Deep diving with Donald V. Helmberger

Daoyuan Sun

Laboratory of Seismology and Physics of Earth’s Interior, School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China

It has been more than a year since Don left us. He left us so suddenly. We planned to have a phone call after he settled down at his new house. However, it never happened. Although he had some medical issues persistently in his last year, he had been so dedicated to science that he kept working on multiple papers about Earth’s deep interior. Our unfinished paper is about to provide an alternative explanation of the anomalous SPdKS+SKPdS,which has been routinely used to image the Ultralow Velocity Zone (ULVZ). I am so grateful to Don that he brought me into the deep Earth, taught me how to read seismograms, and always inspired and supported me as my family.

Joining the Seismo Lab in 2003 as a graduate student, I started with a project with Tom Ahrens and Paul Asimow on both preheating shock wave experiments and thermodynamics calculation for MgO-FeO-SiO2system under lower mantle conditions. The Seismo Lab is a unique place in having an open environment and advocating interdisciplinary research. Students have to choose two distinct projects, a requirement for the PhD oral examination. That was how I came to know Don while I was looking for my second project.

Don knew that I was working on experiments for lower mantle studies, so he convinced me to work on an oral project of studying the African Large Low Shear Velocity Province (LLSVP, preferred to be called a “Superplume”at that time) following Sidao Ni’s work. Because I had no experience in seismology at all, he had the greatest patience to show me all the literature in his magic filing cabinets and guide me to plot seismograms. To make sure I understood what he was talking about, he always wrote notes down and marked what’s important on the plot of seismograms. I got lucky to pass the oral exam and the committee’s suggestion was to take more classes of thermodynamics. However, like many other Chinese students who also worked with Tom and Don at the same time, we eventually gravitated to Don as our thesis advisor. “Oral exam” plus the “coffee hour” provides two luxurious, intense, and career-impacting experiences for first-year graduate students. With the absolute freedom to explore and try different things, students not only learn broad knowledge,but also learn how to be creative and cooperative.

In 2004, a breakthrough in the study of the core-mantle boundary (CMB) was the discovery of the post-perovskite phase, which directly supports the D” discontinuity as a phase boundary. In fact, in an earlier paper in 1999, Igor Sidorin, Mike Gunris, and Don Helmberger (Sidorin et al.,1999) had proposed this idea from seismological observation, in which a solid-solid phase transition can explain well the observed topography of the D” discontinuity. Don was so excited by the new mineralogical evidence. Then,my first paper with Don (Sun DY et al., 2006) was to look at lower mantle triplication data sampling Central America and attempted to reexamine the idea of the phase boundary. We found that a phase boundary model can indeed explain the observed Scd phase. However, the existence of strong lateral variations suggests significant effects of presence of slab debris on phase changes. For most of my thesis work, I tried to include more data to provide a new mapping from the tomographic model to the lower mantle phase boundary by including chemical differences.

Working with Don was such an easy job. All you need to do is to feed him with a load of seismograms and wait for him to put different marks on the wiggles. Then you repeat this process the next day. Don was indeed an artist,drawing all kinds of lines on the seismograms and then telling you what happened in the Earth. Don was very creative and full of ideas for explaining observed seismic images. Once we made a 3D image of ULVZ (Figure 1).Don instantly linked the figure to the Alps (or the San Gabriel Mountain outside his window) and the Tour de France, which makes the interpretation of “Rolling hills on the core-mantle boundary” so easy and vivid (Sun DY et al., 2013). During the period when finite-frequency tomography and banana-donut kernel developed, Don was preparing a talk at SEDI. To explain what we thought about the banana-donut kernel, we simply split a banana and scanned it for the slides (Figure 2). “Seismology is fun”, Don always said.

Figure 1. A 3D image of ULVZ was named “Tour de CMB”by Don. The original manuscript including this figure was not accepted because of some oversimplified assumptions. Later, a revised manuscript (Sun DY et al., 2013) was published.

Figure 2. Don gave a talk showing the banana-donut kernel using a “real” example at the 11th SEDI meeting held in Kunming, China in 2008.

The good collaboration between Don, Mike Gurnis,and Jennifer Jackson, as well as the cooperation among many students, made the Seismo Lab the best and most exciting place in the world to study the Earth’s deep interior. It is not about having a product line. There were always some group discussion going on by exchanging ideas among seismology, geodynamics, and mineral physics, which were simply driven by the curiosity of understanding the D” layer, ULVZ, and LLSVP. Don always encouraged me from the beginning to participate in the discussion and express my ideas, which helped me a lot to better explain the wiggles to others and to gain a broad understanding of the deep Earth.

