Velocity model building with long-offset and full-azimuth data: a case history for full-

waveform inversion Wei Huang*, Hongda Ma, Denes Vigh, Jerry Kapoor, Kun Jiao, Xin Cheng, Dong Sun, WesternGeco

Summary

In the last few years, there has been an increased focus on

designing advanced acquisition methods for better subsalt

imaging. These acquisition methods usually offer large-

offset, full-azimuth datasets with higher signal-to-noise

ratio and rich content of low frequency data. To fully

exploit the capability of these large-offset data sets, full-

waveform inversion is often adopted as the tool to build a

high-fidelity, high-resolution velocity model. In this paper,

we describe our general steps and QC measurements in

full-waveform inversion model building for a field data set.

Comparison of reverse time migration (RTM) images

between the initial tomography velocity and full-waveform

inversion velocity validate the uplift provided by full-

waveform inversion.

Introduction

Wide-azimuth (WAZ) towed-streamer acquisition has

proven to be a successful technique for subsalt imaging in

the Gulf of Mexico. Numerous survey and imaging projects

have been undertaken to achieve quality subsalt images.

However, the rapid development in imaging and modeling

algorithms demand a more advanced acquisition technique

that offers even better signal-to-noise ratio, illumination,

and azimuth information. One of the viable approaches that

offers an even distribution of azimuth information is the

circular shooting geometry. The concept of circular

geometry for towed-streamer marine acquisition was

introduced in the early 1980s by French (1984), where the

full-azimuth data set can be acquired by a single vessel

sailing along overlapped circles. Successive efforts and

developments in acquisition design further this idea by

implementing multi vessel long-offset circular shooting

geometry (Moldoveanu and Kapoor, 2009). Multi-vessel

long-offset circular shooting involves two recording vessels,

each with their own sources, and two additional source

vessels, all sailing in large (12- to 15-km diameter)

interlinked circles, which is schematically shown in figure

1. The trace density of this type of survey is greater than

that of typical WAZ designs, resulting in a higher fold and

improved signal-to-noise ratio for subsalt imaging (Huang

et al., 2013).

However, big-volume, large-offset and full- azimuth data

sets bring new challenges for velocity model building and

imaging. The first challenge comes from how we can fully

exploit the extra information from the far-offset data; the

second challenge stems from the substantial computational

cost demanded by the large-volume datasets. Reflection

tomography is a global optimization method that minimizes

the residual depths from common-imaged-gathers (CIG);

however, in the Gulf of Mexico (GoM) geological setting,

reflection tomography has its limitations when there exists

large velocity contrast, e.g., the presence of a salt body.

Tomography using diving waves can be an alternative for

velocity model building with long-offset data.

One of the other advanced techniques that can offer the

ability to resolve the velocity field and fully exploit the rich

information offered by far-offset data is full-waveform

inversion (FWI). Although first introduced in the 1980s

(Tarantola, 1984), only recently has FWI been successfully

applied to WAZ data sets (Vigh et al., 2009). It is

recognized that, to lessen the sensitivity of the initial

velocity, FWI must start with low frequencies and long

offsets. (Bunks et al., 1995; Pratt and Shipp, 1999).

One of the other reasons preventing the application of FWI

to large-volume data sets is the high computational cost

associated with FWI. FWI is a data-fitting technique based

on finite–difference forward modeling, which requires a

Figure 1: Schematic plot of lay out of multi-vessel long-offset

circular shooting acquisition Figure 2: Survey location in GOM and total about 400000 of

shots were recorded in this area

© 2013 SEGSEG Houston 2013 Annual Meeting Page 4750

Model building with long-offset and full-azimuth data

number of iterations to obtain an optimal velocity field.

Recent synthetic studies suggest using statistical sampling

to achieve a solution with less cost (van Leeuwen and

Hermann, 2012). Application of this statistical sampling is

of great interest for 3D very large data sets.

Application of FWI to real-world data sets is quite different

from synthetic tests, where a ground-truth velocity model is

readily given. There are many challenges for velocity

model building with FWI, e.g., higher noise level,

uncertainness of the initial model, and others. The model

building process is far from being as standardized as that of

current layer-stripped ray-based tomography updates. In

this study, we first give a general description of the field

data set used for this study. We then outline our general

velocity model building steps for FWI and discuss the

benefit we can get from FWI model building.

