing in the breeze C. were flowing in the breeze D. flowing in the breeze 8. The children went home from the grammar school, their lessons ____ for the day. A. finishing B. finished C. had finished D. were finished 9. On Sundays there were a lot of children playing in the park, ___ parents seated together joking.
精神分裂症的发病原因是什么 精神分裂症是一种精神病，对于我们的影响是很大的，如果不幸患上就要及时做好治疗，不然后果会很严重，无法进行正常的工作和生活，是一件很尴尬的事情。因此为了避免患上这样的疾病，我们就要做好预防，今天我们就请广州协佳的专家张可斌来介绍一下精神分裂症的发病原因。 精神分裂症是严重影响人们身体健康的一种疾病，这种疾病会让我们整体看起来不正常，会出现胡言乱语的情况，甚至还会出现幻想幻听，可见精神分裂症这种病的危害程度。 (1)精神刺激：人的心理与社会因素密切相关，个人与社会环境不相适应，就产生了精神刺激，精神刺激导致大脑功能紊乱，出现精神障碍。不管是令人愉快的良性刺激，还是使人痛苦的恶性刺激，超过一定的限度都会对人的心理造成影响。 (2)遗传因素：精神病中如精神分裂症、情感性精神障碍，家族中精神病的患病率明显高于一般普通人群，而且血缘关系愈近，发病机会愈高。此外，精神发育迟滞、癫痫性精神障碍的遗传性在发病因素中也占相当的比重。这也是精神病的病因之一。 (3)自身：在同样的环境中，承受同样的精神刺激，那些心理素质差、对精神刺激耐受力低的人易发病。通常情况下，性格内向、心胸狭窄、过分自尊的人，不与人交往、孤僻懒散的人受挫折后容易出现精神异常。 (4)躯体因素：感染、中毒、颅脑外伤、肿瘤、内分泌、代谢及营养障碍等均可导致精神障碍，。但应注意，精神障碍伴有的躯体因素，并不完全与精神症状直接相关，有些是由躯体因素直接引起的，有些则是以躯体因素只作为一种诱因而存在。 孕期感染。如果在怀孕期间，孕妇感染了某种病毒，病毒也传染给了胎儿的话，那么，胎儿出生长大后患上精神分裂症的可能性是极其的大。所以怀孕中的女性朋友要注意卫生，尽量不要接触病毒源。 上述就是关于精神分裂症的发病原因，想必大家都已经知道了吧。患上精神分裂症之后，大家也不必过于伤心，现在我国的医疗水平是足以让大家快速恢复过来的，所以说一定要保持良好的情绪。
with用法小结 一、with表拥有某物 Mary married a man with a lot of money . 马莉嫁给了一个有着很多钱的男人。 I often dream of a big house with a nice garden . 我经常梦想有一个带花园的大房子。 The old man lived with a little dog on the lonely island . 这个老人和一条小狗住在荒岛上。 二、with表用某种工具或手段 I cut the apple with a sharp knife . 我用一把锋利的刀削平果。 Tom drew the picture with a pencil . 汤母用铅笔画画。 三、with表人与人之间的协同关系 make friends with sb talk with sb quarrel with sb struggle with sb fight with sb play with sb work with sb cooperate with sb I have been friends with Tom for ten years since we worked with each other, and I have never quarreled with him . 自从我们一起工作以来，我和汤姆已经是十年的朋友了，我们从没有吵过架。 四、with 表原因或理由 John was in bed with high fever . 约翰因发烧卧床。 He jumped up with joy . 他因高兴跳起来。 Father is often excited with wine . 父亲常因白酒变的兴奋。 五、with 表“带来”，或“带有,具有”，在…身上，在…身边之意
独立主格篇 独立主格，首先它是一个“格”，而不是一个“句子”。在英语中任何一个句子都要有主谓结构，而在这个结构中，没有真正的主语和谓语动词，但又在逻辑上构成主谓或主表关系。独立主格结构主要用于描绘性文字中，其作用相当于一个状语从句，常用来表示时间、原因、条件、行为方式或伴随情况等。除名词/代词+名词、形容词、副词、非谓语动词及介词短语外，另有with或without短语可做独立主格，其中with可省略而without不可以。*注：独立主格结构一般放在句首，表示原因时还可放在句末；表伴随状况或补充说明时，相当于一个并列句，通常放于句末。 一、独立主格结构： 1. 名词/代词+形容词 He sat in the front row, his mouth half open. Close to the bank I saw deep pools, the water blue like the sky. 靠近岸时，我看见几汪深池塘，池水碧似蓝天。 2. 名词/代词+现在分词 Winter coming, it gets colder and colder. The rain having stopped, he went out for a walk.
