Itt is now commonplace for 3-D data sets to be processed as partial offset volumes to exploit the AVO information in the data. However, there has been significant asymmetry in the way these volumes could be calibrated and inverted. The amplitudes of near-offset, or intercept, stacks relate to changes in acoustic impedance and can be tied to well logs using synthetics based on acoustic impedance (AI) or inverted, to some extent, back to AI using poststack inversion algorithms. However, there have been no simple analogous processes for far-offset stacks.
现在，将3D数据集作为部分偏移量进行处理以利用数据中的AVO信息已经很常见了。然而，这些体积的校准和反演方式存在显著的不对称性。近炮检距或截距叠加的振幅与声阻抗的变化有关，可以使用基于声阻抗（AI）的合成函数与测井记录联系起来，或者在某种程度上使用叠后反演算法反演回AI。然而，对于远偏移距叠加，还没有简单的类似过程。

The symmetry can be largely restored using a function I call elastic impedance (EI). This is a generalization of acoustic impedance for variable incidence angle. EI provides a consistent and absolute framework to calibrate and invert nonzero-offset seismic data just as AI does for zero-offset data. EI, an approximation derived from a linearization of the Zoeppritz equations (Appendix, part 1), is accurate enough for widespread application.
这种对称性可以用一个我称之为弹性阻抗（EI）的函数在很大程度上恢复。这是变入射角声阻抗的一般化。EI提供了一个一致的和绝对的框架来校准和反演非零偏移距地震数据，就像AI对零偏移距数据所做的那样。EI是由Zoeppritz方程线性化得到的一个近似值（附录，第1部分），其精度足以广泛应用。

As might be expected, EI is a function of $P$$P$PP-wave velocity, $S$$S$SS-wave velocity, density, and incidence angle. To relate EI to seismic, the stacked data must be some form of angle stack rather than a constant range of offsets. There are several ways of constructing suitable data sets by either careful mute design or by linear combination of intercept and gradient functions. (Part 2 of the Appendix reviews these methods.)
正如所预期的，EI是 $P$$P$PP 波速度、 $S$$S$SS 波速度、密度和入射角的函数。为了将EI与地震联系起来，叠加数据必须是某种形式的角度叠加，而不是一个恒定的炮检距范围。有几种方法可以通过仔细的静音设计或通过截距和梯度函数的线性组合来构建合适的数据集。(Part附录2回顾了这些方法。）

EI was initially developed by BP in the early 1990s to help exploration and development in the Atlantic Margins province, west of the Shetlands, where Tertiary reservoirs are typified by class II and class III AVO responses. Figure 1 shows a suite of logs from the Foinaven discovery well drilled in 1992. The ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} elastic-impedance $\log$$\log$log\log, $\mathrm{EI}(30)$$\mathrm{EI}(30)$EI(30)\mathrm{EI}(30), is broadly similar in appearance to the acoustic-impedance $\log$$\log$log\log although the absolute numbers are lower; it is a prop-
EI最初由BP在20世纪90年代初开发，以帮助设得兰群岛西部大西洋边缘省的勘探和开发，其中第三系储层以II类和III类AVO响应为代表。图1显示了1992年钻探的Foinaven发现井的一套测井曲线。 ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} 弹性阻抗 $\log$$\log$log\log 、 $\mathrm{EI}(30)$$\mathrm{EI}(30)$EI(30)\mathrm{EI}(30) 在外观上与声阻抗 $\log$$\log$log\log 大致相似，尽管绝对数值较低;这是一个适当的选择。
erty of EI that the level decreases with increasing angle.
EI值随角度的增加而减小。
At this well, the sands are predominantly class III and so have slightly higher amplitudes at ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} than at normal incidence. This can be more clearly seen in Figure 2 in which the EI log has been scaled to have approximately the same shale baseline as the AI log. When the sands are class II, a more dramatic difference is evident between the AI and EI logs.
在该井中，砂主要为III类，因此在 ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} 处的振幅略高于垂直入射时的振幅。这可以在图2中更清楚地看到，其中EI测井已被缩放为具有与AI测井大致相同的页岩基线。当砂层为II类时，AI和EI测井曲线之间的差异更为明显。