Field Data Description

The multi vessel long-offset circular shooting data set used

in this study is located primarily in the Keathley Canyon

area of the GoM, and part of the survey area lies in the

Sigsbee Escarpment. The geology is characterized by

extensive salt sheets with intervening deep-water sediment-

filled mini-basins. The salt canopy is characterized by

simple-to-complex salt features, some of which have a

thickness of up to 30,000 ft and some are extremely

shallow, i.e., just under the water bottom. There are several

major discoveries in this area, including the Lucius,

Moccasin, and Hadrian prospects. The overall goal of this

study is to employ FWI and the large-offset data to enhance

the subsalt image.

The fully imaged area shown in figure 2 is approximately

2901 km2 (124 OCS blocks). The record length for each

shot is 16.8 s and the maximum offset was around 15,000

m. A total of more than 400,000 shot gathers were recorded,

which were further super-grouped into around 100,000

shots for computational efficiency. Standard pre-migration

processing was performed before the FWI, e.g., de-noise

and de-multiple.

.

Full waveform inversion flow and results

The full waveform inversion used for this study is

implemented in time domain using acoustic wave equation.

A conjugate gradient method was adopted for updating the

velocity field by iteratively reducing the global misfit:

2

mod2

1∑∑ −=

S R

obs ddE (1)

where E is the global misfit, obsd and modd are the

observed and modeled shots respectively.

The inversion utilized anisotropic propagators using tilted

transverse isotropy, and the inversion updates only velocity.

ε and δ are derived from well information and

extrapolated to the target area. θ and φ are derived from a

vintage vertical transverse isotropic RTM image. The

starting velocity was a less-detailed ray-based tomography

velocity. The subsalt velocity was built by superposing a

regional velocity gradient below the salt.

Equipped with the initial velocity model and preprocessed

datasets, the first step for field data FWI model building is

wavelet estimation. Wavelet estimation is the key step to

achieve a successful FWI update, especially for field data.

Correct setting of the acquisition parameters is also critical

to the success of a FWI velocity update, e.g., source-

detector depth, dead trace information, and others. Unlike

the synthetic case where the source wavelet is always

readily given, the source wavelet for field data is generally

contaminated by factors such as noise, ghost, and

Figure 3: Wavelet estimation for target frequency (2.5Hz) : A)

Inverted wavelet . B) Overlay of modeled and observed shots

Figure 4: Global misfit reduction over FWI iterations

© 2013 SEGSEG Houston 2013 Annual Meeting Page 4751

Model building with long-offset and full-azimuth data

uncertainties in the velocity model. To incorporate these

effects, we adopt an approach based on the variable

projection method to estimate the source wavelet during

inversion. Validation of the source wavelet is done by

comparing the modeled and real data water bottom and

direct arrival in time and phase. Figure 3 gives the inverted

source wavelet and sample shots from modeling and

observed, where phase information of the water bottom and

direct arrival is correctly modeled.

After achieving a valid starting source wavelet, together

with the initial velocity, FWI at 2.5 Hz were performed for

this pilot study. To lessen the contamination from the

residual multiples, we limited the data used for the FWI

update to be above the first multiple. To make the inversion

more efficient, statistical sampling was adopted for this

FWI implementation, whereas different subsets of the shots

were used for consecutive FWI update.

In the absence of well control, we do not have an

independent direct measurement of the FWI update. Global

misfit drop is a natural measurement of a FWI update

because the kinematics of FWI are to reducing the global

misfit. The global misfit drop is demonstrated in figure 4.

After FWI update , around 20% of the global misfit drop

was observed for this study. However, the global misfit

drop may not be sufficient to validate the updated velocity

by FWI. QC measurements were performed to validate our

FWI update. The similarity between the forward-modeled

shots and the observed shots was first investigated.

The forward-modeled shot gather using the FWI-updated

velocity model and the initial modeled shot gather at 2.5 Hz

are shown in figure 5. The top row of figure 5 presents the

modeling comparison from the near cable and the bottom

row shows the far cable. The near cable contains data

information from about 200 m to 8 km, while the far cable

shots contain up to 15 km. Both the near-cable and far-

cable shot gathers from the FWI model show a higher

resemblance in phase and time to the observed shots than to

that of the initial model. To quantify the resemblance

between the observed data and modeled data, we apply

zero-lag cross correlation between the modeled and

observed shots. The correlation between observed and

modeled was done in five different time windows for these

gathers. Figures 6(A) and 6(B) show an example of the

correlations for the initial model and the FWI-updated

models, respectively. A histogram of the correlations over

shot-gather domain is also presented in figure 6(C). It is

observed that the peak of the correlation move from 0.45 to

around 0.62 after FWI update, suggesting a higher

resemblance globally.