The question having been settled, we wound up the meeting. 也可以The question settled, we wound up the meeting. 但含义稍有差异。前者强调了动作的先后。 We redoubled our efforts, each man working like two. 我们加倍努力，一个人干两个人的活。 3. 名词/代词+过去分词 The job finished, we went home. More time given, we should have done the job much better. *当表人体部位的词做逻辑主语时，不及物动词用现在分词，及物动词用过去分词。 He lay there, his teeth set, his hands clenched, his eyes looking straight up. 他躺在那儿，牙关紧闭，双拳紧握，两眼直视上方。 4. 名词/代词+不定式 We shall assemble at ten forty-five, the procession to start moving at precisely eleven. We divided the work, he to clean the windows and I to sweep the floor.
独立主格结构 一、概念 “独立主格结构”就是由一个相当于主语的名词或代词加上非谓语动词、形容词（副）词或介词短语构成的一种独立成分。该结构不是句子，也不是从句，所以它内部的动词不能考虑其时态、人称和数的变化，它与主句之间不能通过并列连词连接，也不能由从句阴道词引导，通常用逗号与主句隔开。独立主格结构在很多情况下可以转化为相应的状语从句或者其他状语形式，但很多时候不能转化为分词形式，因为它内部动词的逻辑主语与主句主语不一致。 二、独立主格的特点
1.当独立主格结构中的being done表示“正在被做时”，being不可以被省略。 2.当独立主格结构的逻辑主语是it, there时，being不可以省略。 三、独立主格结构的用法。 一般放在句首，表示原因时还可放在句末；表伴随状况或补充说明时，相当于一个并列句，通常放于句末。
四、非谓语动词独立主格结构。 “名词或代词+非谓语动词”结构构成的独立主格结构称为非谓语动词的独立主格结构。名词或代词和非谓语动词具有逻辑上的主谓关系。 1.不定式构成的独立主格结构 不定式构成的独立主格结构往往表示还未发生的行为或状态，在句中常 作原因状语，有时做条件状语。 Lots of homework to do, I have to stay home all day. 由于很多作业要做，我只好待在家里。 So many children to look after, the mother has to quit her job. 如此多的孩子要照顾，这个妈妈不得不辞掉她的工作。 2.动词+ing形式的独立主格结构 动词-ing形式的句中作状语时，其逻辑主语必须是主句的主语，否则就 是不正确的。动词-ing形式的逻辑主语与主句的主语不一致时，就应在 动词的-ing形式前加上逻辑主语，构成动词-ing 形式的独立主格结构，逻辑主语与动词间为主谓关系，是分词的动作执行者，分词表示的动作 时逻辑主语发出的动作。 We redoubled our efforts, each man working like two. 我们加倍努力，每个人就像在干两个人的活。 The governor considering the matter, more strikers gathered across his path. 总督思考这个问题时，更多的罢工工人聚集到他要通过的路上。 The guide leading the way, we had no trouble getting out of the forest. 在向导的带领下，我们轻松地走出了森林。 3.过去分词形式的独立主格 过去分词形式的独立主格结构是由“逻辑主语+过去分词”构成。逻辑主 语与动词之间为动宾关系，它是分词的动作承受者，这一结构在句中作 时间状语，原因状语、伴随状语、条件状语等。 This done, we went home.做完这个，我们就回家了。 All our savings gone, we started looking for jobs. 积蓄用完后，我们都开始找工作。 More time and money given, we can finish the work in advance. 如果给予更多的时间和金钱，我们能提前完成这个工作。 五、其他形式的独立主格结构
精神分裂症的病因是什么 精神分裂症是一种精神方面的疾病，青壮年发生的概率高，一般 在16～40岁间，没有正常器官的疾病出现，为一种功能性精神病。 精神分裂症大部分的患者是由于在日常的生活和工作当中受到的压力 过大，而患者没有一个良好的疏导的方式所导致。患者在出现该情况 不仅影响本人的正常社会生活，且对家庭和社会也造成很严重的影响。 精神分裂症常见的致病因素： 1、环境因素：工作环境比如经济水平低低收入人群、无职业的人群中，精神分裂症的患病率明显高于经济水平高的职业人群的患病率。还有实际的生活环境生活中的不如意不开心也会诱发该病。 2、心理因素：生活工作中的不开心不满意，导致情绪上的失控，心里长期受到压抑没有办法和没有正确的途径去发泄，如恋爱失败， 婚姻破裂，学习、工作中不愉快都会成为本病的原因。 3、遗传因素：家族中长辈或者亲属中曾经有过这样的病人，后代会出现精神分裂症的机会比正常人要高。 4、精神影响：人的心里与社会要各个方面都有着不可缺少的联系，对社会环境不适应，自己无法融入到社会中去，自己与社会环境不相
