In memory of Donald V. Helmberger

Lupei Zhu

Department of Earth and Atmospheric Sciences, Saint Louis University St. Louis, MO 63108, USA

When I received the shocking news on August 13,2020 that our beloved Don passed away, I was deeply saddened. The feeling was worsened by the COVID-19 pandemic that essentially locked down everything so most of us were not able to attend his memorial ceremony. On Nov. 11, 2021, more than a year later, I took an early flight from St Louis to LAX to attend the memorial observance and reception honoring him in the Athenaeum of Caltech.While sitting in the 4-hour-long flight fully packed with passengers wearing masks, I tried to recollect the times I spent with Don almost 30 years ago. For a moment, my faded memory woke up and those images flashed through my mind like a river through a floodgate. They went so quickly that I was only able to write down a few glimpses of them.

I knew Don by name through my undergraduate advisor, Prof. Huilan Zhou, who visited the Seismo Lab and worked with him in the early 1980s. I first met Don on a sunny day in the summer of 1993 when I arrived at Caltech as a new graduate student. Upon entering the Seismo Lab’s South Mudd building, I followed the standard procedure to see my designated academic advisor Professor Rob Clayton. After a brief conversation, he gave me a tour of the lab’s facilities. While chatting with him by the drinking water station on the third floor, I saw a tall and athletically fit man holding a cup walking towards us from the other end of the hallway. Rob introduced me to him and told me this was Professor Helmberger. I had seen his photo in the Seismo Lab’s brochure when I applied to Caltech, but the person before me definitely did not fit in my stereotype of professors at that time. He was wearing a colorful Hawaiian short-sleeve shirt and a pair of two-strap sandals, like he was just back from the beach. He said to me something funny. Although I didn’t get his joke, his casual outfit and humorous demeanor helped me relax and made me like him immediately.

The first year of Caltech for graduate students was hectic and stressful (Figure 1). In addition to taking required courses of math, physics, and intros to geology,geophysics, and planetary sciences, we needed to conduct two research projects with two faculty members and to take the oral exam at the beginning of the second year.Those who failed the exam were usually asked to leave,with a consolation master’s degree. Some did get a second chance, but the psychological damage seemed irreversible.For my first project, I proposed to work with Don to model seismic regional waveforms of stations on the Tibetan Plateau for its crustal structure. I had participated in the first Sino-US broadband seismic recording experiment on the plateau between 1991 and 1992 (Owens et al., 1993)and had a copy of the data with me. Don seemed quite interested in this unique data set. My second project was with Prof. Hiroo Kanamori to estimate crustal thickness variation in Southern California using the receiver function technique. After a summer of intense work, I presented the two propositions and preliminary results to my exam committee. After the exam, I was asked to wait in the library next to the exam room while they had a closed-door discussion on the outcome. It seemed to me forever before they finally walked out the room to congratulate me for passing the exam. Don signed the form the next day to become my dissertation advisor.

Figure 1. Photo of Seismo Lab faculty, staff, and graduate students in 1994. Don is sitting 2nd from the right in the 2nd row,with Rob Clayton (5th), and Hiroo Kanamori (6th). The author is sitting at the center of the 1st row.

Being Don’s advisee was a pleasant as well as productive experience. As I acknowledged late in my dissertation: “He seemed always enthusiastic in whatever I did. He is truly a waveform master. Under his guidance, I learned how to appreciate the beauty of a seismogram. It is amazing that once you devote yourself to it, each wiggle of the waveform is willing to tell you a secret about our Earth” (Zhu LP, 1998). Years later, after becoming a professor and having my own graduate students, I tried to emulate Don’s advising style and realized that it was not an easy task to motivate students to excel in their research endeavor. Don did it by being a role model for his students. He made himself available to students all the time and made us feel that he was truly interested in what we were doing.

In 1995 I started to work with Don on determining focal mechanisms and depths of earthquakes using their regional seismic waveforms. His student Lianshe Zhao had just developed a novel method called “cut and paste”(CAP) to cut the waveforms into the Pnland surface wave segments and to compare them with synthetic waveforms separately by waveform cross-correlation (Zhao LS and Helmberger, 1994). I am sure that Lianshe got the idea by watching how Don compared observed and synthetic seismograms. At that time, there were no graphical computer terminals. Don simply printed the observed seismogram on a transparency and synthetics on a piece of paper. He then overlaid the transparency on top of the paper, shifted the data back and forth, and evaluated the similarity between the two. Lianshe implemented this manual process with computer code. While using Lianshe’s code, I noticed that his use of waveform crosscorrelation coefficient as the waveform fitness discarded the data’s amplitude information which should help constrain the earthquake’s focal mechanism and depth. I rewrote the code by replacing it with the L2 norm of the waveform differences. Though an incremental improvement in my opinion, Don was quite excited about it and encouraged me to turn it into a paper with his suggested title “Advancement in source estimation techniques using broadband regional seismograms”. The manuscript was submitted to BSSA in April, 1996. Surprisingly, it was accepted, without revision, just two month later (Zhu LP and Helmberger, 1996a). So far, this first paper with Don still holds the record of shortest acceptance time of all my publications.