Ray-based CIG are another important QC measurement of

the quality of the updated velocity model. The Kirchoff

gathers were observed to be flat over the whole area. An

example of the gather change around the Hadrian area after

the FWI update is given in figure 7 (A) and 7(B),

After these QC measurements, a reverse time migration at

18 Hz was run to see the impact of the velocity change by

the FWI update. Figure 7 presents the velocity and

corresponding RTM image for the target line around the

Hadrian prospect. The updated velocity field shows more

details, especially in the shallow part. The updated velocity

Figure 6: Coreelaions at (2.5Hz) : A) correlation for initial modeling B) correlation for FWI modeling C) global correlation histogram

Figure 5: Shot gathers filtered at 2.5 Hz (A) recorded near cable (B)

initial modeling of near cable (C) FWI modeling of near cable (D)

recorded far cable (E) initial modeling of far cable (F) FWI

modeling of far cable

© 2013 SEGSEG Houston 2013 Annual Meeting Page 4752

Model building with long-offset and full-azimuth data

follows the general trend of the geology. A narrow low-

velocity zone was observed in the depth of 10000, which

could potentially be beneficial for high resolution pore-

pressure prediction. In the RTM image comparison, we

observe a significant improvement in the continuity and

focusing of the subsalt structure, thereby justifying the FWI

result.

Conclusions

In this paper, we outlined the general step and QC

measurements for a pilot project using a far-offset and full-

azimuth dataset. Starting with reflection tomography

velocity and wavelet matching, we run iterations of FWI

update. In order to reduce the humongous computational

cost required by the large volume 3-D dataset, a statistical

sampling scheme was used in this study. Various QC

measurements were performed to qualify our velocity

update using FWI. Reverse time migration was performed

and it was concluded that even though the velocity updates

are limited to shallow area, the subsalt events can become

more coherent.

Figure 7: Comparison between initial and FWI updated: A) gather from initial model; B) gather from FWI updated model; C) velocity

from initial model; D) velocity from FWI updated model; E) RTM image from initial model; F) RTM image from FWI updated model.

© 2013 SEGSEG Houston 2013 Annual Meeting Page 4753

EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2013 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web.

REFERENCES

Bunks, C., F. M. Saleck, S. Zaleski, and G. Chavent, 1995, Multicscale seismic waveform inversion: Geophysics, 60, no. 5, 1457–1473, http://dx.doi.org/10.1190/1.1443880.

French, W. S., 1984, Circular seismic acquisition system: United States Patent 4,486,863.

Huang, W., K. Jiao, D. Vigh, J. Kapoor, H. Ma, and K. D. Dingwall, 2013, Salt exit velocity retrieval using full-waveform inversion: 75th Conference and Exhibition, EAGE, Extended Abstracts.

Moldoveanu, N., and J. D. Kapoor, 2009, What is the next step after WAZ for exploration in the Gulf of Mexico: 79th Annual International Meeting, SEG, Expanded Abstracts, 41-45.

Pratt, R. G., and R. M. Shipp, 1999, Seismic waveform inversion in the frequency domain, Part2: Fault delineation in sediments using crosshole data: Geophysics, 64, no. 3, 902–914, http://dx.doi.org/10.1190/1.1444598.

Tarantola , A., 1984, Inversion of seismic reflection data in the acoustic approximation: Geophysics, 49, no. 8, 1259–1266, http://dx.doi.org/10.1190/1.1441754.

van Leeuwen, T. and F. J. Hermann, 2012, Fast waveform inversion without source encoding: Geophysical Prospecting, 61, no. s1, 10–19, http://dx.doi.org/ 10.1111/j.1365-2478.2012.01096.x.

Vigh, D., W. E. S. Starr, and K. D. Dingwall, 2009, 3D prestack time domain full waveform inversion: 71st Conference and Exhibition, EAGE, Extended Abstracts.

© 2013 SEGSEG Houston 2013 Annual Meeting Page 4754