M-OSRP Objectives To address and solve prioritized seismic E&P challenges (isolated task sub-series, intrinsic and circumstantial nonlinearity, and purposeful perturbation) Arthur B. Weglein M-OSRP 2006 Annual Meeting, June 5 ~ June 7, 2007

Seismic Challenges Why challenges? Seismic goals are basically unchanged, therefore Methods bumping into assumptions are the source of these challenges; Deep water, complex media and boundaries.

Introduction In this introduction we explain how the strategy/plan behind the M-OSRP program (and its projects) represents an effective response to a suite of pressing seismic challenges

A research strategy responding to pressing challenges requires: Defining the challenges and their priority; and, Developing methods that can Address the pressing issues. Avoid the pitfalls of previous approaches that failed

When assumptions are not satisfied methods can fail. Two responses : (1) develop new procedures to improve the satisfaction of assumptions, requirements and prerequisites; and (2) develop new methods that totally avoid the assumptions that impede current capability.

We recognize the value in each type of response and adopt distinctly different attitudes for different issues: 1. Help improve requirements e.g., recorded data collection/extrapolation. - we cannot (yet) develop a method that avoids this requirement for seismic data. - hence, we seek to help satisfy that requirement.

2. For subsurface information, e.g. velocity, -We recognize that it is: Difficult to progress that requirement for level of detail and accuracy required under complex conditions. There is a comprehensive framework with the potential to avoid that prerequisite

The inverse scattering series represents a set of unique opportunities and properties: 1. Multi-D 2. Direct inverse – neither optimization nor objective functions 3. Comprehensive – inputs primaries and multiples 4. Transparency 5. Can accommodate any form or type of a priori information and/or absence of a priori information

The inverse scattering series represents a set of unique opportunities and properties: 1. Multi-D 2. Direct inverse – neither optimization nor objective functions 3. Comprehensive – inputs primaries and multiples 4. Transparency 5. Can accommodate any form or type of a priori information and/or absence of a priori information Impressive, but taken on its own, will not be an effective response to the challenge.

To recognize and avoid the pitfalls of previous attempts to respond to these challenges requires the introduction of a set of additional concepts: Tasks within the series Isolated task specific subseries Purposeful perturbation Model-type independent subseries A specific order to the achievement of these tasks The inverse scattering series plus these five concepts represent an effective response.

This strategy avoids the need for subsurface information but heightens the need for the completeness and definition of the seismic experiment. Requires: Data Source signature in water and Deghosted data Hence, the latter represent critical projects in our program and strategy.

M-OSRP Projects Data interpolation/extrapolation Deghosting and wavelet estimation Beyond attenuation: internal multiple elimination Depth imaging without the velocity model Direct improved estimation of changes in elastic properties and density Implementation of the inverse scattering series internal multiple attenuation and free surface multiple elimination algorithms: code development project Towards Q compensation without an adequate Q estimate: the inverse scattering series in an anelastic world

The inverse scattering series …direct inversion based on scattering theory

The inverse scattering series …direct inversion based on scattering theory

Seismic data and processing objectives Intrinsic and circumstantial non-linearity The inverse scattering series is the only direct multidimensional method which deals with either intrinsic or circumstantial non-linearity separately or in combination The ability to achieve processing objectives without knowing or determining propagation properties of the earth

Non-linear inversion for a single reflector 1-D Normal Incidence Example c0 c1

Two parameter 2D acoustic inversion 1D acoustic two parameter earth model (bulk modulus and density or velocity and density)

Two parameter 2D acoustic inversion The 3D differential equations: Then Where

Inverse Scattering Series Linear Non-linear

Two parameter 2D acoustic inversion For 1D acoustic earth model Solution for first order (linear)

Two parameter 2D acoustic inversion Relationship of is shown in the fig.1. z Fig.1

Two parameter 2D acoustic inversion x One interface model a z Fig. 2

Two parameter 2D acoustic inversion “Linear migration-inversion”

Two parameter 2D acoustic inversion Solution for second order (first term beyond linear)

Two parameter 2D acoustic inversion 1. The first 2 parameter direct non-linear inversion of 1D acoustic medium for a 2D experiment is obtained.

Two parameter 2D acoustic inversion 2. Tasks for the imaging-only and inversion-only within the series are isolated.

Two parameter 2D acoustic inversion 3. Purposeful perturbation.

Two parameter 2D acoustic inversion 4. Leakage.