The seismic data around Foinaven suffer from very strong peg-leg multiples. Even after demultiple, the sig-nal-to-noise ratio of the near-trace data is often poor, especially from the class II events, whereas the far-offset data are generally of good quality. EI allows the well data to be tied directly to the high-angle seismic which can then be calibrated and inverted without reference to the near offsets.
Foinaven周围的地震数据受到非常强的短程多次波的影响。即使经过多次分解，近道数据的信噪比也往往很差，特别是来自II类同相轴的数据，而远偏移距数据的质量一般都很好。EI允许将井数据直接与高角度地震相关联，然后可以在不参考近炮检距的情况下对其进行校准和反演。

Figure 3 shows part of the $\mathrm{EI}(30)\log$$\mathrm{EI}(30)\log$EI(30)log\mathrm{EI}(30) \log from another Foinaven well overlain on an inverted ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} angle stack. The data were inverted using a constrained sparse spike algorithm for which the EI $\log$$\log$log\log provided the basis for the constraints and was used to QC the result.
图3示出了另一个Foinaven井的 $\mathrm{EI}(30)\log$$\mathrm{EI}(30)\log$EI(30)log\mathrm{EI}(30) \log 的一部分，其覆盖在倒置的 ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} 角堆叠上。使用约束稀疏尖峰算法对数据进行反演，其中EI $\log$$\log$log\log 提供了约束的基础，并用于对结果进行QC。

An EI log provides an absolute frame of reference and so can also calibrate the inverted data to any desired rock property with which it correlates. In the case of Foinaven, a strong correlation was found between $\mathrm{EI}(30)$$\mathrm{EI}(30)$EI(30)\mathrm{EI}(30) and hydrocarbon pore volume, and this relationship was used to estimate the in-place volumes for the field from the inverted ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} seismic volume.
EI测井提供了一个绝对的参考系，因此也可以将反演数据校准到与之相关的任何所需岩石性质。在Foinaven的情况下，在 $\mathrm{EI}(30)$$\mathrm{EI}(30)$EI(30)\mathrm{EI}(30) 和烃类孔隙体积之间发现了强相关性，并且该关系用于根据反演的 ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} 地震体积来估计该油田的就地体积。

Figure 4 shows a section from the inverted ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} volume used to design the trajectory of the first high-angle development well. The oil sands correlated closely with the areas of low elastic impedance. The EI volume was used to design the trajectories of all subsequent development wells.
图4显示了用于设计第一个大斜度开发井的轨迹的倒置的 ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} 体积的截面。油砂体与低弹性阻抗区关系密切。EI体积用于设计所有后续开发威尔斯井的轨迹。

Figure 1. Comparison of an AI curve with a ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} EI curve for the Foinaven discovery well 204/24a-2.
图1. Foinaven发现井204/24 a-2的AI曲线与 ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} EI曲线的比较。

The EI formula is an approximation and may not be applicable in all circumstances; however, the loss of accuracy is easy to calculate and minimize (Appendix, part 3). In most situations, more general seismic data quality issues and particularly uncertainty in the estimation of incidence angle are probably larger than errors in the implied reflectivity from the EI values.
EI公式是一个近似值，可能并不适用于所有情况;然而，准确度的损失很容易计算并最小化（附录，第3部分）。在大多数情况下，更一般的地震数据质量问题，特别是入射角估计的不确定性可能大于EI值的隐含反射率误差。

Estimating Poisson’s ratio from seismic data has prompted much comment in the literature and was the subject of a workshop at SEG’s 1998 Annual Meeting. One approach is to invert a ${90}^{\circ }$${90}^{\circ }$90^(@)90^{\circ} angle stack (see part 2 of the Appendix) which, in theory, has amplitudes that are approximately proportional to changes in Poisson’s ratio. However, the construction of quantitatively accurate Poisson’s ratio stacks is notoriously difficult because of sensitivity to residual moveout and bandwidth variations.
从地震数据中估计泊松比在文献中引起了很多评论，并且是SEG 1998年年会研讨会的主题。一种方法是反转 ${90}^{\circ }$${90}^{\circ }$90^(@)90^{\circ} 角度叠加（参见附录第2部分），理论上，其振幅与泊松比的变化近似成比例。然而，定量精确的泊松比叠加的建设是出了名的困难，因为剩余时差和带宽变化的敏感性。

