Efficient wavefield reconstruction at half the Nyquist rate

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. A43-A46
Author(s):  
Ali Gholami ◽  
Alan Richardson ◽  
Toktam Zand ◽  
Alison Malcolm
Keyword(s):  
Waveform Inversion ◽  
Time Derivative ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Simple Method ◽  
Imaging Condition ◽  
Full Waveform ◽  
Time Migration ◽  
Adjoint State ◽  
Nyquist Rate

We have developed a simple method to halve the memory required to store the forward wavefield for the imaging condition in adjoint-state methods such as reverse time migration and full-waveform inversion. It stores the wavefield at only half the Nyquist rate, and it uses the wave equation to calculate the second time derivative, allowing approximate reconstruction of the forward wavefield at the required Nyquist rate. We have determined that the method produces an image with the Marmousi model that is not visibly different compared to a traditional (full Nyquist) implementation.

From classical reflectivity-to-velocity inversion to full-waveform inversion using phase-modified and deconvolved reverse time migration images

Geophysics ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. S31-S49 ◽  
Author(s):  
Chen Tang ◽  
George A. McMechan
Keyword(s):  
Waveform Inversion ◽  
Time Integration ◽  
Multiscale Approach ◽  
Full Waveform Inversion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Velocity Inversion ◽  
Full Waveform ◽  
Time Migration ◽  
Gradient Based

To obtain a physical understanding of gradient-based descent methods in full-waveform inversion (FWI), we find a connection between the FWI gradient and the image provided by reverse time migration (RTM). The gradient uses the residual data as a virtual source, and RTM uses the observed data directly as the boundary condition, so the FWI gradient is similar to a time integration of the RTM image using the residual data, which physically converts the phase of the reflectivity to the phase of the velocity. Therefore, gradient-based FWI can be connected to the classical reflectivity-to-velocity/impedance inversion (RVI). We have developed a new FWI scheme that provides a self-contained and physically intuitive derivation, which naturally establishes a connection among the amplitude-preserved RTM, the Zoeppritz equations (amplitude variation with angle inversion), and RVI, and combines them into a single framework to produce a preconditioned inversion formula. In this scheme, the relative velocity update is a phase-modified and deconvolved RTM image obtained with the residual data. Consistent with the deconvolution, the multiscale approach applies a gradually widening low-pass frequency filter to the deconvolved wavelet at early iterations, and then it uses the unfiltered deconvolved wavelet for the final iterations. Our numerical testing determined that the new method makes a significant improvement to the quality of the inversion result.

Efficient snapshot-free reverse time migration and computation of multiparameter gradients in full waveform inversion

Geophysics ◽  
2021 ◽  
pp. 1-79
Author(s):  
Johan O. A. Robertsson ◽  
Fredrik Andersson ◽  
René-Édouard Plessix
Keyword(s):  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Principle Of Superposition ◽  
Model Parameter ◽  
Inversion Model ◽  
Full Waveform ◽  
Time Migration ◽  
Anisotropic Elastic

Computing images in reverse time migration and model parameter gradients from adjoint wavefields in full waveform inversion requires the correlation of a forward propagated wavefield with another reverse propagated wavefield. Although in theory only two wavefield propagations are required, one forward propagation and one reverse propagation, it requires storing the forward propagated wavefield as a function of time to carry out the correlations which is associated with significant I/O cost. Alternatively, three wavefield propagations can be carried out to reverse propagate the forward propagated wavefield in tandem with the reverse propagated wavefield. We show how highly accurate reverse time migrated images and full waveform inversion model parameter gradients for anisotropic elastic full waveform inversion can be efficiently computed without significant disk I/O using two wavefield propagations by means of the principle of superposition.

Breakthrough acquisition and technologies for subsalt imaging

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB41-WB51 ◽  
Author(s):  
Denes Vigh ◽  
Jerry Kapoor ◽  
Nick Moldoveanu ◽  
Hongyan Li
Keyword(s):  
Velocity Field ◽  
Inversion Layer ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Low Frequencies ◽  
Full Waveform ◽  
Time Migration

The recently introduced method of wide-azimuth data acquisition offers better illumination, noise attenuation, and lower frequencies to more accurately determine a velocity field for imaging. For the field data experiment to demonstrate the technologies, we used a Gulf of Mexico (GOM) wide-azimuth data set that allows us to take advantage of possible low frequencies, relatively large crossline offsets, and increased illumination. The input data was processed through true 3D azimuthal surface-related multiple elimination (SRME) with zero-phasing and debubble. Eliminating the surface-related multiples aids the velocity determination and helps uncover the subsalt sediments at the final imaging stage. After the initial velocity derivation, which was constrained to wells and geology, full-waveform inversion (FWI) was used to further update the velocity field to achieve an enhanced image. The methodology used follows the top-down approach where suprasalt sediment model is developed followed by the top of salt, salt flanks, base of salt, and finished with a limited subsalt update. To approximate the observed data by using an acoustic inversion procedure, the propagator includes effects of attenuation, anisotropy, acquisition source, and receiver depth. The geological environment is salt related, which implies that the observed data is highly elastic, even though it is input to an acoustic full waveform inversion. To use the proper constraints for the inversion, layer-stripping method is used to develop the high-resolution velocity field. The inversion stages were carefully quality controlled through gather displays to ensure the kinematics were honored. We then demonstrated the benefit of the FWI velocity field by comparing the images derived with the traditional ray-based tomographic velocity field versus the velocity field derived by FWI performing reverse time migration to produce these images. Finally, the images were compared at key well locations to evaluate the robustness of the workflow.

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