Two parameter 2D acoustic inversion (velocity and density) Solution for second order (first term beyond linear)

Two parameter 2D acoustic inversion 1. Leakage and a special parameter

Two parameter 2D acoustic inversion 2. Purposeful perturbation

The pressing challenge of seismic E&P: Imaging and target identification beneath complex, ill-defined media

The pressing challenge of seismic E&P: Imaging challenges derive from assumptions behind velocity and imaging algorithms… …inadequacies in either/both can cause failure or mislocated targets

A model of the imaging challenge U D R When the wave experiences a complex medium and/or a complex boundary the resulting wave response is complex. Complex = D R U

A model of the imaging challenge D and U under complex conditions are approximated by simple forms d and u Complex = dR u R = d-1 complex u-1 Therefore, R is complex and the image beneath the salt is a fog. The removal of multiples is also a problem in complex and ill-defined media

Two approaches Avoid the assumptions behind current imaging algorithms Improve current methods; satisfy prerequisites. Indirect -model matching -CFP -CRS -optimal offset traj. -flat common image gathers Avoid the assumptions behind current imaging algorithms Direct -M-OSRP/inverse scattering series

…based on non-linear multiplication of events Multiple removal …based on non-linear multiplication of events FS WB Salt Target

Mississippi Canyon example Input Predicted multiples (2D) Output Input Predicted multiples (2D) Output 1.7 3.4 Seconds Water bottom Top salt Base salt Internal multiples Common Offset Panel (1450 ft) Common Offset Panel (2350 ft)

Imaging of primaries …the deepest primary is imaged through non-linear multiplication of shallower primaries, without any subsurface information FS WB Salt Target

Let’s first examine the 1D normal incidence acoustic case to get a hint at how to go to more complex models. where αn is nth order in the measured values of the data.

For an incident spike wave field, The first equation is and, Non-linear AVO Indication of mislocated reflector

For 1 reflector Depth of water bottom

For 1 reflector (continued) Water bottom is well-located

For 2 reflectors Correct depth Wrong depth

For 2 reflectors (continued) Continue with the term with the integral in Comes from integral

For 2 reflector (continued) Relates to duration of velocity error problem Relates to amplitude of the velocity error Where the problem resides From outside the integral

Imaging results of Shaw et al. Vertically-varying models, 1 example at normal incidence and 1 example with offset

Normal incidence imaging results

Pre-stack imaging results

cascaded series in the data Imaging Primaries: cascaded series in the data 1-D Normal Incidence Example Cascaded series means each term in the imaging series is itself a series. Choose c0(z)= constant and A(w)=1 here.

1-D Normal Incidence Example The inverse series: Provides , order by order, in terms of the measured values of s n is n-th order in the data, i.e., in the measured values of s

One Layer Example c0 c1 c0 xs xm a b For a spike incident field

One Layer Example (cont’d.) Substitute ys in the equation for a1

a1 c0 c1 c0 c0 < c1 a b’ b

One Layer Example (cont’d.) The second term in the inverse series, 2 , is given by (in general) And for the specific one-layer case

a2 d (z - b ) c0 > c1

The boxes serve two functions: (1) Eliminate internal multiples (2) Correct the amplitude of the a1+a2+... towards a But they don’t correct the depth of the deeper reflector from b to b. This depth correction is carried out by the terms

xs xm a b b b Forgetting about the issue of amplitude, we want (c0<c1) xs xm a b b b

Therefore the shift is a power series in b-b’ Therefore the shift is a power series in b-b’. And b-b’ is a power series in R. Hence, imaging is a cascaded series in the data.

Extending the imaging algorithm Fang Liu’s high-order imaging algorithm Considering testing on field data need to extend to a model beyond a velocity-only varying acoustic model

where αn is nth order in the measured values of the data.

Fang Liu et.al.

Large contrast model with mild lateral variations

Salt model with rapid lateral variations

Imaging project Challenges derive from assumptions/limitations in: Velocity determination Imaging algorithms -- two separate sets of challenges and how and where within the series these two distinct, and sometimes coupled issues occur.

Stages: Recognize the potential Locate the potential Gather-up the potential Test and evaluate Apply and determine place in the imaging toolbox How hard does the series have to work to achieve a certain goal? The answer depends upon several factors. Among them are: Is the process time to time or time to depth? Do you have reliable a-priori information (e.g., that there is a surface between water and air.) what is the extent and magnitude of the issue being addressed.

Data and isolated task subseries -- all wave theory methods want data collected on the measurement surface where wave theory predicts it has arrived. -- frequency ( ) Free surface ( one at a time) Internal multiple ( all frequencies of the data needed to predict one frequency of the internal multiple. However, that dependence is the same as needed for a FK migration with water speed.) Pre-stack FK migration surface data

Data requirements (For Imaging subseries ) Imaging appreciates low Kz in the data. The lower you can go in Kz, the greater the efficacy. The longer the offset and the lower the temporal frequency, the greater the derived benefit. (doesn’t require zero frequency data.) As with FSMA, all inverse scattering series require the wavelet; the source wavelet … not the wavelet at depth.

Data requirements (For Imaging subseries ) You are trading information about the subsurface for a more complete and better defined acquisition. Recent advances on generating data with specifically lower frequency content ( for mainly Basalt imaging Application ) and the advances in being better able to record those lower frequencies represent a contemporaneous development and opportunity