EI can provide an optimum compromise. Part 4 of the Appendix shows how one variant of EI has values equal to AI at normal incidence and to ${\left({\mathrm{V}}_p/{\mathrm{V}}_s\right)}^2$${\left({\mathrm{V}}_p/{\mathrm{V}}_s\right)}^2$(V_(p)//V_(s))^(2)\left(\mathrm{V}_{p} / \mathrm{V}_{s}\right)^{2} at ${90}^{\circ }$${90}^{\circ }$90^(@)90^{\circ} (this being closely related to Poisson’s ratio) with a smooth transition
EI可以提供最佳折衷。附录的第4部分显示了EI的一个变体如何在正常入射时具有等于AI的值，在 ${90}^{\circ }$${90}^{\circ }$90^(@)90^{\circ} 时具有等于 ${\left({\mathrm{V}}_p/{\mathrm{V}}_s\right)}^2$${\left({\mathrm{V}}_p/{\mathrm{V}}_s\right)}^2$(V_(p)//V_(s))^(2)\left(\mathrm{V}_{p} / \mathrm{V}_{s}\right)^{2} 的值（这与泊松比密切相关），并具有平滑过渡

Figure 2. Detail from Figure 1, but with the EI(30) curve scaled so that the shale baseline is approximately the same as the AI curve. This shows the percentage decrease in impedance at the oil-sand interface is greater than ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} at normal incidence, consistent with the class III response of these sands.
图2.图1中的细节，但EI（30）曲线按比例缩放，使页岩基线与AI曲线大致相同。这表明，在垂直入射时，油砂界面处的阻抗降低百分比大于 ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} ，与这些砂的III类响应一致。
between. This allows the user to construct as high an angle stack as is stable and then to calibrate or invert it using the equivalent EI log.
之间。这允许用户构建尽可能高的稳定角度叠加，然后使用等效EI测井对其进行校准或反演。

Because of the difficulties and uncertainties of constructing angle stacks, a method of quality-controlling the results using available well data is important. EI provides a simple mechanism to produce synthetic seismograms for variable incidence angle. $A{V}_p$$A{V}_p$AV_(p)A V_{p} term can be factored out of the EI expression and the remaining angle-dependent expression can be used in place of the density log in conventional synthetics software (equation 1.3). The $V_p\log$$V_p\log$V_(p)logV_{p} \log is then calibrated with a time-depth relationship in the usual way.
由于构造角度叠加的困难和不确定性，使用可用的井数据对结果进行质量控制的方法是重要的。EI提供了一个简单的机制来产生可变入射角的合成地震图。可以从EI表达式中去除 $A{V}_p$$A{V}_p$AV_(p)A V_{p} 项，并且可以使用剩余的角度相关表达式来代替常规合成软件中的密度测井曲线（等式1.3）。然后以通常的方式用时间-深度关系校准 $V_p\log$$V_p\log$V_(p)logV_{p} \log 。

Figure 5 shows near- and far-offset ties to a west of Shetlands well. There is much variation of amplitudes
图5显示了设得兰群岛油井以西的近偏移和远偏移联系。振幅变化很大

Figure 3. Part of an EI(30) log overlain on the inverted ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} angle stack. The log was used to constrain a conventional poststack sparse spike inversion and to QC the result.
图3. EI（30）测井曲线的一部分覆盖在倒置的 ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} 角叠加上。利用该测井曲线约束常规叠后稀疏脉冲反演，并对反演结果进行质量控制。

Figure 4. A section through the inverted ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} volume, showing the path of the first development well. The location of oil-bearing sands encountered by the well correlates with the areas of low elastic impedance (yellow).
图4.通过倒置的 ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} 体积的剖面，显示了第一口开发井的路径。油井遇到的含油砂的位置与低弹性阻抗区域（黄色）相关。
with offset in this area, and the two angle stacks are quite different. Despite this, both well ties are of good quality.
在这个区域有偏移，并且两个角度叠加是完全不同的。尽管如此，这两个良好的关系是良好的质量。

