Why depth migration

The impact of spatially varying and frequency dependent attenuation of the seismic wavefield is clearly visible on the full stack section after Kirchhoff depth migration. Before left is the full stack section after Kirchhoff depth migration. Geological complexities in the overburden for example structure, gas hydrates, shallow gas and carbonate reefs result in spatially varying and frequency dependent attenuation of the recorded seismic wavefield. DUG MigQ is a pre-stack depth migration-based workflow that compensates for laterally and vertically varying attenuation or quality factor Q.

In order to compensate for attenuation a Q model must first be estimated. Download Brochure Contact Sales. HPCaaS Overview. HPC Data Services. Software and Algorithm Support. About DUG. Because the conventional migration methods of one-way wave equation are frequently based on the limited Taylor expansion, their shortcoming is the limited imaging angles. To overcome this restriction, the optimization methods are utilized to recalculate coefficients of partial fraction, thus achieving better imaging performance [ 14 — 16 ].

But this improvement has its limits, and these methods seem to make it difficult to make the imaging angle reach 90 degrees. As a very important migration method, reverse time migration RTM is a hot issue in imaging researches, because it can handle various waves in arbitrarily velocity models including turning waves. More importantly, it has no dip limitations [ 17 , 18 ], so it can image complicated models that are unable to be imaged by one-way wave equation.

Although RTM has its advantages, it also has weak points. The most challenging problem it faced is storage. In order to compute the imaging amplitudes, RTM needs to restore all of the wavefields, which will require a huge memory cost. Researchers are seeking different techniques to solve this problem, such as proposing the random boundary method to avoid the storage of wavefields [ 19 ]. Another big problem of the RTM method is the low-frequency artifacts existing in the imaging sections.

To address this issue, Yoon and Marfurt [ 20 ] proposed a Laplacian filter. Although RTM has some weaknesses and it still has a long way to go to solve them completely, it is still a concern in the field of imaging. A two-way wave equation-based depth migration method as the latest development is a second-order partial differential equation in respect of coordinates, so two boundary conditions are needed to make it solvable in the domain of depth [ 21 , 22 ].

It is very hard to meet the requirements of boundary conditions, so researchers have separated the two-way wave equation mathematically and developed one-way wave equation migration methods. In order to handle the boundary conditions, You et al. Because the two-way wave equation depth migration method is on the base of full-wave equation, theoretically it also has no limited imaging angles.

However, compared with the RTM method, it needs less storage memory and produces less low-frequency artifacts. Therefore, it is a promising migration method. In this study, we propose to image OBS multiple waves with the two-way wave equation depth migration method, which is the first application to OBS data. The South Shetland margin lies in the northeastern tip of the Pacific margin of the Antarctic Peninsula. It marks the convergence zone boundary where the Antarctic and the former Phoenix plates are subducting beneath the South Shetland microcontinental block.

The continental margin shows a complicated tectonic setting, where a trench-accretionary prism-fore-arc basin sequence can be identified [ 24 , 25 ]. The subduction process is now believed to take place due to sinking and rollback of the oceanic plate, coupled with the extension of the Bransfield Strait marginal basin [ 25 — 28 ].

In this area, seismic data collected in the Italian Antarctic cruises have shown the presence of a possible gas hydrate reservoir along this margin [ 29 — 32 ].

Like tight sandstone, gas hydrate is an unconventional energy source with great economic potential [ 33 , 34 ]. Recent studies have pointed out that long-term ocean warming may have an influence on the stability of gas hydrate reservoir [ 35 ].

If gas hydrates decompose and release methane, it could lead to climate change. As a result, it is of great significance to increase our information on gas hydrates, including a good image of the gas hydrate system in this area. The data were concentrated on the continental slope with a strong bottom simulating reflection BSR recognized in the second survey. The two major objectives of this survey were to confirm the presence of a possible hydrate reservoir and to rebuild the tectonic background of this area.

Two GI guns were used as the seismic source with an overall volume of 3. The OBS comprised a three-component geophone and a hydrophone. Vertical and horizontal components are usually used to study compressional and shear waves, respectively. During the OBS investigation, its real position on the seafloor is uncertain, since it might displace quite a few hundreds of meters away from the stationing position where it was designed to be on the sea surface, considering oceanic currents and water depths.

Recognizing the accurate seafloor position of an OBS is a precondition to a precise velocity field and a satisfying image section because velocity analysis is quite susceptible to the error of OBS position. Thus, the first procedure we have to operate is OBS relocation. In most cases, we utilize direct waves to estimate the OBS location on the seafloor. The relocation of OBS is an inverse issue, the purpose of which is to locate the OBS position as well as to reduce the residual between calculated and observed travel times of direct waves as much as possible.

The accurate seafloor positions of OBSs were calculated by the direct arrivals from the different shots, presuming a consistent water column velocity, while the depth of seafloor was obtained from bathymetric data. To test the quality of the relocated OBS position, the linear normal travel time correction for the water column was conducted on OBS data. If the position was accurate, direct waves should appear flat after the correction as a result of the elimination of the water column with offset Figure 2.

Nevertheless, the deconvolution was not quite effective, still accompanied by noticeable ringing noises. In this case, we chose the hydrophone component instead of the vertical component to recognize phases. The vertical component, instead of the hydrophone component, showed an obvious ringing phenomenon which was the result of the effect of coupling between the seafloor and the instrument. Furthermore, the primaries and multiples are evident in the hydrophone component Figure 3.

Before migration, the primaries and multiples of OBS data need to be separated. The most commonly used method is to separate the wavefields into upgoing as well as downgoing wavefields by merging the hydrophone with the vertical components dual-sensor or PZ summation; [ 38 ].

