Estimation of broad features or the low-frequency part of acoustic impedance from conventional reflection data is an essential yet challenging step for quantitative interpretation of seismic data due to its band-limited nature. A missing low-frequency part leads to non-uniqueness in the solution as well as placing restrictions in recovering the absolute impedance values. The current industry practice fills this gap by assuming either an initial impedance model or statistical restrictions on such a model. Doing away with such assumptions but using only first principles (Zoeppritz's equations) and homogeneous layered earth model, we have formulated a set of linear equations that are then solved for an unknown reflection co-efficient using singular value decomposition (SVD) approach with time sampled seismic trace as the input data. The present work demonstrates the effectiveness of reconstructing a broad and smooth impedance profile from first principles and even from acquired seismic reflection data. It also illustrates the method's success with real data, while determining in one go the unknown scale factor linking the true and the relative seismic amplitudes, and the smallest singular value to be retained in the solution from only the knowledge of the average value of the acoustic impedance over the depth range in question. Thus, the salient feature of this work is the ability to reconstruct an approximate impedance profile from field data without the aid of an initial model or statistical assumption on the reflectivity series. This approximate impedance profile can serve as a reliable initial input for more refined inversion or geologic interpretation.

中文翻译：

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仅使用第一原理从观测到的地震反射数据估计声阻抗剖面的广泛趋势

根据常规反射数据估算声阻抗的宽泛特征或低频部分，由于其频带有限，因此对于地震数据的定量解释而言是必不可少的挑战性步骤。缺少低频部分会导致解决方案中的不唯一性，并限制恢复绝对阻抗值。当前的行业惯例通过假设初始阻抗模型或对该模型的统计限制来填补这一空白。消除了这些假设，但仅使用第一原理（Zoeppritz方程）和均质层状地球模型，我们制定了一组线性方程，然后使用奇异值分解（SVD）方法对时间采样进行求解，以求未知的反射系数地震轨迹作为输入数据。本工作证明了从第一原理甚至从采集的地震反射数据重建宽而平滑的阻抗曲线的有效性。它还说明了该方法在实际数据上的成功，同时仅通过了解声学平均值即可一口确定链接真实地震幅度和相对地震振幅的未知比例因子以及要保留在解决方案中的最小奇异值。在所讨论的深度范围内的阻抗。因此，这项工作的显着特征是无需借助初始模型或对反射率序列的统计假设即可从现场数据重建近似阻抗曲线的能力。这种近似的阻抗曲线可以作为可靠的初始输入，用于更精细的反演或地质解释。