Seismic data inversion using an optimal least square reverse time migration

Document Type : Research Article

Author

Department of Mining Engineering, Faculty of Engineering, Lorestan University

Abstract

Due to the drawbacks of the beam-based seismic imaging methods, the use of the wavefield-based imaging methods such as reverse-time migration (RTM) as a suitable alternative has been widely used in the recent years. However, as the RTM is implemented using wave field reconstruction and cross-correlation imaging condition, it produces artifacts which is the major challenge of RTM. Therefore, in this paper, the inversion of seismic data is used by integration of RTM modeling operators and least squares migration to produce subsurface image. The least squares reverse time migration (LSRTM) method is implemented using the steepest decent and adaptive gradient methods in an iterative procedure including forward migration and inverse migration to solve the least squares problem. The LSRTM algorithm tries to fit a better depth model to the observed data based on the least-squares. Then the migrated images’ results of LSRTM procedure are presented using the steepest decent and adaptive gradient algorithms in different iterations which compared with each other and with conventional RTM. Finally, the misfit error and also the wavenumber spectra versus normalized amplitude has been compared for the disputed methods.
Summary
In this paper, the inversion of seismic data is used by integration of RTM modeling operators and least squares migration to produce subsurface image. The least squares reverse time migration (LSRTM) method is implemented using the steepest decent and adaptive gradient methods in an iterative procedure including forward migration and demigration to solve the least squares problem.
 
Introduction
There are several methods of seismic migration and the main objective of those is to place the reflectors in their true positions. One way for seismic migration is the algorithms that directly apply imaging conditions; on the other hand, the inversion-based imaging method implemented through different strategies to obtain a better depth model that fits the observed data. One of these inversion methods named least square migration solves the inverse problem through direct migration and demigration. The least squares migration has the main advantage that it can gradually reduce errors caused by initial migration. In this paper, particularly the reverse time migration (RTM) is used as an operator of migration and demigration.  Therefore, two numerical schemes are developed to implement least-squares migration with the reverse time migration method.
 
Methodology and Approaches
The Helmholtz equation is used to derive the forward modeling operators named reverse time migration (RTM) operator with the Born approximation that is donated as linear inversion. Thus, the linear least square reverse time migration (LSRTM) is the inversion procedure to obtain the final image. LSRTM uses the RTM results as the initial reflectivity model and Born modeling to simulate the seismic data. The reflectivity model is updated by calculating the differences between observed and calculated data through the conventional an adaptive gradient. After multiple iterations, the differences are minimized and this is taken to suggest that the final reflectivity model reflects the real subsurface interface.
 
Results and Conclusions
The results indicate that the LSRTM through an adaptive gradient procedure can successfully produce the subsurface migrated image free of artifacts including the steep dip structures during a reasonable computational cost.

Keywords

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1- مقدمه

مهاجرت یکی از مراحل اصلی پردازش داده‌های لرزه‌ای بوده و هدف اصلی آن تصویر نمودن بازتابنده‌ها در جای واقعی خود و کاهش اثرات ناشی از پراش[i] است. روش‌های مختلفی برای مهاجرت داده‌های لرزه‌ای وجود دارد. الگوریتم‌های مهاجرت عمقی و زمانی مرسوم با استفاده از برون‌یابی میدان‌های موج چشمه و گیرنده و اعمال شرایط تصویرسازی، تصاویر لرزه‌ای را تولید می‌کنند[1]. عدم تطابق کامل بین اصول تصویربرداری ایده‌ال و فیزیک پیچیده در شرایط واقعی دلالت بر آن دارد که همیشه بین خروجی روش‌های مهاجرت و مدل واقعی زمین اختلافاتی وجود دارد. از آنجایی که این اختلاف اجتناب ناپذیر است، یک راه‌حل برای به حداقل رساندن آن، پیشنهاد وارون‌سازی[ii] داده‌های لرزه‌ای برای تصحیح تصویر مهاجرت‌یافته به سمت بازتاب‌پذیری واقعی است. بازتاب‌پذیری[iii] به زبان ساده میزان انرژی بازتابی است که از تفاوت سرعت و چگالی در دو لایه مختلف ناشی می‌شود و بصورت امپدانس صوتی[iv] یا ضریب بازتاب[v] نیز معرفی می‌شود.


[i] Diffraction

[ii] Inversion

[iii] True reflectivity

[iv] Acoustic impedance

[v] Reflection coefficient

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Journal of Analytical and Numerical Methods in Mining Engineering
Volume 11, Issue 26
April 2021
Pages 13-21

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History

  • Receive Date: 22 May 2020
  • Revise Date: 25 October 2020
  • Accept Date: 26 October 2020

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