Exploring Earth’s boundaries with Donald V.Helmberger

Voon Hui Lai

Research School of Earth Sciences, The Australian National University, ACT 2601, Australia

Seismic waveform modeling is one of the most powerful tools for understanding Earth’s structure, since it allows waveforms to be quantitatively predicted using physical source representations and a velocity model. In the late 1960s, Don Helmberger developed the foundations of generalized ray theory (GRT) using the Cagniard-de Hoop method (Helmberger, 1968). This advance ushered in a new era of computing synthetic seismograms at local to teleseismic distances in applications ranging from studying strong motions generated by earthquakes to modeling Earth’s interiors from basin to core. Over the intervening period, rapid improvements in computational power could have seen semi-analytical methods such as GRT superseded by large-scale numerical waveform simulations. Instead, the insights and intuition afforded by GRT on how the seismic waveforms are affected by source and structural effects have proven invaluable. In essence,our models of the seismic source and Earth’s structure are only as good as our understanding of the input seismic data.

As his final PhD student, I have heard many legendary stories of how Don teased out subtle differences in seismic waveforms to discover important structures and dynamics within the Earth. I will be forever grateful that I got to witness this act first-hand by exploring three very different problems with Don. Our first adventure together involved investigating the poorly understood lower crust and upper mantle structure along North American - Pacific plate boundary, not bottom-up, but rather from north to south(Lai et al., 2017). SH waves generated by earthquakes in the Mendocino triple junction and recorded at the Southern California Seismic Network are sensitive to the sharp lateral variation of velocity across the plate boundary(Figure 1). We were able to model anomalous travel times across the region using 3D waveform simulations,confirming the presence of a strong oceanic upper mantle buttressed against a weaker continental margin crust that localizes plate boundary deformation and accounts for the observed asymmetric strain rates.

Our second adventure began when we noticed that, in the rupture study of regional earthquakes near Los Angeles Basin by Lui et al. (2016), the shaking duration of longperiod waves (＞ 2 seconds) was anomalously long for earthquakes occurring at shallow depths (Figure 2). Using beamforming analyses and 3D waveform simulations of carefully selected local events, we were able to identify that the shaking duration is depth-dependent and is a path effect caused by the local sedimentary basin. To better predict the long duration of shaking, we needed to improve our velocity models, paying particular attention to shallow heterogeneities and the attenuation structure (Lai et al.,2020).

For our final adventure, I was drawn into the deep Earth when Don showed me record sections of S-diffracted phases exhibiting strange multipathing behavior and we started brainstorming all the possible reasons to explain the multipathing. Upon closer investigation, we found that, in the region where Sdiff multipathing occurs, there is a coincident, rapid variation in differential ScS-S travel times that can only be explained by complex interaction between an ultra-low velocity zone and a subducted slab at the very edge of the Pacific Large Low Shear Velocity Province (Lai et al., 2022). Many previous studies in this region have only focused on a single seismic phase but with Don’s expertise across all seismic waves, we were able to combine multiple phases to shed light on such complicated structural variation, which cannot be observed by ScS or Sdiff alone. This discovery is particularly exciting, as the interaction between these structural anomalies may be responsible for promoting upwelling and it occurs near the predicted source location of the Hawaiian hotspot plume (Figure 3).

Figure 1. Time delay observed in Californian seismic network from a Mendocino event (modified from Lai et al., 2017).(left) Map shows the measured time shifts between the observed long period (30–50 s) SH waves for the 2014 M6.8 Mendocino event and synthetics from the 1D ‘Gil7’ model. Cooler color indicates the observed waves arrive earlier than predicted by 1-D synthetics and vice-versa. (right) Azimuthal record section of broadband SH waves recorded by stations along the profile (see map) from the event, plotted with reduced time (distance/4.7 km/s). The red arrow marks where the San Andreas Fault intersects the profile. SH waves arrived at the coast earlier than at the eastern border of California by 14 seconds. This time difference can be explained with a sharp velocity change in the lower crust-upper mantle across the plate boundary, which is not present in the current 3-D community velocity models.

Figure 2. Depth-dependent shaking duration at Los Angeles Basin (modified from Lai et al., 2020). (left) Tangential velocity waveforms for five local events with depths ranging between 1.0 and 12.5 km occurring just outside the Los Angeles Basin. Stations LAF and STS which are within the basin show an additional ～50 s of shaking but not SDD which has a travel path completely outside the basin. (right) Record section shows the comparison between tangential velocity data (in black) for a shallow event and the 3-D synthetics (in red) generated for the Community Velocity Model CVM-S.4.26.M01. The current 3-D model can predict the initial arrivals but not the late strong shaking which requires shallow heterogeneities and improved attenuation model.

Figure 3. Schematic cartoon showing the ULVZ-slab interaction near the edge of the Pacific LLSVP (reproduced from Lai et al. (2022)). The modeling of Sdiff multipathing and ScS-S differential travel times suggests a ULVZ structure driven towards the edge of the Pacific LLSVP while potentially pushed by a subducted slab, a configuration that may trigger plume generation due to strong thermal instabilities.

Apart from a keen eye for seismic wiggles, Don imparted many great lessons to me on how to become a truly well-rounded scientist. He understood that science cannot be undertaken in a vacuum. From early on, he actively paired me with different researchers both within and outside the Seismo Lab in order to gain new skills,learn how to collaborate, and most importantly, develop different perspectives on analyzing and interpreting data.He was very encouraging when I decided to put these new skills into practice by starting my own research collaborations with other faculty members. In these projects, I soon found myself scrutinizing the waveforms so closely – holding record sections up against the lights –just the way he used to during our afternoon discussions.His constant reminders to separately identify the effects of source and structure on seismic waveforms helped me to avoid many interpretation pitfalls when I was analyzing the source dynamics of debris flows and caldera collapse.His example of seeking out collaboration encouraged me to make new connections, which greatly expanded my scientific network and opened my mind to many exciting new developments in the broader geophysics field.

Don’s boundless enthusiasm and selflessness in mentoring has transformed many generations of seismologists,including myself. Despite already having a long list of major discoveries under his belt, he was constantly thinking (while staring out at the San Gabriel Mountains,and later a giant world map after he moved office) about how we can better image the Earth, especially the boundaries, at higher resolution. There are still so many unanswered questions to be studied, for instance the effect of anisotropy on waveforms in oceanic crust and the deep Earth, which would have kept him and will keep many of us busy for a long time. During my last phone call with him, after teasing my incapability to adapt to the cold Canberran winter (he grew up in northern Minnesota), he asked, “Are you having fun looking at the waveforms?”and I proudly replied, “I am!” “Great. Keep having fun!”,he responded. I smiled then, and I smile now knowing that deep down, I will continue to do so in his spirit and to his honor.