# Haiyan Zhang

**Haiyan Zhang** is being honored with the J. Clarence Karcher Award for significant research accomplishments involving the inverse-scattering approach to multiple elimination. Her work extended the theory from acoustic to elastic waves, identified the terms in the series that encapsulate the reflection process, developed a practical nonlinear AVO methodology that accommodates the case where only P-wave data are available, and developed a direct nonlinear inversion of multiparameter 1D elastic media using the inverse-scattering series. She has authored or co-authored seven papers in professional journals and three more have been submitted to Geophysics. She has also, with four others, been awarded a US patent for solving the inverse-scattering series problem using an iterative approach.

## Biography Citation for the J. Clarence Karcher Award

*Contributed by Arthur Weglein*

Haiyan Zhang has made significant and landmark contributions to exploration and production seismology that will provide new concepts and algorithms for AVO analysis, and, in addition, a fundamentally new platform and framework for understanding and addressing all target identification and inversion problems. The benefits and important lessons from her research include that: (1) a very important distinction exists between direct and indirect inversion; (2) the direct solution of any math–physics problem provides a unique definitiveness, clarity, and, perhaps most importantly, the assurance that you are actually solving the problem you set out to solve; (3) direct solutions to inverse problems, being direct, provide all the aforementioned benefits of direct solutions; (4) the direct inversion framework and resulting algorithms are not shared or achievable, or even understandable, by any indirect method, e.g., not achievable by searching locally or globally, with cost-functions, model matching, “full wave-form” inversion, iterative linear inversion, common-image gather flatness or weighted summing over trajectories; and (5) that the common wisdom and trend in inverse theory and inverse application circles, both inside and outside the petroleum industry, that go so far as to even define inversion as indirect inversion, has a concomitant set of serious conceptual and algorithmic pitfalls.

Zhang’s methods are derived starting with the elastic wave equation for heterogeneous media, and then developing direct elastic inversion methods to solve the nonlinear relationship between reflection data and changes in Earth’s mechanical properties. The only multi-D direct inversion method for an acoustic or elastic Earth is the inverse scattering series. The elastic inverse scattering series was pioneered by Ken Matson for removing ocean-bottom and onshore multiples. Matson’s research extended the marine towed-streamer landmark contributions of Paulo M. Carvalho and Fernanda V. Araújo. Zhang took the next daunting step, locating and developing a direct elastic target identification capability from within the elastic inverse scattering series. The mathematical complexity caused several eminent colleagues to state that the “mathematical mess that Haiyan is addressing would never be unscrambled.” She persisted, persevered, and succeeded in extracting the subseries for direct target identification.

Her algorithms can be simplified and reduced to allow, for the first time, direct inversion for changes in elastic-mechanical properties across a single reflector. Zhang provides explicit equations for changes in mechanical properties in terms of reflection data. This explicit and unique term-by-term expansion requires all PP, PS, SS…components. Direct inversion methods that require an elastic model (as in AVO application) or measurements on an elastic measurement surface unequivocally require all components of data, as necessary and sufficient data, and not only PP data. Thus solving, e.g., the forward PP Zoeppritz equation, “in an inverse sense,” either linearly or nonlinearly for “changes in Earth mechanical properties” is in fact an indirect mode-matching scheme that is fundamentally at odds with what the only direct inverse solution unambiguously describes as necessary and sufficient data. There is absolutely no way to understand that direct inversion data requirement, let alone the direct inversion algorithms, from any indirect inversion perspective, including the full wave-form and model-matching point of view, since PP data have enough “degrees of freedom.” Solving the inverse problem directly is not the same as solving a direct forward problem in “an inverse sense.” The clarity and definitiveness of direct inverse solutions for parameter estimation and AVO applications start with directly inverting the elastic wave equation.

These insights were exemplified in Zhang’s thesis and papers based on her PhD research. Her thesis showed that her direct nonlinear elastic inversion algorithms added value on 4D field data by distinguishing between pressure and fluid saturation, and that distinction influences a “drill” or “no-drill” decision. Haiyan has impeccable professional and personal integrity and is a delightful and wonderful human being. I look forward to celebrating further significant scientific contributions.