A principal benefit of EI within BP has been its value as a communication and integration tool. EI allows AVO information to be displayed in a way that can be understood more intuitively by nongeophysical specialists. It is easily incorporated into petrophysical systems allowing AVO information to be communicated throughout the earth-science community. EI can be used to display rockproperty data, either from wireline or core measurements, in a way that can be directly related to far-offset stacks.
在BP内部，EI的一个主要好处是它作为一种沟通和整合工具的价值。EI允许AVO信息以非地球物理专家可以更直观地理解的方式显示。它很容易纳入岩石物理系统，使AVO信息在整个地球科学界进行交流。EI可用于显示来自电缆或岩心测量的岩石属性数据，其方式可直接与远偏移距叠加相关。

Shear-wave data are now recorded routinely in many wells so the calculation of, say, an $\mathrm{EI}(30)$$\mathrm{EI}(30)$EI(30)\mathrm{EI}(30) log within any petrophysical package is straightforward. The combination
剪切波数据现在在许多威尔斯井中进行常规记录，因此计算任何岩石物理数据包中的0#测井数据都很简单。相结合
of an AI and EI curve is often simpler to relate to the seismic response than, say, ${\mathrm{V}}_s$${\mathrm{V}}_s$V_(s)\mathrm{V}_{s} or Poisson’s ratio logs. An example is shown in Figure 6 that is a standard BP petrophysical display from the Gulf of Mexico.
AI和EI曲线的斜率与地震响应的关系通常比0#或泊松比测井更简单。图6所示为墨西哥湾标准BP岩石物理显示图。

With this type of data established within a petrophysical database the EI concept can help with more general rock-property studies. Figure 7 shows AI/EI crossplots of data from 19 Gulf of Mexico wells for shales, brine, and oil sands. By measuring average impedance values we can quickly estimate the AVO response of various lithology combinations. This particular data set, for example, shows that the percentage increase in amplitude from 0${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} for a shale/brine sand interface ( $\sim 18\mathrm{\%}$$\sim 18\mathrm{\%}$∼18%\sim 18 \% ) is almost exactly the same as for a shale/oil sand interface ( $\sim 17\mathrm{\%}$$\sim 17\mathrm{\%}$∼17%\sim 17 \% ). So, for
通过在岩石物理数据库中建立这种类型的数据，EI概念可以帮助进行更一般的岩石性质研究。图7显示了来自墨西哥湾19口威尔斯页岩、盐水和油砂的数据的AI/EI交会图。通过测量平均波阻抗值，可以快速估计不同岩性组合的AVO响应。例如，该特定的数据集示出了对于页岩/盐水砂界面（ $\sim 18\mathrm{\%}$$\sim 18\mathrm{\%}$∼18%\sim 18 \% ）从0到0#的幅度的百分比增加与对于页岩/油砂界面（ $\sim 17\mathrm{\%}$$\sim 17\mathrm{\%}$∼17%\sim 17 \% ）几乎完全相同。所以

Figure 5. Low- and high-angle synthetic ties for a west of Shetlands well. The left side of the display is a conventional AI synthetic match to a ${10}^{\circ }$${10}^{\circ }$10^(@)10^{\circ} angle stack. The right side is a ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} EI-based synthetic tied to a ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} angle stack.
图5.设得兰群岛西部油井的低角度和高角度合成系材。显示器的左侧是与 ${10}^{\circ }$${10}^{\circ }$10^(@)10^{\circ} 角度堆栈的常规AI合成匹配。右侧是一个基于 ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} EI的合成，与 ${30}^{\circ }$${30}^{\circ }$30^(@)30^{\circ} 角度堆栈绑定。

Figure 6. Standard petrophysical display for a Gulf of Mexico well (MC619-1). The two right tracks show the AI and $\mathrm{EI}(30)$$\mathrm{EI}(30)$EI(30)\operatorname{EI}(30) curves. In this example, the upper sand would be expected to generate little response at normal incidence and a tough-peak pair at far offsets.
图6.墨西哥湾油井（MC 619 -1）的标准岩石物理显示。右侧两条轨迹显示AI和 $\mathrm{EI}(30)$$\mathrm{EI}(30)$EI(30)\operatorname{EI}(30) 曲线。在本例中，预计上部砂层在法向入射角下几乎不会产生响应，而在远偏移距下则会产生一对强峰值。