In practice, the hydrophone and the vertical geophone usually show different instrument responses and instrument sensitivities, as well as different coupling characteristics with the seafloor; thus, the two component data have differences in amplitudes and phases.

Therefore, it is necessary to perform a match on the two components prior to PZ summation [ 39 ]. After calibrating the vertical component to the hydrophone component, the upgoing and downgoing wavefields can be separated as where is upgoing wavefield, is downgoing field, is hydrophone component, is vertical component after calibration, is water density, and is acoustic velocity. OBS is deployed at the seafloor, the boundary between acoustic and elastic mediums, so the wavefields just above and below the seafloor needed to be separated [ 39 — 41 ].

After the initial signal is generated by a source and travels via the water column, it is partly reflected when meeting the water-sediment interface and partly transferred into the seafloor. For instance, the travel time of the direct arrival is almost equal to the time it takes for the wave to be reflected at the seafloor and arrives at the receiver just above the seafloor.

Above the seafloor, the direct wave consists of upgoing and downgoing wavefields, while it shows only the downgoing wavefield beneath the seafloor, as well as the multiples at receiver sides.

Analogously, when a reflection event propagates upward and meets the water-sediment interface, it is partly transferred into the water column and partly reflected into the seafloor. Accordingly, the reflected signal consists of upgoing and downgoing components just beneath the seafloor, but it has only an upgoing component just above the seafloor. In this study, we performed the wavefield separation on the base of the method as described in Ref.

In a 2D case, the acoustic wave equation with initial boundary conditions can be written as follows [ 22 ]: where is the wavefield at time , is the medium velocity, is the grid space and the continuing step, and are the recorded seismic data at and depth levels, and is the derivative wavefield. It is well to know that two initial boundary conditions are required because the two-way wave equation is a second-order partial derivative differential equation. In conventional marine exploration, we usually collect wavefields at the surfaces.

Therefore, only one boundary condition can be provided. In order to handle this issue, because the velocity of sea body is constant, the common approach is to use a migration method based on one-way wave equation to calculate the derivative wavefields, which can be expressed as where and is the extrapolated step. It seems that directly solving equation 2 in the depth domain is very hard.

We attempt to transfer the time variable of equation 1 into the frequency domain, which can be expressed as where is angular frequency and is frequency-domain wavefield. Combining equation 4 and two boundary conditions, the two-way wave equation used for depth extrapolation scheme can be expressed as where and are the results of Fourier transform of and on time, respectively [ 22 ]. All in all, we can use the wavefields recorded at the surface to compute the derivative wavefields and then utilize equation 5 to perform wavefield depth extrapolation recursively.

Obviously, equation 5 is a first-order partial derivative differential equation, and a classical Runge-Kutta method is used to approximate it.

To perform wavefield depth extrapolation, how to calculate operator is a key core. In order to handle this issue, we need to discretize the Helmholtz operator as a matrix form at a certain frequency point for a medium with arbitrary changes in velocity: where.

Analyzing equation 6 , we can find that operator is a symmetric matrix. So matrix decomposition can be implemented, which can be written as where matrix includes the eigenvalues of , stands for its eigenvectors, and superscript denotes transposition.

However, when performing the wavefield depth extrapolation, one unavoidable question is the evanescent waves. Sandberg and Beylkin [ 22 ] analyzed that the evanescent waves are produced because of negative values of the operator. Based on this understanding, we introduce a matrix decomposition method to remove the negative values of the operator so as to suppress the evanescent waves; more details can be found in Ref.

For imaging multiple waves by using the OBS data, we prefer to utilize the mirror principle; the schematic diagram of the mirror principle is drawn in Figure 4. OBS is usually located at the seafloor, and its position can be settled by the direct wave.

Assuming the sea surface is flat, therefore we can find a mirrored OBS which has the same distance to surface as the actual OBS. In summary, we can use the mirrored OBS data to image multiple waves. The wavefield was calculated by a full-wave equation wavefield simulation method, as shown in Figure 6. Viewing the wavefield propagation, we can clearly observe the primary waves, because the longer traveling paths of multiple waves, the weaker the amplitudes of multiple waves than that of primary waves.

Then, the primary waves were used to perform depth migration and the mirror principle was utilized to perform the imaging of multiple waves. Figure 7 shows the imaging results of primary and multiple waves. It can be clearly seen that the primary waves cannot image some parts of the interface such as the boundary of the model and the seafloor, while the multiple waves allow imaging the boundary of the model successfully and provide a boarder imaging illumination, especially for the seafloor reflector.

This is because multiple waves penetrate into the subsurface several times and have longer traveling paths as well as contain abundant reflection information Figure 8. This simple experiment testifies the advantages of multiple waves in imaging over primary waves.

As discussed before, as a conventional migration method, reverse time migration has been widely used in the subsurface imaging. In order to testify the imaging performances of the two-way wave equation depth migration method, the reverse time migration was also applied to image OBS multiples. By comparing the imaging results produced by our proposed migration and reverse time migration methods, we can see that their imaging results are very similar Figure 7.

But the RTM method needs about 6. That is an outstanding advantage of the depth migration method but can achieve a similar imaging result. For the real OBS data, we used the mirror principle to image the multiple waves based on the two-way wave equation depth migration method. But for a fair comparison, the imaging result of primary waves was also included. The velocity field obtained by the tomographic inversion of arrivals of selected reflectors.

The velocity field can be used to perform the pre-stack depth migration of the data. This procedure is particularly important in areas with lateral velocity variations and complex geometries. The final result gives a section where the structures are closer to the real case than in time sections.