适应，精神和心情就会受到一定的影响，大脑控制着人的精神世界， 有可能促发精神分裂症。 5、身体方面：细菌感染、出现中毒情况、大脑外伤、肿瘤、身体的代谢及营养不良等均可能导致使精神分裂症，身体受到外界环境的 影响受到一定程度的伤害，心里受到打击，无法承受伤害造成的痛苦，可能会出现精神的问题。 对于精神分裂症一定要配合治疗，接受全面正确的治疗，最好的 疗法就是中医疗法加心理疗法。早发现并及时治疗并且科学合理的治疗，不要相信迷信，要去正规的医院接受合理的治疗，接受正确的治 疗按照医生的要求对症下药，配合医生和家人，给病人创造一个良好 的治疗环境，对于该病的康复和痊愈会起到意想不到的效果。
教学参考：With引导的独立主格结构 https://www.doczj.com/doc/bf14679153.html, 2005/03/14 09:41 英语辅导报 with独立主格结构是英语的一种重要的句法现象，在句子结构方面具有相对独立的特点。多年 来也一直是命题的热点、重点，因此应该引起我们的高度重视。众所周知，with引导的独立主格结 构非常活跃，虽然它在句子中只作状语，但是可以表示伴随、方式、原因、结果等各种复杂的情况。现将with引导的独立主格结构加以小结。 一、句法结构 【结构一】with＋名词(代词)＋介词短语 【例句】He sat there thinking, with his chin on his hand. 他手托下巴，坐在那儿沉思。 The old man stood there, with his back against the wall. 那位老人背倚着墙站在那里。 Mary was sitting near the fire, with her back towards the door. 玛丽靠近火炉坐着，背对着门。 【结构二】with＋名词(代词)＋形容词 【例句】He stared at his friend with his mouth wide open. 他张大嘴巴凝视着他的朋友。 The man raised his head with eyes full of wonder and mystery. 这人抬起头来，眼里充满了好奇。 He stood there trembling, with his face red with cold. 他站在那儿瑟瑟发抖，脸都冻红了。 【结构三】with＋名词(代词)＋副词 【例句】With production up by 60%, the company has had another excellent year. 产量上升了60%, 公司又是一个好年景。 The stupid Emperor walked in the procession with nothing on. 这位愚蠢的皇帝一丝不挂地行进在 游行队伍中。 The naughty boy stood before his teacher with his head down. 这个淘气的男孩低着头站在老师面前。 He put on his socks with the wrong side out. 他把袜子穿反了。 【结构四】with＋名词(代词)＋名词 【例句】She used to sit reading in the evening with her pet dog her only companion. 她从前总爱在 晚上坐着看书，她的宠物狗便是她惟一的伙伴。
with独立主格结构是英语的一种重要的句法现象，在句子结构方面具有相对独立的特点。多年来也一直是命题的热点、重点，因此应该引起我们的高度重视。众所周知，with 引导的独立主格结构非常活跃，虽然它在句子中只作状语，但是可以表示伴随、方式、原因、结果等各种复杂的情况。现将with引导的独立主格结构加以小结。 一、句法结构 【结构一】with ＋名词(代词)＋介词短语 【例句】He sat there thinking, with his chin on his hand. 他手托下巴，坐在那儿沉思。 The old man stood there, with his back against the wall. 那位老人背倚着墙站在那里。 Mary was sitting near the fire, with her back towards the door. 玛丽靠近火炉坐着，背对着门。 【结构二】with ＋名词(代词)＋形容词 【例句】He stared at his friend with his mouth wide open. 他张大嘴巴凝视着他的朋友。 The man raised his head with eyes full of wonder and mystery. 这人抬起头来，眼里充满了好奇。 He stood there trembling, with his face red with cold. 他站在那儿瑟瑟发抖，脸都冻红了。 【结构三】with ＋名词(代词)＋副词 【例句】With production up by 60%, the company has had another excellent year. 产量上升了60%, 公司又是一个好年景。 The stupid Emperor walked in the procession with nothing on. 这位愚蠢的皇帝一丝不挂地行进在游行队伍中。 The naughty boy stood before his teacher with his head down. 这个淘气的男孩低着头站在老师面前。 He put on his socks with the wrong side out. 他把袜子穿反了。 【结构四】with ＋名词(代词)＋名词 【例句】She used to sit reading in the evening with her pet dog her only companion. 她从前总爱在晚上坐着看书，她的宠物狗便是她惟一的伙伴。