Don just loved the seismological data. He always tried to look at individual waveform records one by one. When you saw the huge paper-record drawers in his office, you would understand why he is the master of seismograms.He just knows every wiggle. Don had shown that all you need to be a first-class seismologist is a pencil, a ruler, and of course tons of paper (some may not like this idea). He taught me the best way to compare two seismograms by scanning one on a transparent film and overlaying them against the glass window. It definitely works!

Of course, Don had his idea on big data. When USArray data was available for the first time, Don was so excited, just like a child seeing boxes of candy. He urged me to plot every record. 700 stations! For the whole month, Don’s office was all covered with plots on A4 papers from the table to the floor, with Don’s notes and tape stitching the papers. During the whole month, he marked too many strange waveforms and found too many interesting structures, and we became lost in piles of seismograms. Then he said, “we need a colored map”.That is where the idea of “multi-path detector” (Sun DY et al., 2009; Sun DY and Helmberger, 2011) comes from,which allows us to focus on a group of stations with the most waveform distortion and detect sharp edges in a systematic and efficient way. However, Don always went back to those stations with complicated waveforms and marked them with all kinds of notes again, whereupon the magic started again.

Don had a special gift for training students. He spent so much time with students and respected every student as an individual. There was always a line for students waiting to talk to him. I was once selected as one of the “night owls”in the division, so it was unlikely that Don would find me in the office in the morning. However, he was very patient and never complained. But I did see his “See me” notes on my computer screen almost every day (Figure 3). Only after I graduated did I realize that this was his way of pushing me forward, but in a gentle, motivating, and caring way.

Figure 3. Don’s “See me” notes. Only a small portion of the notes is shown. The left is the lecture notes from Don’s“Advanced Seismology” class showing a Cagniard path.

After I graduated from Caltech in 2009, I went to the DTM, Carnegie Institution of Science, and then the University of Southern California (USC) as a postdoc. We made phone calls regularly and worked on different papers(Sun DY et al., 2010; Sun DY and Helmberger, 2011).During this time, we were quite interested in the SPdKS+SKPdS phase to study the structure of ULVZ. We found that Generalized Ray Theory (GRT) code and the old finite-difference (FD) code is not ideal for this problem. Don encouraged me to spend time rewriting the finite-difference code. Subsequently, Dunzhu Li further refined source excitation and out-of-plane geometric spreading correction and implemented the code on the GPU (Li DZ et al., 2014). The two-dimensional FD code has been widely used among different groups for both global and regional small-scale studies. Don is the pioneer in using the GRT to study the deep Earth. He knew all the details of the original F77 code. Whenever I wanted to modify the code and got lost in multiple “GOTO”statements, Don could clearly point out the problems I was encountering. Don also liked to promote new numerical codes, such as FD and SPECFEM. In particular, we later realized that the 3D effect is so important and the original GRT code has limits. However, the GRT code was still Don’s favorite. After taking Don’s “Advanced Seismology” class five times, I do realize that the GRT is the key to understanding “waveform modelling”, where each wiggle is related to a specific ray. Don always told me that“modelling is not about fitting the data exactly”. Instead,you must understand how the wave propagates and what is the sensitivity of the model parameter. “Data never lie”.

When I was at USC, I started working with Meghan Miller on the shallow mantle. Since I still lived in Pasadena and Meghan Miller also had a visiting office in the Seismo Lab, I always stayed at Caltech on Fridays and weekends. Don had shown great interest in our work and had continued to offer great insights. He always rated my work “five stars” and telling me “what a brilliant idea”,which gave me a lot of confidence. In 2014, I moved back to China and had a faculty position at the University of Science and Technology of China. Over the phone, Don told me so many things, big and small, about surviving in academia. But the most important thing is to “keep doing good science”, Don used to say. He was so happy about every little achievement I had made.

Don is the most modest guy I have ever met. He always put his students first. He always inspired and took good care of his students and the people around him. He not only trained me to be a seismologist, but also mentored me in many different aspects of science and life. Don always said, “Earth is so complicated”, “After I die, I prefer to go to the deep Earth and see what the hell is going on there”. We know that Don is definitely up in heaven, taking care of everyone as he always does. My students and I will keep working on the deep Earth and keep studying the wiggles that we know will make Don happy and proud.