My second paper with Don was also published in 1996(Zhu LP and Helmberger, 1996b). By applying my new CAP method to the 1991–1992 Tibet data, I found three earthquakes at depths ～70 km beneath the southern Tibetan Plateau. Because the Plateau has a very thick (～70 km)crust, there was a question of whether these events occurred in the lower crust or the uppermost mantle, given the uncertainties of the focal depths and crustal thicknesses. I used what I learned in Don’s GE261 class of synthetic seismograms and Don’s generalized ray theory code to show convincingly that these three earthquakes occurred 5 to 10 km below the Moho. In other words, the seismic waveform data provided much better relative positions of the earthquakes with respect to the Moho than their absolute depths.

The high-water mark of my PhD research with Don came in 1998. I was analyzing teleseismic waveforms of seismic stations on the Tibetan Plateau and was puzzled by some anomalous azimuthal variations of P-wave waveform shape and travel time at a few stations located in the northern margin of the plateau. The first P waves of events from the north arrived about 1s earlier than events from the south (Figure 2). This was not uncommon because of Earth’s lateral velocity variation. What was intriguing was that the first P-wave pulse split into two pulses separated by about 1s for events from the east or west (Figure 2).One day, after a sleepless night, I came up with an idea that the anomalous variations were caused by a sudden decrease of crustal thickness of the plateau, i.e., a Moho step, at its northern boundary (Figure 2). I talked with Don about the idea and sought his advice of how to compute the waveform of a plane wave through an arbitrarily shaped Moho. He quickly pulled out a paper in which he and his former student, Patricia Scott, developed an efficient numerical method using the Kirchhoff-Helmholtz integration (Scott and Helmberger, 1983). With this method, I was able to constrain the location, width, and height of the Moho step by modeling the observed waveforms and to infer its tectonic implications. The work was published in journal Science (Zhu LP and Helmberger, 1998), two months after I got my PhD degree from Caltech.

Figure 2. The left panel shows vertical components of seismic records from two earthquakes that occurred beneath the Kuril Islands. Arrows point to the anomalous double-pulse P waveform shape at stations TUNL (a) and K13 (b). (c) shows traveltime residuals of the first P-wave arrivals (the shaded squares) at station TUNL from earthquakes in distance range of 30 to 50 degrees. (d) denotes a north-south cross section along the 95°E meridian showing the surface topography (exaggerated by a factor of two), major faults, and the possible crustal structure used in modeling P waveforms at TUNL, from Zhu LP and Helmberger (1998).

Looking back, I would say that the five years of graduate study at Caltech were the happiest and most productive time of my life. I attribute this mostly to Don because not only did he provide insightful guidance to my research, he also supported me financially. During that time, my wife and I were living in a Caltech-owned lease property with our daughter. Worrying that my graduate assistantship might not be enough to support a family of three, Don tried to hire my wife to scan and digitize old seismogram film records for him. He also got me a consulting job from Woodward Clyde Consultants firm in Pasadena. There was, however, a problem. My wife didn’t have the work permit then and my student visa didn’t allow me to work off campus. Don came up with a solution to offer us to live in his rental property in Altadena for free as compensation. My wife and I checked out the house. It was definitely bigger than our bungalow on Wilson avenue, but we declined Don’s generous offer because of the extra commute to work and because Caltech provided those on-campus housing properties to students at very low cost. Nevertheless, I was grateful to Don who always took care of his students in every way.

All of us knew that Don was a great scientist, but not many know that he was also an entrepreneur. In 2001 while I was a post-doctoral associate at USC, Don,Chandan Saikia, and I started a company called Global SeisNet. We were equal share partners of the limited liability company. Each of us put in $313.59 cash to get the company set up and registered. I remember that our first board meeting was in a coffee shop on California Blvd. Don was quite optimistic about the prospect of the company to grow into a multi-billion-dollar enterprise in the seismic consulting business, like the Woodward Clyde Consultants. When that happened, he suggested to me, I could quit my up-coming faculty position at Saint Louis University which I just accepted. Global SeisNet did successfully get an SBA Phase-I grant in the first year from DoE to develop a waveform-based method of locating earthquakes and explosions. We completed the project in time. Unfortunately, we were not selected for Phase II. The company ran out of money and was dissolved in 2003, along with my hope of early retirement.

Don retired from Caltech in 2017. I last met Don in August, 2018 in a symposium in Singapore organized by his former students to celebrate his 80th birthday and more than half century of academic career. He looked as sharp as when I first met him 25 years ago. It is very unfortunate that he left us two years later. In his memorial observance and reception at Caltech, I told others that I owe Don a lot for what I have today. I can only repay my debt by educating my students the way he did and hope that they will do the same to their students, so that Don will live among us forever.

Acknowdgements

I would like to thank Xiaodong Song, Thorne Lay,Zhongwen Zhan, and Yan Zhu for their comments that helped to improve the manuscript.